Seasonal Variability of Near-Inertial/Semidiurnal Fluctuations and Turbulence in the Subarctic North Atlantic

Eric Kunze aNorthWest Research Associates, Seattle, Washington

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Ren-Chieh Lien bApplied Physics Lab, University of Washington, Seattle, Washington

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Caitlin B. Whalen bApplied Physics Lab, University of Washington, Seattle, Washington

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James B. Girton bApplied Physics Lab, University of Washington, Seattle, Washington

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Barry Ma bApplied Physics Lab, University of Washington, Seattle, Washington

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Maarten C. Buijsman cUniversity of Southern Mississippi, Stennis Space Center, Mississippi

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Abstract

Six profiling floats measured water-mass properties (T, S), horizontal velocities (u, υ), and microstructure thermal-variance dissipation rates χT in the upper ∼1 km of the Iceland and Irminger Basins in the eastern subpolar North Atlantic from June 2019 to April 2021. The floats drifted into slope boundary currents to travel counterclockwise around the basins. Pairs of velocity profiles half an inertial period apart were collected every 7–14 days. These half-inertial-period pairs are separated into subinertial eddy (sum) and inertial/semidiurnal (difference) motions. Eddy flow speeds are ∼O(0.1) m s−1 in the upper 400 m, diminishing to ∼O(0.01) m s−1 by ∼800-m depth. In late summer through early spring, near-inertial motions are energized in the surface layer and permanent pycnocline to at least 800-m depth almost simultaneously (within the 14-day temporal resolution), suggesting rapid transformation of large-horizontal-scale surface-layer inertial oscillations into near-inertial internal waves with high vertical group velocities through interactions with eddy vorticity gradients (effective β). During the same period, internal-wave vertical shear variance was 2–5 times canonical midlatitude magnitudes and dominantly clockwise-with-depth (downward energy propagation). In late spring and early summer, shear levels are comparable to canonical midlatitude values and dominantly counterclockwise-with-depth (upward energy propagation), particularly over major topographic ridges. Turbulent diapycnal diffusivities KO(10−4) m2 s−1 are an order of magnitude larger than canonical midlatitude values. Depth-averaged (10–1000 m) diffusivities exhibit factor-of-3 month-by-month variability with minima in early August.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Eric Kunze, kunze@nwra.com

Abstract

Six profiling floats measured water-mass properties (T, S), horizontal velocities (u, υ), and microstructure thermal-variance dissipation rates χT in the upper ∼1 km of the Iceland and Irminger Basins in the eastern subpolar North Atlantic from June 2019 to April 2021. The floats drifted into slope boundary currents to travel counterclockwise around the basins. Pairs of velocity profiles half an inertial period apart were collected every 7–14 days. These half-inertial-period pairs are separated into subinertial eddy (sum) and inertial/semidiurnal (difference) motions. Eddy flow speeds are ∼O(0.1) m s−1 in the upper 400 m, diminishing to ∼O(0.01) m s−1 by ∼800-m depth. In late summer through early spring, near-inertial motions are energized in the surface layer and permanent pycnocline to at least 800-m depth almost simultaneously (within the 14-day temporal resolution), suggesting rapid transformation of large-horizontal-scale surface-layer inertial oscillations into near-inertial internal waves with high vertical group velocities through interactions with eddy vorticity gradients (effective β). During the same period, internal-wave vertical shear variance was 2–5 times canonical midlatitude magnitudes and dominantly clockwise-with-depth (downward energy propagation). In late spring and early summer, shear levels are comparable to canonical midlatitude values and dominantly counterclockwise-with-depth (upward energy propagation), particularly over major topographic ridges. Turbulent diapycnal diffusivities KO(10−4) m2 s−1 are an order of magnitude larger than canonical midlatitude values. Depth-averaged (10–1000 m) diffusivities exhibit factor-of-3 month-by-month variability with minima in early August.

© 2023 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Eric Kunze, kunze@nwra.com

1. Introduction

Internal waves are ubiquitous in the World Ocean (Garrett and Munk 1979), spanning length scales as large as ∼O(100) km in the horizontal to as small as ∼10 m in the vertical. Established generation mechanisms are at the Coriolis frequency f primarily by wind forcing (Pollard and Millard 1970; Price 1983; Gill 1984; D’Asaro 1985; Alford et al. 2016; Alford 2020), diurnal and semidiurnal frequencies by tide/topography interactions (Ray and Mitchum 1997; Egbert and Ray 2001; Althaus et al. 2003; Rudnick et al. 2003; Nash et al. 2006; Lee et al. 2006; Garrett and Kunze 2007; Melet et al. 2013; Buijsman et al. 2020), and continuum (ωf) intrinsic frequency lee waves by abyssal flow/topography interactions (Scott et al. 2011; Nikurashin and Ferrari 2011; Melet et al. 2014). Low modes propagate to fill in basins (Alford 2001; Zhao 2019; Kelly et al. 2013) while nonlinear wave–wave (McComas and Müller 1981; Henyey et al. 1986; Dematteis et al. 2022) and wave–eddy (Müller et al. 2015; Dong et al. 2023) interactions fill in the internal-wave wavenumber–frequency spectra and ultimately cascade wave energy to the finescale where intermittent shear instabilities generate microscale turbulence (e.g., Kunze et al. 1990; Polzin et al. 1995; Polzin 1996). Internal waves are the primary source of turbulent dissipation and mixing in the stratified ocean interior (Kunze 2017a; MacKinnon et al. 2017; Whalen et al. 2020), which controls the upwelling limb of the meridional overturning circulation (de Lavergne et al. 2016; Kunze 2017b), deep-ocean stratification (Munk 1966), energy budgets (Wunsch and Ferrari 2004; Kunze 2017a), and mixing of solutes, which also influences the supply of nutrients to the euphotic zone and hence biological productivity. At mid- and lower latitudes, diapycnal diffusivities K associated with canonical levels of the Garrett and Munk (1979) internal-wave model spectrum are ∼0.05 × 10−4 m2 s−1 (Gregg 1989), modulated by the balanced mesoscale eddy field (Kunze et al. 1995; Whalen et al. 2012; Raja et al. 2022; Essink et al. 2022) and internal tide generation (Kunze 2017a), while much lower internal-wave (D’Asaro and Morison 1992) and turbulence (Padman and Dillon 1987) levels are found under Arctic sea ice (Fer 2014).

