Enhanced Diapycnal Mixing due to Near-Inertial Internal Waves Propagating through an Anticyclonic Eddy in the Ice-Free Chukchi Plateau

a. Hydrographic and current measurements

Using the R/V Mirai of the Japan Agency for Marine-Earth Science and Technology (JAMSTEC), we positioned a fixed-point observation (FPO) station at 74.75°N, 162.0°W in the Northwind Abyssal Plain (NAP) during the Arctic cruise 2014 (MR14-05; Inoue 2014), where the bottom depth is approximately 1880 m. The FPO station was approximately 200 km away from the pack ice region and remained in place for almost 3 weeks during 7–25 September 2014 (Fig. 1). During MR14-05, we continuously collected a series of meteorological and oceanographic variables. Surface wind velocity was measured using an anemometer (Koshin Denki) mounted on the foremast at an altitude of 25 m. Hydrographic variables such as water temperature, salinity, and dissolved oxygen (DO) were measured using a ship-based conductivity–temperature–pressure (CTD) system (Sea-Bird Electronics, Inc.; Fig. 2). The measurements were averaged into 1-db pressure bins after statistical screening procedures (Inoue 2014). The accuracies of the temperature and salinity measurements were ±0.001°C and ±0.002, respectively.

Time vertical sections of (a) temperature (°C), (b) oxygen saturation (%), (c) Brunt–Väisälä frequency (CPH), and (d) light transmission (%). In each panel, σ_θ contours are plotted at 0.25 kg m⁻³ interval. Grayscale bars at top of each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition; see the text for detailed acronym definitions).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Time vertical sections of (a) temperature (°C), (b) oxygen saturation (%), (c) Brunt–Väisälä frequency (CPH), and (d) light transmission (%). In each panel, σ_θ contours are plotted at 0.25 kg m⁻³ interval. Grayscale bars at top of each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition; see the text for detailed acronym definitions).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Time vertical sections of (a) temperature (°C), (b) oxygen saturation (%), (c) Brunt–Väisälä frequency (CPH), and (d) light transmission (%). In each panel, σ_θ contours are plotted at 0.25 kg m⁻³ interval. Grayscale bars at top of each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition; see the text for detailed acronym definitions).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Throughout the FPO program, the horizontal current velocity was obtained using a vessel-mounted ADCP (75-kHz Ocean Surveyor, Teledyne RD Instruments) installed at the ship hull bottom. The ADCP measures oceanic current speed and direction at a depth of 20–250 m by transmitting high-frequency sound waves. The instrument was configured to obtain a velocity profile with 8-m vertical bin every 5 min. The measured currents were decomposed into east–west (u) and north–south (υ) components, from which the ship movement velocity was removed in the processing. Alignment error, which is caused by a misalignment angle between a hull-mounted transducer and forward axis of moving vessel, was corrected following the method of Joyce (1989). Postprocessing showed that the useful maximum range was limited to approximately 250 m because of backscattered signal strength decaying with further increasing depth. The 5-min data were averaged into 1-h bins to eliminate high-frequency noise. According to the manufacturer, the horizontal velocity accuracy for the long-term averaging was ±0.2 cm s⁻¹.

b. Presurvey of horizontal velocity in the neighborhood

Preceding the stationary program, we conducted an advanced survey on 6 September to reveal the neighboring current structure using the shipboard ADCP, in which the R/V Mirai collected the velocity data along its track. In the middle of the presurvey, the ship encountered an anticyclonic vortex, whose geometric center was then located at 74.60°N, 160.80°W, nearly 30 km southeast of the FPO station (Figs. 3, 4a). For the eddy center determination we followed the method by A. J. Plueddemann and R. A. Krishfield (2007, unpublished manuscript; see the figure caption in more detail). They made an attempt to estimate an eddy’s center from a drifting platform carrying an underwater current meter, assuming that the eddy was quasi-stationary while a sensor passed it. According to the presurvey, the eddy’s characteristics in terms of the velocity field are overviewed as follows: anticyclonic rotation with maximum tangential velocity of nearly 0.3 m s⁻¹, whose core depth is approximately 80–120 m (Figs. 4b,c). In addition, notice that overlying the southern part of the eddy structure (y < 25 km), there was a surface-intensified westward current, whose maximum velocity was about 32 cm s⁻¹ at the top layer (20 m). With the center position assigned, a radial distance of the maximum tangential velocity would be a measure of core radius r₀ being about 12 ± 2 km.

Trajectory of the anticyclonic eddy that was inferred from the depth-averaged ADCP current. Yellow disks indicate approximately where the core was on the date of September, corresponding to a red digit. The blue arrow indicates the depth-averaged ADCP current when the ship transected the eddy prior to the commencement of FPO program, where a dashed curve shows the ship track. A circle with a black dot inside denotes the FPO position. A dashed rectangular box shows where ADCP data during presurvey are analyzed to determine the eddy position and horizontal velocity structure (see Fig. 4).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Trajectory of the anticyclonic eddy that was inferred from the depth-averaged ADCP current. Yellow disks indicate approximately where the core was on the date of September, corresponding to a red digit. The blue arrow indicates the depth-averaged ADCP current when the ship transected the eddy prior to the commencement of FPO program, where a dashed curve shows the ship track. A circle with a black dot inside denotes the FPO position. A dashed rectangular box shows where ADCP data during presurvey are analyzed to determine the eddy position and horizontal velocity structure (see Fig. 4).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Trajectory of the anticyclonic eddy that was inferred from the depth-averaged ADCP current. Yellow disks indicate approximately where the core was on the date of September, corresponding to a red digit. The blue arrow indicates the depth-averaged ADCP current when the ship transected the eddy prior to the commencement of FPO program, where a dashed curve shows the ship track. A circle with a black dot inside denotes the FPO position. A dashed rectangular box shows where ADCP data during presurvey are analyzed to determine the eddy position and horizontal velocity structure (see Fig. 4).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Graphical summary of an anticyclonic eddy that was encountered during the advanced survey at roughly 30 km southeast relative to the FPO station on September 6: (a) depth-averaged ADCP current (blue arrows) along the ship track (blue dashed line) plotted on the Cartesian plane, where the averaged depth range is 70–120 m; meridional sections of (b) eastward and (c) northward velocity (m s⁻¹); (d) relative vorticity ζ normalized by f₀. In (a), the eddy’s geometric center is inferred based on the depth-averaged horizontal velocity, where the intersection of perpendiculars from the velocity vectors forms a locus of points. The median (filled red square) of intersection points within an inner circle, defined by half an interquartile range of the initial estimate, was taken as the eddy center. The outer dotted circle indicates outer edge of the estimated eddy core with maximum velocity magnitude. In (d), ζ/f₀ is the poor man’s vorticity, computed following Halle and Pinkel (2003) by (1).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Graphical summary of an anticyclonic eddy that was encountered during the advanced survey at roughly 30 km southeast relative to the FPO station on September 6: (a) depth-averaged ADCP current (blue arrows) along the ship track (blue dashed line) plotted on the Cartesian plane, where the averaged depth range is 70–120 m; meridional sections of (b) eastward and (c) northward velocity (m s⁻¹); (d) relative vorticity ζ normalized by f₀. In (a), the eddy’s geometric center is inferred based on the depth-averaged horizontal velocity, where the intersection of perpendiculars from the velocity vectors forms a locus of points. The median (filled red square) of intersection points within an inner circle, defined by half an interquartile range of the initial estimate, was taken as the eddy center. The outer dotted circle indicates outer edge of the estimated eddy core with maximum velocity magnitude. In (d), ζ/f₀ is the poor man’s vorticity, computed following Halle and Pinkel (2003) by (1).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Graphical summary of an anticyclonic eddy that was encountered during the advanced survey at roughly 30 km southeast relative to the FPO station on September 6: (a) depth-averaged ADCP current (blue arrows) along the ship track (blue dashed line) plotted on the Cartesian plane, where the averaged depth range is 70–120 m; meridional sections of (b) eastward and (c) northward velocity (m s⁻¹); (d) relative vorticity ζ normalized by f₀. In (a), the eddy’s geometric center is inferred based on the depth-averaged horizontal velocity, where the intersection of perpendiculars from the velocity vectors forms a locus of points. The median (filled red square) of intersection points within an inner circle, defined by half an interquartile range of the initial estimate, was taken as the eddy center. The outer dotted circle indicates outer edge of the estimated eddy core with maximum velocity magnitude. In (d), ζ/f₀ is the poor man’s vorticity, computed following Halle and Pinkel (2003) by (1).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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The distance of 30 km between the eddy-detecting site during presurvey and the FPO station is feasibly within reach for the eddy. According to a back of the envelope calculation, a 10–20 cm s⁻¹ migration speed enables the eddy core (~10 km in radius) to step into the FPO domain within 1–2 days. There is no way to verify this, but we suspect the surface-intensified current facilitated the eddy’s traveling toward the FPO station. From some crucial similarities in the observed horizontal velocity field (i.e., rotational sense, tangential velocity strength, and depth of maximum velocity), we postulate that the anticyclonic eddy encountered during the presurvey was the same vortex that we intensively investigated during the FPO program. With the lack of information about its three-dimensional velocity structure, once the FPO started, the knowledge from this advanced survey will be referred to in the following analyses for the eddy during FPO.

c. Microstructure measurement and ε estimate

We used a Turbulence Microstructure Acquisition Profiler (TurboMAP; JFE Advantech Co., Ltd.) to perform oceanic microstructure measurements during the entire FPO period of 7–25 September 2014 except for 19 September (cancelled because of a severe storm). The TurboMAP is a loosely tethered free fall profiler equipped with two airfoil shear probes, a fast-response thermistor, and a CTD package (Wolk et al. 2002). We collected 177 vertical profiles of microscale variables as the underwater device descended from the surface to approximately 400 m. The instrument’s descending speed was 0.5–0.6 m s⁻¹, and the microscale current shear sampling rate was 512 Hz. We regularly conducted observations at 6-h intervals throughout the FPO period (a few profiles were obtained at 10–15-min intervals during each run).

The TKE dissipation rate ε was calculated using the isotropic relation , where ν is the seawater molecular viscosity, represents the small-scale velocity shear variance, and 〈.〉 represents an average of the variable (Hinze 1959). The shear spectra were integrated through iterative calculations between the upper bound of the Kolmogorov wavenumber (Landahl and Mollo-Christensen 1992) and the lower bounds of one cycle per meter. To validate the ε estimate, each spectral profile of the observed shear variance was compared with theoretical curves by Nasmyth (1970) and Panchev and Kesich (1969). The instrument fall speed (approximately 0.5 m s⁻¹) was used to convert data from the frequency to wavenumber domain using Taylor’s “frozen turbulence” hypothesis. These procedures were performed for the definite interval of a 2-s-long segment, equivalent to 1.0–1.2 m of actual depth. The unresolved shear variance in high-wavenumber portions, which are affected by noise, was estimated using the empirical theoretical shape (Stips and Prandke 2000). The dissipation rate in the upper 5 m was unreliable because of the initial adjustment to free fall.

The noise level in ε is assessed following the methods of Wolk et al. (2002) and Guthrie et al. (2015). To estimate the ε noise floor, a noise spectrum of current shear was created by taking the average of the most quiescent segments (lowest fifth percentile). Then, integrating the spectrum from 1 to 100 cycles per meter (CPM) revealed the noise level in ε of approximately 1–3 × 10⁻¹⁰ W kg⁻¹. For reference, Wolk et al. (2002) estimated the noise level in ε to be roughly 5 × 10⁻¹⁰ W kg⁻¹ for their shear probes carried on their previous version of TurboMAP instrument.

a. Hydrographic and current features

In the study region, the upper ocean comprises the following distinct water masses with characteristic hydrographic properties (Fig. 2a; cf. Steele et al. 2004; Shimada et al. 2001): surface mixed layer (SML; σ_θ ≤ 23.5 kg m⁻³, θ ≥ 0°C, S ≤ 27.5), Pacific Summer Water (PSW; σ_θ ~ 25.0; θ ~ 0.2°C, S = 30.0–31.5), Pacific Winter Water (PWW; σ_θ = 25.5–27.0, θ ~ −1.5°C, S ~ 32.5), lower halocline layer (LHL; σ_θ = 27.0–27.5, θ = −1.0°C–−0.5°C, S = 33.0–34.0), and upper Atlantic Water (UAW; σ_θ ≥ 27.5, θ = 0.0°–0.8°C, S ≥ 34.5), where σ_θ is the potential density anomaly, θ is potential temperature, and S is salinity.

During the main eddy period of terms I and II, the water layers in the range of 25.5 ≤ σ_θ ≤ 26.5 were vertically stretched, having approximately 140-m core thickness, contrasting the reduced thickness of surrounding water being approximately 100 m thick (see density contours in Fig. 2). During this time, water temperature was relatively low, being below −1.6°C at 100–200-m depth, identical to the PWW core, which is approximately 0.2°C colder than the average temperature in the same layer over the entire FPO period (Fig. 2a). Density stratification was relatively weak in the PWW core, representing the cold “halostad” structure characterized by S ~ 32.5 (Shimada et al. 2005). The buoyancy frequency N was approximately 2 cycles per hour (CPH), contrasting N ~ 5 CPH for the surrounding water (Fig. 2c).

The DO concentration was relatively high in the eddy core (Fig. 2b); the oxygen saturation was 90%–100% (equivalent to DO = 320–340 μmol kg⁻¹) inside the eddy and 80% or lower (280–310 μmol kg⁻¹) in the surrounding water. The high DO concentrations have been previously reported for cold-core eddies comprising the Pacific and Chukchi shelf waters (e.g., Muench et al. 2000). Figure 2d illustrates a low light transmission of 93%–95% during the eddy period, specifically centered at its deeper segment of σ_θ = 26.2–26.5 kg m⁻³. This implies significant influences by sediments and particles of shelf origin. From these hydrographic properties, we hypothesized that the eddy was formed during the previous winter/spring in the Chukchi Sea or somewhere between Barrow Canyon and Northwind Ridge in the Canada Basin, where water originating from the Chukchi Sea is present on a massive scale (e.g., Shimada et al. 2001).

During the transection of the eddy in the FPO period, the maximum horizontal velocity was 0.30–0.35 m s⁻¹, recorded at 70–130-m depth (i.e., upper PWW; Fig. 5); the depth of maximum current strength, centered on approximately 100 m, can be viewed as the eddy’s vertical core plane. The PWW core coincident to the maximum velocity is a common feature of deep-core eddies in the Canada Basin (e.g., Newton et al. 1974; Manley and Hunkins 1985; A. J. Plueddemann and R. A. Krishfield 2007, unpublished manuscript; Zhao et al. 2014). At the core depth, the eastward velocity component was slightly positive during term I, with an intermittent change to negative (e.g., 9–10 September), before promptly returning to positive (Fig. 5a). The northward velocity was generally positive throughout terms I–II (Fig. 5b).