Here, we describe seasonal variability of near-inertial/semidiurnal internal waves and turbulence in the upper 1 km of the Iceland and Irminger Basins in the subarctic North Atlantic where the semidiurnal frequency lies in the near-inertial frequency band so that both wind and tides are energy sources for near-inertial waves. Surface forcing by winter low pressure systems is expected to lead to seasonality of upper-ocean downward energy propagation of near-inertial waves (clockwise-with-depth velocity profiles). While storminess tends to be enhanced in the winter, storms are intermittent (D’Asaro 1985) and more efficiently generate surface-layer inertial oscillations in shallow mixed layers (Pollard and Millard 1970) which are then transformed into downward-propagating near-inertial internal gravity waves by interaction with planetary β (Gill 1984; D’Asaro 1989; Garrett 2001) and the mesoscale eddy field (Kunze 1985; Kunze et al. 1995; D’Asaro 1995; Young and Ben Jelloul 1997; Asselin et al. 2020; Thomas et al. 2020; Raja et al. 2022; Essink et al. 2022). Semidiurnal internal tide generation by surface tidal currents interacting with rough topography (Garrett and Kunze 2007; Buijsman et al. 2020) is expected year-round with upward energy propagation near the bottom. Vic et al. (2021) report internal-tide generation at the crest of Reykjanes Ridge between Iceland and Irminger Basins comparable to winter generation of near-inertial internal waves using seven 2-yr-long full-depth current-meter mooring time series. They report semidiurnal internal-tide replenishment time scales of ∼1 week and near-inertial replenishment time scales of ∼2 weeks, similar to time scales reported at 55°–65° latitude by Alford and Whitmont (2007). Internal-wave and turbulence seasonal variability in the broader eastern subpolar North Atlantic have not previously been reported. Superposition of bottom- and surface-forced near-inertial internal gravity waves, as well as with their reflections from the surface and bottom, will obscure sources unless turbulent damping sufficiently weakens the waves as they propagate.

In these basins, the North Atlantic Current carries warm water into the Norwegian Sea and cold Arctic waters are carried equatorward by the East Greenland Current in the upper ocean, while the Denmark Strait Overflow (Saberi et al. 2020) and Faeroe Bank Channel Overflow (Hansen and Østerhus 2000) carry intermediate waters formed during winter in the Iceland and Greenland Seas (Brakstad et al. 2019; Huang et al. 2020) in the subpolar limb of the Atlantic meridional overturning circulation (AMOC). Roughly half of the lower limb 15 Sv (1 Sv ≡ 106 m3 s−1) overturning circulation appears to originate from Nordic seas while the remainder forms during deep winter convective events southeast of Greenland and over Reykjanes Ridge north of 62°N (Petit et al. 2020).

Here, we describe seasonal variability of near-inertial/semidiurnal internal waves, including rotary-with-depth variability, and turbulence in the upper 1 km of Iceland and Irminger Basins. Section 2 describes the χT-augmented EM-APEX profiling floats used for this study and the half-inertial-period pair sampling. Section 3 describes the subinertial eddy flow characteristics from half-inertial-period pair averages, section 4 describes the near-inertial/semidiurnal velocity profile behavior from half-inertial-period pair differences, and section 5 describes turbulent dissipation rates ε and diapycnal diffusivities K inferred from temperature microstructure. Observational conclusions are summarized in section 6, while section 7 discusses possible reasons for the switch from clockwise-with-depth (downgoing near-inertial energy propagation) predominance in late summer–early spring to counterclockwise-with-depth (upgoing) predominance during late spring and early summer which is at odds with the year-round dominance of clockwise-with-depth variance in the lower-latitude pycnocline (D’Asaro and Perkins 1984; Pinkel 1985; Waterhouse et al. 2022).

2. EM-APEX float measurements

As part of the multi-investigator NISKINE (Near-Inertial Shear and Kinetic Energy in the North Atlantic) project to characterize near-inertial wave and turbulence variability in the eastern subarctic North Atlantic, EM-APEX profiling floats (Sanford et al. 2005) augmented with dual FP07 microthermistors (Lien et al. 2016) were deployed near the northern edge of the North Atlantic Current in Iceland Basin (57°–58°N, 21°–24°W, Coriolis frequency f = 1.23 × 10−4 rad s−1, inertial period 14.15 h) during a 29 May–17 June 2019 process cruise. Six floats were left behind to drift freely and measure subinertial eddy, near-inertial/semidiurnal, and temperature microstructure fields in the upper ∼1 km of the eastern subpolar North Atlantic (Fig. 1) for the duration of their battery lives. Float durations ranged from 223 to 624 days to acquire 3500 profiles. The shortest float time series ended in August 2020, but three floats continued to transmit data until winter–spring 2021, the longest ending in early April 2021, just short of two years. At these subpolar latitudes, near-inertial and semidiurnal internal gravity waves have similar frequencies (M2 = 1.13f) so that their consistency relations (Müller et al. 1978; Lien and Müller 1992), in particular, their rotary with time and depth properties (Leaman and Sanford 1975), are nearly identical. With only their sources to distinguish them, it is not possible to tell them apart in the water column with our sampling; Vic et al.’s (2021) and Voet et al.’s (2023, manuscript submitted to Oceanography) 24- and 18-month-long mooring time series at 58°–59°N were able to distinguish inertial and semidiurnal peaks. As the floats disperse, their statistics become less local and more representative of the broader Iceland and Irminger Basins.