Time vertical section of ADCP horizontal current (unfiltered) during FPO program: (a) u (m s⁻¹) and (b) υ (m s⁻¹) components. Contours are σ_θ at 0.25 kg m⁻³ interval. Grayscale bars at top of each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Time vertical section of ADCP horizontal current (unfiltered) during FPO program: (a) u (m s⁻¹) and (b) υ (m s⁻¹) components. Contours are σ_θ at 0.25 kg m⁻³ interval. Grayscale bars at top of each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Time vertical section of ADCP horizontal current (unfiltered) during FPO program: (a) u (m s⁻¹) and (b) υ (m s⁻¹) components. Contours are σ_θ at 0.25 kg m⁻³ interval. Grayscale bars at top of each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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b. Inferred pathway

The anticyclone’s relative location and movement can be deduced under some assumptions based on the strength and direction of ADCP horizontal velocity obtained at the fixed station (Figs. 6a,b). In this analysis, we utilized the depth-averaged subinertial (low passed) velocity at the FPO station (see figure caption for details). By fitting the observed current with an ideal profile of anticyclonic circulation (axisymmetric vortex with zero radial velocity), the eddy’s geometric position relative to the FPO station can be uniquely determined in terms of radial and angular positions in the polar coordinate system. Here, we also assumed an insignificant background current compared with the azimuthal circulation u_θ within the eddy. This assumption is justified by the weak velocity magnitude of <0.05 m s⁻¹ during term IV (20–25 September) when the eddy was apparently no longer influential to the velocity field at the fixed site (Fig. 6b).

(a) Movement of FPO station relative to the anticyclonic eddy. The dot color indicates the day of September (DoS) in 2014. Point “O” indicates the geometric center of the eddy. The solid and dashed circular lines denote radial distances of r = r₀ and r = 2r₀, respectively, where r₀ is the core radius. (b) Low-passed horizontal velocity averaged between 70- and 120-m depth, which is used to determine the relative position of the FPO station shown in (a). In (a) and (b), Greek numbers indicate distinct terms of relative eddy position: (I) inner core for DoS 7–12, (II) transition region for DoS 13–16, (III) outer shell for DoS 17–19, and (IV) absence of eddy for DoS 20–25 (see text for detailed definition of each period).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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(a) Movement of FPO station relative to the anticyclonic eddy. The dot color indicates the day of September (DoS) in 2014. Point “O” indicates the geometric center of the eddy. The solid and dashed circular lines denote radial distances of r = r₀ and r = 2r₀, respectively, where r₀ is the core radius. (b) Low-passed horizontal velocity averaged between 70- and 120-m depth, which is used to determine the relative position of the FPO station shown in (a). In (a) and (b), Greek numbers indicate distinct terms of relative eddy position: (I) inner core for DoS 7–12, (II) transition region for DoS 13–16, (III) outer shell for DoS 17–19, and (IV) absence of eddy for DoS 20–25 (see text for detailed definition of each period).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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(a) Movement of FPO station relative to the anticyclonic eddy. The dot color indicates the day of September (DoS) in 2014. Point “O” indicates the geometric center of the eddy. The solid and dashed circular lines denote radial distances of r = r₀ and r = 2r₀, respectively, where r₀ is the core radius. (b) Low-passed horizontal velocity averaged between 70- and 120-m depth, which is used to determine the relative position of the FPO station shown in (a). In (a) and (b), Greek numbers indicate distinct terms of relative eddy position: (I) inner core for DoS 7–12, (II) transition region for DoS 13–16, (III) outer shell for DoS 17–19, and (IV) absence of eddy for DoS 20–25 (see text for detailed definition of each period).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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For the fitting procedure, we hypothesize the solid-body rotation for the inner core region (r ≤ r₀; recall r₀ is the radius of maximal tangential velocity), where the magnitude of u_θ linearly increases with r; for the outer shell region (r > r₀), u_θ shows a rapid decay in terms of r, expressed by a 1/r² profile, instead of 1/r for the typical Rankine vortex. The velocity profile proportional to r⁻² for the outer region was obtained by least squares fitting with ADCP data for earlier Mirai surveys that closely examined deep-core anticyclones in the Canada Basin (Fig. 1; Kawaguchi et al. 2012; Kawaguchi and Nishino 2014).

Figure 6a illustrates how the eddy migrated during the FPO program. Note that the FPO station’s movement is “relative” to the eddy’s center in the eddy-fixed coordinate. In this representation, the station was initially located to the west or northwest of the eddy’s center. It then moved toward the southwest until approximately 19 September (end of term III), with some crooked motions. Subsequently, it changed its direction toward the southeast and traveled farther away from the eddy location. Once it moved beyond r ≫ r₀, particularly after 20 September (term IV), the eddy’s circulation no longer influenced the current field near the station, making the estimated distance/position inaccurate.

From the velocity at the fixed station, we inferred the eddy’s sequential trajectory on a real geographical map (Fig. 3). This depicts a horizontal picture that initially the eddy unsteadily wandered to the northeast, temporarily moving back and forward (e.g., during 10–12 September), and finally joined a northwest path. Regarding the driving force of the eddy’s traveling, it is rather uncertain from the data currently available. Most likely, the eddy behaved that way as consequences of a random drift, since there was no dominant background current in the neighborhood (Figs. 5, 6b). One might suspect the topographic β effect for the eddy propagation. For this is a possibility, a feasible scenario would be dynamics of the continental shelf waves, in which the anticyclonic vortex with a negative vorticity anomaly may be propagating along the isodepth, with the shallower water on its right hand. We guess that this mechanism could partially contribute to the eddy’s migration because it actually showed a counterclockwise movement roughly along the 1800-m isodepth (Fig. 3). For another possibility, there might be the self-propelling mechanism due to a dipolar vortex. This can produce a rather intricate behavior because of a difference in the decay rate of cyclonic and anticyclonic vortices (e.g., Fig. 1.10 in van Heijst 2010). As far as the authors are concerned, no significant signatures of the cyclonic vortex, which can be paired with the present anticyclone, have been detected during both the FPO and presurvey.

c. Dynamical balance

The eddy’s Rossby number (Ro = ζ/f₀), expressed as a ratio between the relative vorticity and the local Coriolis frequency, is then estimated to characterize the approximate dynamical balance of the eddy. The steady-state momentum equation in the radial direction is expressed as follows:

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where the first term is the pressure gradient per unit mass, the second term is the centrifugal force, and the third term is the Coriolis acceleration. The Rossby number makes a rough estimate of relative strength between the centrifugal force and the Coriolis, with Ro ~ 1 indicating an eddy in cyclogeostrophic balance and Ro ≪ 1 consistent with a quasigeostrophic balance.

For the quantitative discussion of Ro = ζ/f₀, we use the knowledge from the pre-ADCP survey (section 2b). Figure 4d displays the virtual structure of ζ/f₀ during the active ship transection across the anticyclonic eddy that we suppose is the same one observed during the FPO. For this, the relative vorticity is calculated using the following approximation proposed by Halle and Pinkel (2003): , where the ship moved in the ocean where mesoscale structures are “frozen” in place [they refer to this approximation as poor man’s vorticity (PMV)]. Here, is velocity component of subinertial (low passed) current perpendicular to the ship track, and c is the coordinate along the ship track, which is approximately along the north–south (y) axis.

According to these assumptions, we can identify characteristic features of the negative vorticity pool that was centered at y = 20–30 km and surrounded by positive vorticity regions (Fig. 4d). Near the horizontal eddy center, the negative vorticity reached its greatest magnitude at a vertical core depth of ~100 m, being roughly −0.5 to −0.2, which rapidly diminished at shallower and greater depths away from the core depth; the magnitude decreased to nearly zero on the deeper side, that is, below 250 m, but the shallower side of the eddy core remains nonzero values, |ζ/f₀| > 0.3, toward 20-m depth, corresponding to the very top of the ADCP record. We should mention that the relative vorticity estimates from PMV have some spatial variation within the central core, contrasting with that from the ideal model of (e.g., Timmermans et al. 2008b) for the axisymmetric forced vortex, which provides a constant vorticity there.