Fig. 1.
Fig. 1.

Trajectories for the six EM-APEX profiling floats deployed near 58°N, 24°W (green dot) to drift freely after a June 2019 process-study cruise, terminating at the open diamonds. Two floats (green and dark blue) stopped transmitting before winter 2020 and did not leave Iceland Basin. The remaining four continued to transmit data until as late as April 2021. Three floats (red, russet, and light blue) crossed Reykjanes Ridge into the Irminger Basin to the west with the red and light blue trajectories lying almost on top of one another, while one (black) was carried across the Iceland–Faeroe Ridge into the eastern Norwegian Sea to the east. All four were carried counterclockwise around basins in slope boundary currents. Float separations shorter than 35 km are solid, longer than 35 km dotted.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

The floats collected roughly 2200 half-inertial-period (7 h) pairs, that is, two profiles collected 7-h apart to be 180° out of phase for near-inertial fluctuations, with pairs collected every 7–14 days. Half-inertial-period velocity profile averages are interpreted as subinertial balanced eddy motions while pair differences as near-inertial/semidiurnal fluctuations following Sanford (1975). This interpretation is valid if there are no strong signals outside the subinertial and near-inertial/semidiurnal bands. The 7–14-day gaps between the half-inertial-period pairs do not resolve time scales for either the eddy field or inertial/semidiurnal energy. That is, flow directions, vertical structure, amplitudes, and the spring–neap cycle are incoherent from profile pair to profile pair. Therefore, subsequent analyses focus on seasonal variability and statistics.

EM-APEX floats measure temperature T, salinity S, and pressure P with 2.5-m vertical resolution using a Sea-Bird Electronics SBE41 CTD. In addition, they are instrumented with two pairs of EM sensors that measure horizontal velocity (u, υ) electromagnetically with 7-m resolution, not attenuating vertical wavelengths longer than 28 m (Sanford et al. 2005). Horizontal velocities are measured relative to a depth-independent constant with less than 0.01 m s−1 uncertainty. Temporal sampling was too coarse to make the customary GPS correction to absolute velocity (Lien and Sanford 2019), but the focus is on baroclinic signals here.

The commercially available floats were augmented with two FP07 microthermistors mounted on their caps sampling at 125 Hz to infer thermal-variance dissipation rates χT every 1 m during ascents. Thermal dissipation rates χT=6κTTz2 where the molecular diffusivity of heat κT = 1.4 × 10−7 m2 s−1 and the turbulent temperature-gradient variance Tz2 is estimated by integrating microscale vertical wavenumber spectra for temperature gradient from 2 cpm to an ∼0.01 cpm upper bound above which the measured temperature-gradient spectra are less than the noise spectrum (Lien et al. 2016). For the slow ∼0.1 m s−1 ascent speeds, all the microscale temperature-gradient variances are captured for ε < 10−8 W kg−1. Corrections for higher ε would be less than a factor of 2.5 (A. Takahashi 2023, personal communication) so would have little impact on averages. Therefore, no corrections were applied for missing variance at high wavenumber for the highest dissipation rates. The float ascent speed is an order of magnitude faster than turbulent flow speeds, so the frozen-turbulence approximation holds.

Turbulent thermal diffusivities KT = χT/2/〈Tz2 (Osborn and Cox 1972) and turbulent kinetic energy dissipation rates ε = KN2〉/γ (Osborn 1980) are inferred under the assumptions that the diapycnal diffusivity K = KT and mixing coefficient γ = 0.2 (St. Laurent and Schmitt 1999; Gregg et al. 2018), where 〈N2〉 is the background buoyancy frequency squared and 〈Tz〉 is the finescale vertical temperature gradient from concurrent 2.5-m resolution Sea-Bird CTD measurements. All FP07 sensors failed before the end of the float missions with durations ranging from October 2019 to January 2021. Data are transmitted ashore by Iridium satellite when the floats are on the surface.

3. Subinertial motions

The six long-duration EM floats provide two measures of the subinertial balanced eddy flow. First, float trajectories show the circulation at the floats’ resting depth (∼300 m before January 2020 and ∼900 m thereafter) on the 7–14-day time scales between half-inertial-period profile pairs (Fig. 1). The four floats that survived winter 2020 all migrated to slope boundaries within 6 months where they drifted for the remainder of their missions. Three (red, russet, and light blue) traversed Iceland Basin westward along diverse paths to be caught in the East Reykjanes Ridge Current and carried southwest. Two of these (red and light blue) traveled counterclockwise around Iceland Basin in boundary currents, crossing the ridge near 59°–60°N during July–September 2020, ultimately being carried in the East Greenland Current southwest along the East Greenland continental slope. The third (russet) was carried west, likely in a North Atlantic Current warm-core ring, and crossed the ridge during December 2019; a short-lived float (dark blue) was also carried west but stopped transmitting before it reached the ridge. The fourth long-lived float (black) was carried along the western flank of Rockall Plateau by the North Atlantic Current to cross the Iceland–Faeroe Ridge into a different stratification environment in the eastern Norwegian Sea to the east. These results are consistent with previous measurements of (i) cyclonic circulation concentrated on the boundaries in Iceland and Irminger Basins (Bower et al. 2002; Lankhorst and Zenk 2006; Daniault et al. 2016; Lozier et al. 2019; Koman et al. 2020) as expected from wind-driven surface divergence and (ii) the tendency for North Atlantic Current anticyclones to migrate west (Houpert et al. 2018; Zhao et al. 2018). The net divergence of most float trajectories to gyre boundaries suggests rapid one-way connection between the interior and boundary in the Iceland Basin.