From the preceding current survey, the eddy’s Rossby number can be estimated to be |ζ/f₀| ~ 1 or less in the core region; in the steady-state momentum balance of (1), the Coriolis force can be more or less scaled as the same order of magnitude with the centrifugal force, implying that the present eddy’s dynamics is in the cyclogeostrophic balance, modestly deviated from the strict geostrophic balance (van Heijst 2010).

d. Life span of the eddy

In general, an eddy’s lifetime T_eddy depends on its horizontal scale because horizontal viscosity likely depletes the mesoscale kinetic energy according to the relation T_eddy = L²/ν_h (Robinson 1983), where L is the eddy’s diameter, and ν_h is the empirical horizontal diffusivity. Providing the eddy’s horizontal scale comparable to double the core diameter (i.e., L ~ 4r₀), we obtain a plausible estimate of T_eddy = 340 days. Here, we assumed ν_h = 10² m² s⁻¹, which is based on a direct observation by Brown and Owens (1981). Although they give a generic value rather than especially for the Arctic, we assume it is applicable in our case; the eddy core is relatively deep and rarely subject to the frictional attenuation from the ice. The life-span evaluated here is similar to the earlier estimate of O(1) yr, derived from the age of chemical tracer (tritium/³He) for a cold-core anticyclone that was found in the southern-central Canada Basin in September 1997 (Muench et al. 2000).

Padman et al. (1990) evaluated the decay time scale of a cyclonic eddy in the ice-covered Arctic Ocean to be about 10 yr, based on their estimate of ε from direct microstructure observation. Their calculation is based on an idea that the mean vertical shear is the main source of turbulent energy dissipation. Kunze et al. (1995) claim that the direct energy transfer between mean flow and turbulence is only negligible in the kinetic energy budget and instead the finescale internal wave energy has to dissipate into turbulence.

a. Comparison of near-inertial current and microscale shear fields

A comparison of the ADCP horizontal current and the microscale current shear indicated the occurrence of NIW-related diapycnal mixing, particularly near the critical level, during the transection of the anticyclonic eddy (Figs. 7, 8).

Time vertical section of near-inertial current velocity (m s⁻¹): (a) zonal and (b) meridional components and (c) RMS of the bandpass current. The contours of σ_θ are plotted at 0.25 kg m⁻³ interval. Grayscale bars at top of each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Time vertical section of near-inertial current velocity (m s⁻¹): (a) zonal and (b) meridional components and (c) RMS of the bandpass current. The contours of σ_θ are plotted at 0.25 kg m⁻³ interval. Grayscale bars at top of each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Time vertical section of near-inertial current velocity (m s⁻¹): (a) zonal and (b) meridional components and (c) RMS of the bandpass current. The contours of σ_θ are plotted at 0.25 kg m⁻³ interval. Grayscale bars at top of each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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(a) Time series of surface wind speed (m s⁻¹; red curves) and stress (N m⁻²; black curves) and time vertical section of (b) TKE dissipation rate ε (W kg⁻¹) on a logarithmic scale. (b₁) Magnification of the vertical range of upper 50 m, but (b₂) full water depth of 300 m. In (a), the thick curve shows a 10-h running average. In (b), contours of σ_θ are plotted at 0.25 kg m⁻³ interval. In (b₁), white contours outline a region of Re = 20 for the significant turbulent intensity. Red arrows in (b₂) mark the significant ε anomalies traveling downward with time. Gray bars at each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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(a) Time series of surface wind speed (m s⁻¹; red curves) and stress (N m⁻²; black curves) and time vertical section of (b) TKE dissipation rate ε (W kg⁻¹) on a logarithmic scale. (b₁) Magnification of the vertical range of upper 50 m, but (b₂) full water depth of 300 m. In (a), the thick curve shows a 10-h running average. In (b), contours of σ_θ are plotted at 0.25 kg m⁻³ interval. In (b₁), white contours outline a region of Re = 20 for the significant turbulent intensity. Red arrows in (b₂) mark the significant ε anomalies traveling downward with time. Gray bars at each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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(a) Time series of surface wind speed (m s⁻¹; red curves) and stress (N m⁻²; black curves) and time vertical section of (b) TKE dissipation rate ε (W kg⁻¹) on a logarithmic scale. (b₁) Magnification of the vertical range of upper 50 m, but (b₂) full water depth of 300 m. In (a), the thick curve shows a 10-h running average. In (b), contours of σ_θ are plotted at 0.25 kg m⁻³ interval. In (b₁), white contours outline a region of Re = 20 for the significant turbulent intensity. Red arrows in (b₂) mark the significant ε anomalies traveling downward with time. Gray bars at each panel denote distinct terms of relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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The raw ADCP record indicated that the horizontal current velocity had an oscillatory nature (Fig. 5). With the application of a 10–15-h (0.83–1.2f₀) bandpass filter (fourth-order Butterworth filter), the horizontal current clearly indicates that a remarkable near-inertial energy packet propagated through stratified layers during the periods of eddy core and transition (terms I and II; Fig. 7). In particular, two vertically distinct maxima of near-inertial currents were identified: 20–60 m (a depth between the SML base and the upper portion of the PSW) and 170–250 m (between the lower PWW and the entire LHL).

The shallower near-inertial energy maximum, coincident to the upper pycnocline, accompanied fairly disturbed isopycnals around σ_θ = 24.5–25.5 kg m⁻³ (approximately 50-m depth; Fig. 7), which was the most prominent on 7–9 and 11–15 September. During these periods, the bandpass current amplitude was approximately 11 ± 4 cm s⁻¹. At depths shallower than an isopycnal of σ_θ = 24.5 (<40 m), the constant phase lines were about upright, implying no significant wave energy transfer in the vertical direction. Nevertheless, the constant phase appeared to extend upward in the upper part of the PSW layer (σ_θ = 24.5–25.5), indicating the apparent downward wave energy propagation (i.e., negative group velocity).

At the deeper maximum of the near-inertial current, the amplitude was noticeably high (6 ± 3 cm s⁻¹) during the core (term I) and transition (term II) periods, particularly on 10–11 and 13–16 September. The bandpassed semidiurnal current clearly indicates that an isolated packet of characteristic wave pattern migrated downward through the stratification in the midsegment between PWW and LHL (Fig. 7), in which the vertical traveling speed of the wave packet was approximately 80 m week⁻¹ (~11 m day⁻¹).

Another near-inertial energy packet with a current amplitude of <2 cm s⁻¹ was observed at 60–150-m depth (mostly overlapping with PWW) during 13–14 September (Fig. 7). This wave current was apparently less energetic than the shallower and deeper NIW maxima, wherein the constant phase lines were nearly upright and the wave pattern remained at a constant depth (Figs. 7a,b).

According to the previous study from the Surface Heat and Energy Balance of the Arctic Ocean (SHEBA) program, based on a drifting ice camp crossing over the ice-covered Chukchi Plateau, the near-inertial internal waves were at most 1–2 cm s⁻¹ in the root-mean-square (RMS) current amplitude (Pinkel 2005). By comparing with this, the present result being the ~10 cm s⁻¹ wave current is suggestive of the increased level of NIW kinetic energy, which we hypothesize is jointly responsible for the internal wave amplification within a vortex structure (Kunze et al. 1995) and the absence of surface insulation for the momentum input because of the ice-free boundary condition.

According to our microstructure measurements, ε was noticeably high at 170–270-m depth (roughly concurrent with the deeper near-inertial peak) on the approximate dates of 9–17 September (midterm I to early term III; Fig. 8b2). During this period, the maximum magnitude of log₁₀(ε) reached the order of −8.5 to −7.5 W kg⁻¹. These high ε anomalies at intermediate depths are also important in terms of diapycnal heat transfer. Indeed, we can estimate increased magnitude of vertical heat flux to be as much as 1.3–3.5 W m⁻² for the corresponding depth, where the vertical heat flux is defined as , c_p is the specific heat, and K_T = 0.2ε/N² is the vertical eddy diffusivity (Osborn 1980).