Second, half-inertial-period pair vector velocity sums V = (U, V) = [v(t) + v(t + 7 h)]/2 provide snapshots of subinertial flow profiles every 7–14 days in the upper ∼800 m (Fig. 2). These are dominated by mesoscale eddies. Average alongstream eddy speeds of 〈|V|〉 = 〈U″〉 = 〈U cosθ + V sinθ〉 ∼ O(0.1) m s−1, where instantaneous subinertial flow orientation θ=Arctan[Vdz/(Udz)] and 〈〉 is the average over all profile pair sums, are intensified in the upper 200–400 m where velocities are only weakly depth dependent, decaying to less than 0.04 m s−1 by 750-m depth (Fig. 2a). The corresponding average subinertial gradient Froude number |Vz|/N ∼ 0.1 so is not unstable to vertical shear instability. Average subinertial depth hodographs, that is, 〈V″(z)〉 versus 〈U″(z)〉 from the profiles (Fig. 2a), are nonrotary with depth (Fig. 2b). Snapshots show little relation to the 7–14-day resting-depth motions (Fig. 1) which are also ∼O(0.1) m s−1. Thus, eddies randomize subinertial flow direction on time scales less than 14 days. Histograms of the depth-average subinertial speed Udz/(dz) peak at ∼0.06 m s−1 (Fig. 2c). Histograms of subinertial depth-averaged flow orientation θ show a tendency for flow slightly north of east (Fig. 2d).

Fig. 2.
Fig. 2.

(a) Profiles of subinertial alongstream flow 〈|V|〉 = 〈U″〉 = 〈U cosθ + V sinθ〉 (red), cross-streamflow 〈V″〉 (blue), buoyancy frequency 〈N〉 (green), and inertial/semidiurnal horizontal kinetic energy 〈hke〉 = 〈u2 + υ2〉/2 (salmon shading) averaged over all EM float half-inertial-period pairs, along with (b) corresponding average subinertial flow depth hodographs, 〈U″〉 vs 〈V″〉, which are rectilinear, that is, nonrotary with depth. Histograms of (c) depth-average profile-pair flow magnitude Udz/(dz) with count n normalized by its maximum value nmx, and (d) depth-average subinertial flow direction θ=Arctan[Vdz/(Udz)]. The dot in (b) is at the top and the open circle is at the bottom of the profile.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Subinertial (eddy) horizontal kinetic energy HKE = (U2 + V2)/2 (Figs. 3b,c and 4b,c) varies from 10−5 to 10−1 m2 s−2, with larger values mostly above 600-m depth. Eddy energy time scales range from a few weeks to several months, more persistent than eddy flow direction (not shown).

Fig. 3.
Fig. 3.

Profile time series from long-duration float 4971 (22-month-long light blue trajectory in Fig. 1) finescale velocity and water-mass measurements. Displayed variables are (a) buoyancy frequency N, (b) subinertial (eddy) horizontal kinetic energy HKE = (U2 + V2)/2, (c) depth-averaged eddy energy, (d) inertial/semidiurnal horizontal kinetic energy hke = (u2 + υ2)/2, and (e) inertial/semidiurnal hke averaged above 150-m depth to capture the surface layer (blue bars and left axis) and below 550-m depth in the permanent pycnocline (red bars and right axis). Light green shading denotes spring and rose shading autumn. The black bar along the upper axis in (c) marks the interval when the float was crossing Reykjanes Ridge. Down and up arrows in (e) mark profiles with clear CW-with-depth (downgoing energy) or CCW-with-depth (upgoing energy) signatures. Float 4971 did not transmit data during March–July 2020.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Fig. 4.
Fig. 4.

As in Fig. 3, but for long-duration float 7808 (22-month-long red trajectory in Fig. 1).

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

4. Seasonal variability of near-inertial/semidiurnal motions

Differences of the 2200 half-inertial-period velocity vector profile pairs, v′ = (u′, υ′) = [v(t + 7 h) − v(t)]/2, are interpreted as near-inertial/semidiurnal oscillations.

Profile time series from the two EM floats with the longest finescale velocity and water-mass measurements span almost 2 years (Figs. 3 and 4), ending their missions in the East Greenland Current (Fig. 1). The seasonal cycle is most clearly seen in buoyancy frequency N (Figs. 3a and 4a) which has a sharp shallow pycnocline with N ∼ 10−2 rad s−1 at 20–30-m depth from May through August overlying a weakly stratified layer to ∼600-m depth. This seasonal pycnocline starts to erode in late August or early September and is eradicated to ∼600-m depth by mid-November to form Subpolar Mode Water (McCartney and Talley 1982; de Jong et al. 2018; Rühs et al. 2021). Thus, the weakly stratified layer to 600-m depth below the seasonal pycnocline in summer is a remnant of the previous winter’s surface mixed layer. Such restratification as occurs below the seasonal pycnocline can be explained by vertical mixing (section 5). Comparison between floats suggests similar stratification profile seasonal cycles in the gyre interior and on slope boundaries. Thus, both near-inertial wave generation and upper-ocean internal-wave propagation experience extremely variable stratification in time and depth while basin-scale lateral variability is weak. The winter mixed layer depth never appears to extend below 600 m, not even when float 7808 passes through the region of strong air–sea buoyancy exchange southeast of Greenland (Petit et al. 2020) during early winter of 2021 (Fig. 4a).