At this point, a simple question arises: Is it reasonable to conclude that vertical shear due to NIW caused the turbulent-scale disturbances and then resulted in the localized increase in ε at similar depths? Let us begin with a comparison between finescale vertical shear and the turbulent dissipation rate as averaged during term II when both scales of velocity perturbation were well defined. The vertical shear is calculated from the 8-m spacing ADCP horizontal velocity. Vertical profiles in Fig. 9b show that the near-inertial horizontal current produces a substantial magnitude of vertical shear, reaching 7 × 10⁻³ and 5 × 10⁻³ s⁻¹ at 50- and 170–250-m depths, respectively. These large vertical shear values are vertically coincident to the high ε anomalies (≥0.6 × 10⁻⁹ W kg⁻¹ for the term-II mean; Fig. 9a). The nice agreement may reinforce the actual linkage between the two independent variables.

Vertical profiles of (a) TKE dissipation rate ε (W kg⁻¹), (b) vertical shear of near-inertial current (s⁻¹), and (c) magnitude of normalized relative vorticity |ζ/f₀|. The relative vorticity is computed by , where the solid-body rotation is assumed in the cylindrical coordinate, is low-passed azimuthal velocity, and r is a radius determined from the analysis in Fig. 6a (an envelope shows an interquartile range). In (a), the vertical dashed-dotted line shows the noise floor for the shear probe; ε = 10⁻¹⁰ W kg⁻¹. In (b), the thick, thin-solid, and thin-dashed curves show the vertical shear of zonal component, meridional component, and their sum, respectively. Note that all profiles are temporally averaged during term II (transition period from core to shell) except for a dashed curve in (a) that shows the average of ε throughout terms I–III (the entire eddy period). A dashed, red horizontal line shows the approximate critical level, where .

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Vertical profiles of (a) TKE dissipation rate ε (W kg⁻¹), (b) vertical shear of near-inertial current (s⁻¹), and (c) magnitude of normalized relative vorticity |ζ/f₀|. The relative vorticity is computed by , where the solid-body rotation is assumed in the cylindrical coordinate, is low-passed azimuthal velocity, and r is a radius determined from the analysis in Fig. 6a (an envelope shows an interquartile range). In (a), the vertical dashed-dotted line shows the noise floor for the shear probe; ε = 10⁻¹⁰ W kg⁻¹. In (b), the thick, thin-solid, and thin-dashed curves show the vertical shear of zonal component, meridional component, and their sum, respectively. Note that all profiles are temporally averaged during term II (transition period from core to shell) except for a dashed curve in (a) that shows the average of ε throughout terms I–III (the entire eddy period). A dashed, red horizontal line shows the approximate critical level, where .

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Vertical profiles of (a) TKE dissipation rate ε (W kg⁻¹), (b) vertical shear of near-inertial current (s⁻¹), and (c) magnitude of normalized relative vorticity |ζ/f₀|. The relative vorticity is computed by , where the solid-body rotation is assumed in the cylindrical coordinate, is low-passed azimuthal velocity, and r is a radius determined from the analysis in Fig. 6a (an envelope shows an interquartile range). In (a), the vertical dashed-dotted line shows the noise floor for the shear probe; ε = 10⁻¹⁰ W kg⁻¹. In (b), the thick, thin-solid, and thin-dashed curves show the vertical shear of zonal component, meridional component, and their sum, respectively. Note that all profiles are temporally averaged during term II (transition period from core to shell) except for a dashed curve in (a) that shows the average of ε throughout terms I–III (the entire eddy period). A dashed, red horizontal line shows the approximate critical level, where .

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Figure 10a depicts a time–depth section of the gradient Richardson number—a squared ratio between a local stratification and the vertical gradient of a horizontal current, which is defined as . According to numerous laboratory and numerical experiments, the shear flow could be mechanically turbulent when the value of Ri is smaller than the empirical threshold of 1/4 [see a review by Thorpe (2005)]. For the calculation, we used the near-inertial bandpass current for the shear component and the buoyancy frequency from the 6-hourly hydrographic observation shown in Fig. 2c, where both variables were interpolated into 1-h bins for the entire FPO period and vertical depth range of 20–250 m. The results show that water parcels satisfying the Ri ≤ ¼ condition are locally spotted at an approximate depth of 40–50 m over 12–15 September and at the depths of 200–250 m during dates centered on 13–17 September. It is emphasized that both the anomalies mainly occurred during term II and are vertically coincident with the local N maxima (Fig. 10a). It is also noted that those dynamically unstable patches of small Ri can be generally accounted for by the strong vertical shear, as shown in Fig. 9, which overcomes the local stratification.

Time–depth sections of (a) the inverse of gradient Richardson number Ri⁻¹ and (b) the dissipation rate ε_IW by Gregg (1989), parameterized from near-inertial bandpassed current (both are represented on a logarithmic scale). Black contours delimit a criterion of Ri = 1/4 (equivalent to log₁₀Ri⁻¹ = 0.602) for the necessary condition of turbulent shear flow. Note that the color scale for ε_IW is different from that in Fig. 8 near the lowest level because of the electronic noise floor, ε = O(10⁻¹⁰) W kg⁻¹, for the observation. Thin contours denote isopycnals with a 0.25 kg m⁻³ interval. Grayscale bars at top of panels define the relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Time–depth sections of (a) the inverse of gradient Richardson number Ri⁻¹ and (b) the dissipation rate ε_IW by Gregg (1989), parameterized from near-inertial bandpassed current (both are represented on a logarithmic scale). Black contours delimit a criterion of Ri = 1/4 (equivalent to log₁₀Ri⁻¹ = 0.602) for the necessary condition of turbulent shear flow. Note that the color scale for ε_IW is different from that in Fig. 8 near the lowest level because of the electronic noise floor, ε = O(10⁻¹⁰) W kg⁻¹, for the observation. Thin contours denote isopycnals with a 0.25 kg m⁻³ interval. Grayscale bars at top of panels define the relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Time–depth sections of (a) the inverse of gradient Richardson number Ri⁻¹ and (b) the dissipation rate ε_IW by Gregg (1989), parameterized from near-inertial bandpassed current (both are represented on a logarithmic scale). Black contours delimit a criterion of Ri = 1/4 (equivalent to log₁₀Ri⁻¹ = 0.602) for the necessary condition of turbulent shear flow. Note that the color scale for ε_IW is different from that in Fig. 8 near the lowest level because of the electronic noise floor, ε = O(10⁻¹⁰) W kg⁻¹, for the observation. Thin contours denote isopycnals with a 0.25 kg m⁻³ interval. Grayscale bars at top of panels define the relative eddy position (see Fig. 6 for the definition).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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To the best of our knowledge, few studies have examined the TKE dissipation rate based on direct microstructure measurements inside particular Arctic eddies. One of those examples is Padman et al. (1990), who estimated ε ≤ O(10⁻⁹) W kg⁻¹ over the core segment in a cyclonic eddy (7 km in solid-body radius) in the ice-covered Canada Basin from a drifting ice camp during the Arctic Internal Wave Experiment (AIWEX). In comparison with their observation, the current estimate of ε ≥ O(10⁻⁸) W kg⁻¹ near the critical level of 170–250 m, seemingly due to the trapping and breaking of NIWs in the anticyclone, is clearly stronger.

b. Finescale parameterization

Furthermore, the connection between the observed dissipation rate and the current properties of internal gravity waves can be argued with the semiempirical parameterization by Gregg (1989; Fig. 10b). This is constructed based on the relative strength between NIW-related vertical shear and density stratification, and consequently their deviations from the canonical Garrett–Munk (GM) values, expressed by

View Expanded

where N₀ = 5.2 × 10⁻³ s⁻¹ (equivalent to 3 CPH) is a reference buoyancy frequency, and ϵ₀ = 7 × 10⁻¹⁰. Here, S₈ is the observed shear having vertical wavelengths greater than 8 m, whereas S_GM is the corresponding shear in the Garrett and Munk spectrum of internal waves. For the calculation, we used the near-inertial bandpass (0.83–1.2f₀) current as in the Ri estimate in Fig. 10a. In the parameterization, is given by

View Expanded

where j* = 3 is the vertical mode number, b = 1300 m is the scale depth of thermocline, k_crit = 0.6 rad s⁻¹ is the critical wavenumber, and E_GM = 6.3 × 10⁻⁵ is the dimensionless energy level. According to Gregg (1989), this parameterization is able to reproduce the observed level of dissipation within a factor of 2 for conditions close to the ideal Garrett and Munk (1975, hereinafter GM75) model that expects internal waves far from the boundaries and energy source.

Overall, the ε_IW parameterization tends to provide a reasonable agreement with the direct observation of ε (Fig. 8b2), consistently producing the increased values of dissipation at the spots where the Ri ≤ ¼ condition is satisfied (Fig. 10a). Particularly during term II, ε_IW showed notable anomalies at depths corresponding to the shallower and deeper N maxima at about 50 and 190–250 m, respectively. For the shallower peak, ε_IW shows the moderate magnitude of −9.5 to −9.0 on a logarithmic scale (Fig. 10b), similar to that of the observed dissipation rate maximum that is somewhat indistinct [Figs. 8b(2), 9a]. Interestingly, the deeper ε_IW peak, with the relatively smaller NIW amplitude than the shallower one (Fig. 7), estimates more significant and extensive increase to exceed the order of −8.5 at maximum. According to a direct comparison, the model tends to exaggerate the observed variability, for example, by 30%–40% greater over the two energetic maxima, on the average field. The parameterized dissipation rate produces the estimate of vertical diffusivity (defined by K_ρ = 0.2ε/N²) to be K_ρ = 1.6 × 10⁻⁴ and 1 × 10⁻⁵ m² s⁻¹ for the deeper and shallower maxima, respectively. Based on their ADCP-based vertical shear, Rainville and Woodgate (2009) presented the similar value of K_ρ = 2 × 10⁻⁴ m² s⁻¹ for the pycnocline layer in the ice-free northern Chukchi Sea.

The general consistency in dissipation rate estimates between the observation and the empirical model is indicative of the relevant mechanical process wherein the larger-scale vertical shear due to the NIW current led to the smaller-scale energy dissipation because of the shear instability (the so-called Kelvin–Helmholtz instability; Thorpe 2005). It is noteworthy that for the comparatively greater amplitude of NIW at the shallower peak (Fig. 7), the dissipation tends to be suppressed by the stronger stratification (Fig. 10b).

c. Spectral analysis of horizontal currents

1) Moored spectrum

Time series of ADCP horizontal velocities were analyzed in terms of the frequency spectrum: the so-called moored spectrum (Figs. 11a,b). We applied this analysis to the velocity data throughout term I to term II, when the negative vorticity is clearly present. According to this, dominant peaks are found at 0.078 (0.96f₀) and 0.076 CPH (0.94f₀) for the shallower (30 m) and deeper (210 m) energy maxima (Fig. 11a). As expected in the Northern Hemisphere, the near-inertial anomalies were detected only in a CW rotation (cf. Levine et al. 1987). The slightly subinertial frequencies are interpreted as evidence that the wind-induced current oscillation at the exact frequency of f₀ = 0.081 CPH was biased by the background current associated with the anticyclone, and eventually it was 4%–6% lowered in frequency. Notice that the slightly subinertial frequencies, centered on 0.95f₀, seem not to significantly change over the full-depth range in the structure (Fig. 11b). Figure 9c illustrated that within the eddy core the Rossby number ζ/f₀ was about −0.3 at the peak, resultantly giving the effective Coriolis frequency of f_eff = 0.85f₀ CPH. Thus, near the core depth, the spectral peak centered on ω = 0.076–0.078 CPH is located in the middle between the lower and upper bounds of the internal wave frequency: f_eff = 0.068 CPH and N = 5 CPH (a typical value of buoyancy frequency), respectively. Note that at the depths below the core, where vorticity magnitude shrinks to smaller than ~0.1f₀ (Fig. 9c), where , so that the NIW solution may not be physically obtained.

(a) Rotary frequency spectrum of ADCP horizontal velocity averaged at depths of 20–50 (solid) and 180–220 m (dashed) during the eddy’s core period of terms I–II: CW (blue) and CCW (red). The dashed black curve represents a universal spectrum by GM75 for NIW. Dashed vertical lines show f₀ and 2f₀. Solid vertical bar shows the 95% confidence interval for 54 degrees of freedom. (b) Rotary wavenumber spectrum as a function of vertical coordinate: (left) CW and (right) CCW. Horizontal axis shows observed frequency normalized by f₀. Calculation was conducted throughout the periods of terms I and II. The spectral energies are depicted in a logarithmic scale, with the contour interval of 0.5.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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(a) Rotary frequency spectrum of ADCP horizontal velocity averaged at depths of 20–50 (solid) and 180–220 m (dashed) during the eddy’s core period of terms I–II: CW (blue) and CCW (red). The dashed black curve represents a universal spectrum by GM75 for NIW. Dashed vertical lines show f₀ and 2f₀. Solid vertical bar shows the 95% confidence interval for 54 degrees of freedom. (b) Rotary wavenumber spectrum as a function of vertical coordinate: (left) CW and (right) CCW. Horizontal axis shows observed frequency normalized by f₀. Calculation was conducted throughout the periods of terms I and II. The spectral energies are depicted in a logarithmic scale, with the contour interval of 0.5.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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(a) Rotary frequency spectrum of ADCP horizontal velocity averaged at depths of 20–50 (solid) and 180–220 m (dashed) during the eddy’s core period of terms I–II: CW (blue) and CCW (red). The dashed black curve represents a universal spectrum by GM75 for NIW. Dashed vertical lines show f₀ and 2f₀. Solid vertical bar shows the 95% confidence interval for 54 degrees of freedom. (b) Rotary wavenumber spectrum as a function of vertical coordinate: (left) CW and (right) CCW. Horizontal axis shows observed frequency normalized by f₀. Calculation was conducted throughout the periods of terms I and II. The spectral energies are depicted in a logarithmic scale, with the contour interval of 0.5.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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In studies that discuss near-inertial waves in the southern part of the Canada Basin and Beaufort Sea (e.g., Timmermans et al. 2007; Rainville and Woodgate 2009; Martini et al. 2014), the latitude (~74.5°N) makes it difficult to precisely identify the predominant energy source in the widespread frequencies of semidiurnal currents: wind-generated inertial currents (f₀ = 0.0806 CPH) and tidal barotropic currents (M₂ = 0.0805 CPH). To distinguish these contributions, we also referenced a barotropic tidal model for the Arctic Ocean (Padman and Erofeeva 2004), along with the detailed analyses of surface wind in section 5. According to the model prediction, the current magnitudes from the M₂ tidal constituent (the most energetic semidiurnal tide) would be only 0.16 and 0.02 cm⁻¹ for the major and minor axes, respectively; this is negligibly small. We would thus conclude that the semidiurnal tidal current unlikely contributed to the energetic near-inertial peak in Fig. 11.