Near-inertial/semidiurnal horizontal kinetic energy hke = (u2 + υ2)/2 (Figs. 3d,e and 4d,e) is an order of magnitude weaker than eddy HKE (Figs. 3b,c and 4b,c), not exceeding 10−2 m2 s−2. Its minimum of less than 10−3 m2 s−2 in the May through July remnant winter mixed layer at 200–400 m coincides with the stratification minimum. Below 400-m depth, near-inertial/semidiurnal hke increases with N (Fig. 2a), consistent with WKB scaling (hke ∝ N; e.g., Leaman and Sanford 1975; Vic et al. 2021). Energetic bursts occur in late August through early winter, as well as sometimes in early spring, exceeding 3 × 10−3 m2 s−2 in the upper 100 m. Stronger surface-layer hke signals when the mixed layer is thinner are consistent with wind stress being distributed over mixed layer depth as in the Pollard and Millard (1970) inertial wind-forcing model. These bursts appear, not just in the surface mixed layer, but extend almost simultaneously (on the 7–14-day resolved time scales) over the measured ∼800-m depth range (Figs. 3e and 4e), indicating rapid transformation and vertical propagation of storm-forced mixed layer inertial oscillations to near-inertial internal waves in the permanent pycnocline. Vertical group velocities Cgz=N2kh2/(fkz3)=(ω2f2)/(fkz) so that high vertical group velocities correspond to high horizontal wavenumbers kh that could be due to the short storm-forcing scales observed in the region (Klenz et al. 2022) or strong interactions with the eddy field (Kunze 1985; Kunze et al. 1995; D’Asaro 1995; Asselin et al. 2020; Essink et al. 2022). Thomas et al. (2020) reported rapid shrinking of surface-layer inertial length scales due to vorticity refraction near the deployment site in the shipboard process cruise measurements.

Visual inspection of all 2200 half-inertial-period pair velocity profile differences (near-inertial/semidiurnal) for rotary-with-depth properties identified the fraction in four categories: clockwise-with-depth (CW, downward energy propagation; Leaman and Sanford 1975), counterclockwise-with-depth (CCW, upward energy propagation), mixed CW and CCW, and too weak to categorize. Binned by month to remove biased high sampling during June 2019, clockwise-with-depth is most common in fall–early winter and late winter–spring while least frequent in January and summer (Fig. 5). Counterclockwise-with-depth dominance is most frequent in July and least common during winter. Weak signals predominate in summer and are least common in spring and December. Mixed rotary-with-depth signals are found throughout the year, but most frequently in March. We caution that Fig. 5 does not include amplitudes. Furthermore, excess CW (CCW) rotary-with-depth energy cannot be equated with excess downgoing (upgoing) energy flux because energy flux depends on group velocity as well as energy (D’Asaro and Perkins 1984; Pinkel 1985; Waterhouse et al. 2022). Group velocity is very sensitive to frequency near the inertial frequency.

Fig. 5.
Fig. 5.

Monthly binned rotary-with-depth fractional occurrence statistics from visual inspection of 2200 half-inertial-period profile pair differences. Clockwise-with-depth (CW; red) is most common in spring (February–May) and fall (September–December); it is least frequent in summer and January. Counterclockwise-with-depth (CCW; blue) is most frequent in July and least common in winter. Mixed CW and CCW signals (green) are common throughout the year but most common during March. Weak profiles where a rotary-with-depth signature could not be identified (gray) are most common during summer and least common in March–April and December.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

To better quantify the rotary-with-depth signals in Fig. 5, the bottom 320 m (∼500–800-m depth) of the half-inertial-period difference (near-inertial/semidiurnal) profiles were Fourier-transformed with depth and binned by season (Fig. 6). This depth range is in the permanent pycnocline to avoid the surface mixed layer. This is somewhat compromised during winter months when mixed layer depth reaches ∼600 m. However, spectra computed over the bottom 640 m of the profiles (∼150–800-m depth) are similar to those in the bottom 320 m. Further, since near-inertial/semidiurnal hke is energized from the surface to ∼800 m almost simultaneously on the 7–14-day resolution of the half-inertial-period pairs (Figs. 3d,e and 4d,e), the spectra are taken to be representative of the full ∼800-m profiles. Rotary-with-depth spectra were computed following Kunze and Sanford (1984) and then buoyancy-frequency-normalized shear spectra as kz2S[CW](kz)/N2 and kz2S[CCW](kz)/N2 where vertical wavenumber kz is in radians per meter. Strain was calculated as ξz = (N2 − 〈N2〉)/〈N2〉 following Polzin et al. (1995), where N2 is local squared buoyancy frequency and 〈N2〉 is a linear fit over the 500–800-m depth range. At more energetic, so more reliable, low vertical wavenumbers (λz > 100 m), the average vertical wavenumber spectra for normalized rotary-with-depth shear spectra are comparable to the canonical Garrett and Munk (1979) model spectral level in summer, but 5 times higher in fall through spring. CW-with-depth dominates over CCW by a factor of 2 during fall and winter, but the two signals are not significantly different in spring and summer. Low-wavenumber strain spectra exceed GM in all seasons and sometimes exceed the shear spectra, pointing to contributions from eddy APE. At high wavenumbers, strain spectra are comparable to GM except in spring.

Fig. 6.
Fig. 6.

Vertical wavenumber spectra of buoyancy-frequency-normalized clockwise-with-depth (CW; downward energy propagation; red solid) shear, counterclockwise-with-depth (CCW; upward energy propagation; blue solid) shear, their ratio (CW/CCW; green solid), and strain ξz (black solid) binned by season from the permanent pycnocline (500–800-m depth) in the half-inertial-period pair difference (inertial/semidiurnal) profiles. Also plotted are GM and saturated spectra (dotted with shear red, strain black). Vertical wavelengths λz are listed above the upper axis of the top row. Standard errors (not shown) are 1–4 times the thicker line width.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Monthly binned buoyancy-frequency-normalized rotary-with-depth shear variances in the permanent pycnocline (Fig. 7) show that both CW- and CCW-with-depth shears become elevated in late summer, remaining so until early spring. CW dominates over CCW starting in September (Fig. 7b) with the arrival of storm forcing in late summer (Fig. 7c) and lingering in the permanent pycnocline into early spring. CCW tends to dominate in early summer.

Fig. 7.
Fig. 7.