Subsequently, the frequency spectra for the two distinct vertical levels are compared with the universal spectral model of GM75 for the internal gravity wave (black, dashed curve; Fig. 11a). As a consequence, the GM75 spectrum restrictedly accounts for the observed spectra, so the velocity variance only shows a reasonable fit in a narrow frequency band of f₀–1.6f₀. In the meantime, we can see a certain level of kinetic energy resided at the high frequencies of roughly >2f₀; it was apparently far beyond the minus two slope presumed by GM75 (Fig. 11a). Particularly, the shallower depth shows the higher velocity variance reaching at least 5–6 times greater than the canonical GM75 value that expects circumstances away from surface boundary of the energy source. Presumably, the NIWs trapped within the anticyclone were rather episodic and intermittent, and they did not fully establish the energy cascade through the wave–wave interaction among the different-scale processes. In addition to this, as shown in Fig. 11b, we should note that the high-frequency wave energy was confined within the shallow depth (<50 m). A sequential comparison between the near-surface ADCP horizontal velocity (at 20 m) and the surface wind strength suggested that the high-frequency perturbations at the shallow depth were a direct response to the local winds, for example, during 7–10 and 15–20 September (figure not shown). We simply speculate the accumulation of wind-induced small-scale perturbations, resulting from breaking surface waves, convection, Langmuir circulation, and so on, generated the noticeable kinetic energy at the relatively high-frequency band (Fig. 11b; see Thorpe 2005, his chapter 9).

2) Dropped spectrum

The vertical wavenumber spectra (the so-called dropped spectrum) obtained from bandpass horizontal velocities were used to examine the dominant vertical scales of internal wave (Fig. 12). Prior to the calculation of the spectra, a WKB stretching for the vertical coordinate was performed using a mean vertical profile of buoyancy frequency N(z) (Leaman and Sanford 1975). This procedure can approximately remove the vertical variation in internal wave properties due to the background stratification (cf. D’Asaro and Morehead 1991).

Wavenumber rotary spectra to compare (a),(b) eddy existing period of terms I–II and (c),(d) noneddy period of term IV: (top) horizontal kinetic energy and (bottom) vertical shear variance. Curves in blue, red, and green, respectively, show CW, CCW, and their sum. In (a) and (c), the GM75-shaped spectra for the reference level and AIWEX are, respectively, shown by solid and broken curves, while the best-fit GM75 profiles for the present data are shown by the dashed. In (b) and (d), the GM75 curve for vertical shear is shown by a dashed line. In each panel, the vertical bar shows the 95% confidence interval. Note that the near-inertial bandpassed velocity is used for the spectral calculation.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Wavenumber rotary spectra to compare (a),(b) eddy existing period of terms I–II and (c),(d) noneddy period of term IV: (top) horizontal kinetic energy and (bottom) vertical shear variance. Curves in blue, red, and green, respectively, show CW, CCW, and their sum. In (a) and (c), the GM75-shaped spectra for the reference level and AIWEX are, respectively, shown by solid and broken curves, while the best-fit GM75 profiles for the present data are shown by the dashed. In (b) and (d), the GM75 curve for vertical shear is shown by a dashed line. In each panel, the vertical bar shows the 95% confidence interval. Note that the near-inertial bandpassed velocity is used for the spectral calculation.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Wavenumber rotary spectra to compare (a),(b) eddy existing period of terms I–II and (c),(d) noneddy period of term IV: (top) horizontal kinetic energy and (bottom) vertical shear variance. Curves in blue, red, and green, respectively, show CW, CCW, and their sum. In (a) and (c), the GM75-shaped spectra for the reference level and AIWEX are, respectively, shown by solid and broken curves, while the best-fit GM75 profiles for the present data are shown by the dashed. In (b) and (d), the GM75 curve for vertical shear is shown by a dashed line. In each panel, the vertical bar shows the 95% confidence interval. Note that the near-inertial bandpassed velocity is used for the spectral calculation.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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The modified vertical coordinate is introduced according to the differential law (Gill 1982):

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where z_* and z are the stretched and original vertical coordinates, respectively. Here, 〈N(z)〉 is the FPO-averaged buoyancy frequency, and N₀ is the reference buoyancy frequency, equal to 3 CPH. With the new vertical coordinate of (4), a water column within the upper 300 m is mapped onto approximately 620 m of stretched depth (Fig. 13b). For this analysis, the velocity at each depth was normalized in terms of the local buoyancy frequency:

View Expanded

where u_*(z) is the normalized velocity component at depth z with units of normalized centimeters per second (ncm s⁻¹), and u(z) is the original velocity component. We also note that the horizontal velocity used for the calculation is near-inertial filtered in advance.

Vertical profiles of (a) FPO-averaged density stratification N, (b) WKB-stretched depth z* [stretched meters (sm)], (c) the effective Coriolis frequency f_eff/f₀, (d) vertical wavenumber m, and (e) vertical group velocity C_gz. Solid curves in (d) and (e) show the WKB solutions using the actual vorticity profile in Fig. 9c. In (d) and (e), dashed curves show the corresponding solutions using a vertically constant vorticity of ζ = −0.35f₀. A dashed, red horizontal line in (c)–(e) approximately shows the critical level, where .

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Vertical profiles of (a) FPO-averaged density stratification N, (b) WKB-stretched depth z* [stretched meters (sm)], (c) the effective Coriolis frequency f_eff/f₀, (d) vertical wavenumber m, and (e) vertical group velocity C_gz. Solid curves in (d) and (e) show the WKB solutions using the actual vorticity profile in Fig. 9c. In (d) and (e), dashed curves show the corresponding solutions using a vertically constant vorticity of ζ = −0.35f₀. A dashed, red horizontal line in (c)–(e) approximately shows the critical level, where .

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Vertical profiles of (a) FPO-averaged density stratification N, (b) WKB-stretched depth z* [stretched meters (sm)], (c) the effective Coriolis frequency f_eff/f₀, (d) vertical wavenumber m, and (e) vertical group velocity C_gz. Solid curves in (d) and (e) show the WKB solutions using the actual vorticity profile in Fig. 9c. In (d) and (e), dashed curves show the corresponding solutions using a vertically constant vorticity of ζ = −0.35f₀. A dashed, red horizontal line in (c)–(e) approximately shows the critical level, where .

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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In the dropped spectral analysis, each rotary component of horizontal velocity variance was compared between the averages of terms I–II and term IV, respectively, representing the presence and absence of the background eddy influence (Fig. 6). For reference, the canonical GM75 spectrum for midlatitude seas and a historical spectrum from the AIWEX (D’Asaro and Morehead 1991) are depicted in the same figure. As briefly mentioned above, the AIWEX was an ice camp expedition, performed during spring 1985, that gathered an extensive set of hydrographic and velocity data for the internal wave activity in the ice-covered Canada Basin (Levine et al. 1987). In this spectral analysis, the GM75 model describes the horizontal kinetic energy spectrum as a function of the nondimensional energy level E₀ and the vertical mode number j*:

View Expanded

View Expanded

View Expanded

where we use the standard values of t = 2.5 and b = 1300 m. The default GM75 spectrum has the particular combination of (E₀ = E_GM = 6.3 × 10⁻⁵, j* = 6). The AIWEX spectrum is expressed using the GM75 model as well, with their best-fit values (E₀ = 3.6 × 10⁻⁶, j* = 20) at high wavenumbers and (E₀ = 1.6 × 10⁻⁶, j* = 60) at low wavenumbers, representing the typical of the quiescent Arctic Ocean (D’Asaro and Morehead 1991).

According to the calculation, the horizontal velocity variance contrasts the two periods with and without the anticyclone, with the respective best-fit values of (E₀ = 3 × 10⁻⁵ and j* = 3) and (E₀ = 9 × 10⁻⁶ and j* = 6; Figs. 12a,c). Under the eddy’s strong influence throughout terms I and II, the cumulative horizontal kinetic energy that is integrated over 2 × 10⁻³ to 2 × 10⁻¹ cycles per stretched meters (hereinafter CPSM) is 2.4 times greater for the clockwise (CW) rotation than for the counterclockwise (CCW), such that the CW energy component apparently dominates the total kinetic energy (sum of CW and CCW; Fig. 12a). This is most prominent at wavenumbers lower than 0.02 CPSM (>50 stretched meters). The dominant CW rotation during the eddy term can be also confirmed by the vertical shear spectrum (Fig. 12b). In those figures, we should also remark that the bandpass filtering for the horizontal velocity somewhat contributed to the reduced kinetic energy at the higher wavenumbers.

Along the WKB-stretched vertical coordinate, the bandpassed horizontal velocity vectors are virtually demonstrated in Fig. 14 (cf. Joyce et al. 2013; D’Asaro and Morehead 1991). According to this, the predominance of CW rotation in near-inertial wave velocity is obvious at stretched depths of 100–225 and 500–600 m. Near the shallower peak, the horizontal vector rotates by 143° over a 125-m vertical width, whereas at the deeper peak it rotates 190° over a 100-m width. The variation in vertical phase gives an estimate of the vertical wavelengths as 315 and 190 m for the respective near-inertial peaks. In the Northern Hemisphere, downward-propagating wave energy is associated with the CW rotation of horizontal current and its vertical shear with increasing depth, whereas the upward-propagating wave is vice versa (Leaman and Sanford 1975). The vast difference between the CW and CCW strengths indicated the dominance of downward energy transfer within the eddy structure (Figs. 12a,b, 14).

Vertical structure of near-inertial bandpass velocity vectors (ncm s⁻¹) along the stretched vertical coordinate z* (sm). The velocity profile (shown at a 5-m interval) was obtained at 0400 UTC on 14 Sep 2014. The red digits beside vectors denote the stretched depths.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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Vertical structure of near-inertial bandpass velocity vectors (ncm s⁻¹) along the stretched vertical coordinate z* (sm). The velocity profile (shown at a 5-m interval) was obtained at 0400 UTC on 14 Sep 2014. The red digits beside vectors denote the stretched depths.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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• Download figure as PowerPoint slide

Vertical structure of near-inertial bandpass velocity vectors (ncm s⁻¹) along the stretched vertical coordinate z* (sm). The velocity profile (shown at a 5-m interval) was obtained at 0400 UTC on 14 Sep 2014. The red digits beside vectors denote the stretched depths.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0150.1

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• Download figure as PowerPoint slide

Contrary to the CW predominance during the eddy period, the eddy absent period (term IV) displayed quite similar levels of kinetic energy between the two rotational components (the ratio of integrated variance CW/CCW is 1.1; Fig. 12c). In a comparison of the total horizontal kinetic energy, the eddy period was more energetic by a factor of 2.3 than the noneddy period. The eddy present energy level closely approaches the canonical GM75 values when vertical wavenumbers are smaller than 0.01 CPSM, whereas the eddy absent one was below the GM75 level at the overall wavenumbers presented. During both periods, the total spectral energy was greater than the mean energy level typical for the AIWEX observation, particularly at lower wavenumbers than 0.02 CPSM.

The present data that we collected from the 3-week-long observation are too short to argue the long-term trend in the internal wave activity in the Arctic. Martini et al. (2014) discussed the trend in the spectral energy levels based on their moored ADCP velocity near the Beaufort continental slope in 2008/09 by comparing with the historical velocity profiles from the AIWEX and the GM75 model. They demonstrated that single shot, strong wind events can increase the kinetic energy to a level near or greater than the universal GM75 spectrum (as we see here); however, the long-term average is still approximately 10 times smaller than that of the GM75 standard even during the ice-free period.

d. WKB scaling

We discuss the vertical kinetic energy flux (F = E_hC_gz) associated with near-inertial waves, which can be assumed as nearly invariance (Kunze et al. 1995), where E_h is the bandpassed kinetic energy density. It is also assumed that the bulk of the trapped NIW energy is lost to turbulence production, dissipation, and mixing. For the invariant energy flux perspective, the vertical group velocity C_gz and vertical wavenumber m of NIWs needs to be identified. Here, the WKB approximation is used to estimate those two variables as a function of the real depth based on representative vertical profiles of N(z) and f_eff(z) (Fig. 13). Generally, the WKB approximation requires that the vertical scales of internal waves are smaller than those of the background variation. This is not strictly true in the case of the Canada Basin water, where the largest vertical wavelengths are on the same order as the depth range of the large vortices. Nevertheless, the WKB predictions facilitate the interpretation of the observations. The WKB approximation validity was examined for the representative profiles in the Canada Basin by Halle and Pinkel (2003).

Here, we consider a situation wherein a wave packet is vertically downward going, starting from the surface, and laterally propagating along the azimuthal band of the maximum tangential velocity. Indeed, the most amplified NIWs were distinctly observed near the horizontal boundary of the eddy’s core, during term II (Fig. 7). According to the WKB scaling, the vertical wavenumber m, and thus vertical wavelength λ_z = 2π/m, are given by the following dispersion relation of internal waves (Gill 1982):

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where K_h is the horizontal wavenumber, and is the intrinsic frequency and taken as a constant of 0.95f₀ (Fig. 11). As mentioned earlier, f_eff(z) is dependent on the local relative vorticity ζ(z), which has vertical variations presumably resulting from the background current’s baroclinicity. In the present case, the curve of f_eff inferred from the velocity observation has the characteristic minimum near the vertical core of ~100-m depth and quickly grows for the bottom slope (Fig. 13c). In this framework, if the frequency is smaller than the effective Coriolis frequency, that is, , the internal waves cannot physically exist, in which they are not free to propagate any further than the critical level, and perhaps they break into turbulence. In the present case, with a nearly constant frequency of = 0.95f₀ (Fig. 11), the critical level would be due to the vorticity change and happen around a depth where ζ = −0.1f₀, corresponding to somewhere over the bottom slope of vortex core (Fig. 13). According to Qi et al. (1995), C_gz(z) is then expressed by

View Expanded

where is assumed.

In the WKB representations above, the horizontal wavenumber (and consequently, horizontal wavelength scale) is an unknown piece. Earlier studies say that typical Arctic internal waves have horizontal lengths on the scale of O(10) km (e.g., Levine et al. 1985). The wavelength compared to horizontal eddy scale has been also reported for a warm-core ring in the Gulf Stream (Joyce et al. 2013) and in the East/Japan Sea (Byun et al. 2010). We presume a horizontal length scale with a priori value of 24 km, roughly equivalent to the present eddy’s core diameter.

The vertical wavenumber based on the WKB approximation is displayed in Fig. 13d. Overall, the solution shows that m tends to be larger (smaller) at depths corresponding to stronger (weaker) stratification, except that the wavenumber approaches infinity near the critical level of approximately 220 m. That is, the downward-going waves leaving the surface layer can experience a couple of diminishing wavelength events near the two N maxima (pycnoclines): the SML base and LHL. Regarding C_gz, the WKB approximation generally shows the most rapid decay within the surface 20 m, followed by a gentle increase toward the core near 100–130-m depth. Below this, C_gz shows another rapid decrease toward the critical level of 220 m, asymptotically approaching zero velocity. Physically, over the vertical two segments, where C_gz diminishes, the downward-propagating energy packet can be stalled. Following the conservation of vertical energy flux, the decrease in C_gz requires the compensation of the same percentage of energy gain over the corresponding vertical segments. Indeed, the observed near-inertial horizontal velocities apparently build up at the corresponding depths of 20–50 and 170–250 m (Fig. 7). Those results from (7) and (8), principally contributed by the vorticity change, are qualitatively consistent with those from the WKB ray-tracing simulation, applied to the warm-core rings in the Gulf Stream, by Kunze et al. (1995, their Fig. 8).