Monthly binned time series of stratification-normalized (a) clockwise-with-depth (downward energy propagation) shear variance (CW; red) and counterclockwise-with-depth (upward energy propagation) shear variance (CCW; blue), and (b) the log of their ratio log10(CCW/CW) ranging from −log2 to log2 (left axis) in the permanent pycnocline (500–800-m depth) (Fig. 6) with arrow directions in (b) indicating net upward (blue) or downward (red) energy propagation with standard errors. CW variance in (a) is elevated by a factor of 3 from late summer through early spring. CCW variance exhibits similar behavior but is weaker. The CCW/CW ratio in (b) tends to be CW-dominated in late summer through early spring and CCW-dominated in late spring through early summer. This is consistent with the visual census of rotary-with-depth statistics (Fig. 5). (c) Inertial wind-work (red bars) and semidiurnal barotropic-to-baroclinic tidal conversion from Buijsman et al. (2020) (blue bars) binned by month following float trajectories (see section 7); elevated tidal conversions coincide with float passages over rough topography (black bars).

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Maps of rotary-with-depth variances (Fig. 8) show a tendency for elevated CCW- over CW-with-depth to line up with the rough topography and elevated semidiurnal barotropic-to-baroclinic tidal conversion on the East Greenland continental slope, Reykjanes Ridge, and the western flank of Rockall Plateau (Figs. 8d–f). This can be seen by comparing Fig. 8c (CW > CCW) and Fig. 8f (CCW > CW) in which Fig. 8f shows more dots aligned with high barotropic-to-baroclinic tide conversion, suggesting a topographic cause for the upward (CCW) energy signature, either semidiurnal internal tide generation or scattering of wind-generated near-inertial waves. This is further illustrated by Fig. 9 of buoyancy-frequency-normalized CCW shear variance binned with respect to internal tide generation along float trajectories. At the highest semidiurnal barotropic-to-baroclinic tidal conversion, which is associated with the topographic ridges (Fig. 8f), there is elevated CCW variance (Fig. 9). This result is consistent with Vic et al. (2021) reporting semidiurnal internal-tide generation exceeding near-inertial wind generation in summer at the crest of Reykjanes Ridge, predominantly into higher (>3) modes.

Fig. 8.
Fig. 8.

Maps of (a),(d) CW-with-depth shear variance, (b),(e) CCW-with-depth shear variance, (c) log of the rotary ratio CW/CCW, and (f) log of CCW/CW for (left) CW-dominated (CW > CCW) profiles and (right) CCW-dominated (CCW > CW) profiles color-coded by season—fall (orange), winter (blue), spring (light green), and summer (dark green). Downgoing dominance (CW/CCW > 1, left) shows no obvious relation to geography or topography, but upgoing dominance (CCW/CW > 1, right) tends to be clustered along the rough topography of the East Greenland continental slope, Reykjanes Ridge, and the west flank of Rockall Plateau. In (a)–(c), gray shading represents water depth (Fig. 1); in (d)–(f), semidiurnal barotropic-to-baroclinic tidal conversion from HYCOM (Buijsman et al. 2020). Dot sizes in (a), (b), (d), (e) are buoyancy-normalized shear variances [index to right of (e)]. Dot sizes in (c) and (f) are proportional to the log of the rotary-with-depth ratios [index to right of (f)].

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Fig. 9.
Fig. 9.

Plot of binned 500–800-m depth buoyancy-frequency-normalized counterclockwise-with-depth shear variance CCW vs semidiurnal barotropic-to-baroclinic tidal conversion M2 (Fig. 8f) along float trajectories. CCW variance increases by a factor of 3 at higher internal-tide generation.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

In summary, the inertial/semidiurnal band in Iceland and Irminger Basins is energized in late summer to early winter with rapid penetration (<14 days) into the permanent pycnocline at 600–800-m depth by resolved vertical wavelengths λz < 800 m (Figs. 3d,e and 4d,e), implying swift vertical propagation of storm-forced inertial oscillations out of the surface mixed layer into the pycnocline as downgoing near-inertial waves. Fall–spring internal-wave shear variance is 5 times the canonical midlatitude GM level. CW-with-depth (downward energy propagation) shear dominates in fall and winter while CW- and CCW-with-depth shear are more comparable during spring and summer (Figs. 5 and 6), CCW dominating in late spring and early summer (Fig. 7). In contrast, Waterhouse et al.’s (2022) global analysis of LADCP and shipboard ADCP profiles found that CW tended to dominate the upper 600 m at lower latitudes regardless of season. At subpolar latitudes, they found near-equipartition of CW- and CCW-with-depth shears in the upper 600 m, but their shipboard sampling was sparse in the subpolar North Atlantic and biased to summer. CCW-with-depth dominance appears to be related to topographic roughness and semidiurnal barotropic-to-baroclinic tidal conversion (Figs. 8 and 9).

5. Seasonal variability of turbulent dissipation and mixing

Early failures of the FP07 thermistors limit turbulent dissipation and mixing inferences to the 18 months from June 2019 to December 2020 (float 7806, FP07 microthermistor #1). However, the microstructure data do span an annual cycle. Data are only excluded from analysis if N2 < 4f2 ∼ 5 × 10−8 s−2 or Tz < 2 × 10−3 °C m−1 to remove unreliable turbulent kinetic energy dissipation rates ε and diapycnal diffusivities K due to sensor noise, or if the two χT estimates do not agree within a factor of 2. Doubling these thresholds had no visible impact on the histograms or averages.

Distributions of microstructure variables from all allowed FP07 data are roughly lognormal with log standard deviations of ∼ ±1 (Fig. 10). Outliers (χT > 10−5°C2 s−1, ε > 3 × 10−7 W kg−1, K > 10−2 m2 s−1) that are three standard deviations in log space above the modes are excluded from subsequent statistics. Linear mean (mode) TKE dissipation rates ε are 2.9 × 10−9 (2.5 × 10−10) W kg−1 (Fig. 10a). Linear mean (mode) thermal diffusivities KT are 0.6 × 10−4 (∼0.1 × 10−4) m2 s−1 (Fig. 10b). Seasonally binned dissipation rates ε span (2–4) × 10−9 W kg−1 and diffusivities K span (0.4–0.9) × 10−4 m2 s−1. Average dissipation rates ε for low (high) buoyancy frequencies (threshold N = 10−3 rad s−1) are 2 (3) × 10−9 W kg−1 and diapycnal diffusivities K are 0.5 (0.6) × 10−4 m2 s−1.

Fig. 10.
Fig. 10.

Histograms of (a) turbulent kinetic energy (TKE) dissipation rate ε and (b) diapycnal diffusivity K inferred from all allowed EM float FP07 microthermistor data with counts n normalized by their maximum value nmax for each panel. Both distributions are roughly lognormal. Linear means are marked with dotted vertical lines with values in the upper-right corner. The linear-mean diapycnal diffusivity K of 0.57 × 10−4 m2 s−1 is an order of magnitude larger than the canonical midlatitude value of 0.05 × 10−4 m2 s−1 (Gregg 1989).

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Profile time series of N, ε, and K for the FP07 thermistor of longest duration (18 months) reveal the strongest microstructure signals in the surface mixed layer, particularly in fall and winter with dissipation rates ε ∼ 10−7 W kg−1 and diapycnal diffusivities K ∼ 10−2 m2 s−1 (Fig. 11); this float is one of the three that crossed Reykjanes Ridge into Irminger Sea (russet trajectory in Fig. 1). Despite the restrictions described above, reliable turbulence estimates are often available in the surface boundary layer, indicative of sufficiently strong mixed layer stratification (N > 2f). The weakest turbulent signals of ε ∼ 10−10 W kg−1 and K ∼ 10−6 m2 s−1 are associated with weak stratification in the remnant winter mixed layer during summer 2019 and the permanent pycnocline below 600 m through December 2019.

Fig. 11.
Fig. 11.

Sample profile time series of (a) finescale buoyancy frequency N, (b) TKE dissipation rate ε, and (c) diapycnal diffusivity K from EM float 7806 (russet trajectory in Fig. 1), FP07 microthermistor 1, which had the longest record at 19 months. Light green shading denotes spring and rose shading denotes fall. The highest dissipation rates ε and diffusivities K occur during deepening and destratification of the surface mixed layer during fall and early winter. Black bars along the bottom axes mark when the float crosses Reykjanes Ridge.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Time series of turbulent kinetic energy dissipation rate ε and diapycnal diffusivity K averaged over 10–1000-m depth from all FP07’s subject to the above-described restrictions exhibit factor-of-3 variability from month to month (Fig. 12). Dissipation rates ε range from 1.2 to 7.0 × 10−9 W kg−1. Diffusivities K range from 0.2 to 4 × 10−4 m2 s−1. Peaks occur in June and September 2019 and January and April 2020, and minima occur in early August, October, and March. The January maximum is the least reliable because of the deep extent of the winter surface mixed layer. A clear seasonal cycle is less evident in turbulence than in the internal-wave field (Figs. 37) although an early August minimum in K recurs in both 2019 and 2020. The strong turbulence peak during September 2019 extends to 1000-m depth (not shown), coincident with the near-inertial/semidiurnal hke bursts (Figs. 3d,e and 4d,e) due to a late summer storm forcing a shallow mixed layer. A similar forcing event does not recur during late summer 2020. The strong peak during January 2020 is confined to the winter mixed layer (Fig. 13). Maximum diffusivities ∼3 × 10−4 m2 s−1 during January 2020 will mix waters over 20 m during their monthly extent. Background diffusivities would take roughly 1000 years to mix over 1000 m. This latter time scale is better associated with the slow diapycnal upwelling limb of the MOC than the abrupt and localized convective downwelling events under strong air–sea buoyancy forcing inferred by Petit et al. (2020).

Fig. 12.
Fig. 12.

Time series of (a) TKE dissipation rate ε and (b) diapycnal diffusivity K from all FP07 data subject to the above-described restrictions averaged over 10–1000-m depth. Both variables exhibit factor-of-3 month-to-month variability with peaks in June and September 2019 and January and April 2020 and a 0.2 × 10−4 m2 s−1 minimum in K (b) for early August during both summers. Light green shading denotes spring and rose shading denotes fall. Black bars indicate crossings of Reykjanes Ridge.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Fig. 13.
Fig. 13.

Average profiles of (a) buoyancy frequency N, (b) TKE dissipation rate ε, and (c) diapycnal diffusivity K. Total averages (black) include ∼O(104) estimates per 10-m bin. Seasonal averages by summer (dark green), fall (orange), winter (blue), and spring (light green) show elevated dissipation rates ε and diffusivities K in the upper 100 m in fall and spring and in the upper 300 m in winter. Diffusivities are also weakly elevated in the permanent pycnocline below 600-m depth during winter, while weak in fall. Diffusivities K are ∼10−4 m2 s−1 in the upper 50–400 m, falling to ∼0.6 × 10−4 m2 s−1 below 600-m depth. Dissipation rates ε decrease more or less monotonically from ∼10−8 W kg−1 in the upper ∼50 m to ∼10−9 W kg−1 at 1000-m depth.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Time- and float-averaged dissipation rate ε profiles diminish from ∼10−8 W kg−1 in the upper 50 m to 10−9 W kg−1 at 1000-m depth (Fig. 13). Diapycnal diffusivities K are ∼10−4 m2 s−1 in the upper 50–400 m and less than 0.6 × 10−4 m2 s−1 below 600-m depth. Dissipation rates and diffusivities are elevated in the upper 100 m during spring and fall and upper 300 m during winter, implying that seasonal variability in Fig. 12 is confined to the upper 100–300 m. There is no obvious minimum associated with the remnant winter mixed layer minimum in N at 150–600-m depth (Figs. 2a, 3a, 4a, and 13a), this feature being eradicated during winter.

Because microthermistor turbulence is less reliable in the absence of temperature and buoyancy stratification, or in the surface layer because of nonlocal forcing (Large et al. 1994), vertical velocity perturbations w′ relative to predicted float fall and rise rates (Cusack et al. 2017) are used to infer convective vertical motions in the surface mixed layer (Fig. 14). These are mostly below the measurement threshold of 0.01 m s−1, but, in winter mixed layers, w′ becomes as large as 0.08 m s−1, implying turbulent dissipation rates εO(Nw2) ∼ O(10−5) W kg−1, consistent with direct microstructure measurements of turbulent kinetic energy dissipation rates in the surface mixed layer under strong atmospheric forcing (e.g., Dillon and Caldwell 1978).

Fig. 14.
Fig. 14.

Profile time series of (a) buoyancy frequency N and (b) vertical velocity perturbations w′ from float 4971 (Fig. 3). Green dots in (a) mark the base of the surface mixed layer. The color bar in (a) is for log10(N).

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

In summary, mean turbulence levels inferred from temperature microstructure [KO(10−4) m2 s−1] are an order of magnitude above canonical midlatitude values (e.g., K = 0.05 × 10−4 m2 s−1, Gregg 1989). This is consistent with the shear spectra being elevated above the canonical Garrett and Munk (1979) model spectrum (Fig. 6) following the finescale parameterization scaling Kαυz22 (Gregg 1989). While there is month-to-month factor-of-3 variability in dissipation rates ε and diapycnal diffusivities K (Figs. 11 and 12), the only recurring seasonal variation is the 0.2 × 10−4 m2 s−1 minimum in K during early August 2019 and 2020 (Fig. 12b).

6. Summary

Six EM profiling floats augmented with FP07 microthermistors were deployed north of the North Atlantic Current in the Iceland Basin of the subarctic North Atlantic to collect half-inertial-period profile pairs in the upper ∼1 km every 7–14 days for the durations of their batteries. Water-mass (T, S) and horizontal velocity (u, υ) profiles were acquired for almost 2 years (22 months) and temperature microstructure χT for 19 months. Four of the floats survived winter 2020 with three carried across Reykjanes Ridge into Irminger Basin to the west and one across the Iceland–Faeroe Ridge into the eastern Norwegian Sea to the east (Fig. 1).

A seasonal pycnocline with N ∼ 10−2 s−1 at 20–30-m depth overlying a 600-m-thick remnant winter mixed layer was eradicated during fall to reform the following mid- to late April (Figs. 3a and 4a). The remnant winter mixed layer survives through summer until the following autumn’s destratification to ∼600-m depth.

Internal-wave shear in the eastern subpolar North Atlantic exhibits a clear seasonal cycle as also seen in moorings over Reykjanes Ridge (Vic et al. 2021) and at 59°6′N, 21°12′W as part of NISKINE (Voet et al. 2023, manuscript submitted to Oceanography), elevated by a factor of 5 above canonical GM levels during fall, winter, and spring (Figs. 6 and 7). Wind-forced near-inertial (14.5 h) and tide/topography-forced semidiurnal (12.42 h) internal waves are dynamically indistinguishable at this latitude. Both forcings contribute to the near-inertial band (Figs. 7c and 8c,f; Vic et al. 2021; Voet et al. 2023, manuscript submitted to Oceanography). CW-with-depth (downgoing energy) shear dominates in late summer through early spring (Fig. 7b) after late-summer storms energize the surface mixed layer and pycnocline almost simultaneously (Figs. 3d,e and 4d,e). Voet et al. (2023, manuscript submitted to Oceanography) report that downward energy propagation is most active in anticyclones which contained twice as much near-inertial energy as the background ocean. During late spring to early summer, CCW-with-depth (upgoing energy) dominates (Fig. 7b) and appears to be localized over the rough topography of the East Greenland continental slope, Reykjanes Ridge, and the west flank of Rockall Plateau (Figs. 8f and 9), consistent with HYCOM model semidiurnal barotropic-to-baroclinic tidal conversion (Buijsman et al. 2020) and mooring measurements across Reykjanes Ridge (Vic et al. 2021). This seasonal variability is consistent with the superposition of fall and winter storm-forced near-inertial waves and a more steady (unresolved spring–neap cycle) semidiurnal internal tide generation as reported by Vic et al. (2021) over Reykjanes Ridge.

While turbulence exhibits month-by-month factor-of-3 variability (Fig. 12), there is no clear seasonal cycle other than a 0.2 × 10−4 m2 s−1 minimum in K during early August of both 2019 and 2020 (Fig. 12), possibly because of the intermittency of storm forcing (D’Asaro 1985) or our mixed space–time sampling. Turbulent dissipation rates ε span (1.2–7.0) × 10−9 W kg−1, and diapycnal diffusivities K span (0.2–4.0) × 10−4 m2 s−1 (Figs. 1013). Diffusivities are over an order of magnitude above canonical midlatitude values (K = 0.05 × 10−4 m2 s−1, Gregg 1989), commensurate with elevated internal-wave shear (Fig. 6). Seasonal variability of near-inertial/semidiurnal horizontal kinetic energy (Figs. 3c,d and 4c,d) extends from the surface to ∼800 m while turbulence variability (Fig. 12) is confined to the upper few 100 m in the surface boundary layer (Fig. 13). Longer and more extensive microstructure measurements would be needed to establish seasonal and interannual variability for turbulence in the eastern subpolar North Atlantic. Float microstructure measurements were not collected southeast of Greenland or north of 62°N along Reykjanes Ridge during winter where convective transformation of upper limb to lower limb AMOC waters has been inferred (Petit et al. 2020).

7. Discussion

EM float measurements in the permanent pycnocline (500–800 m) of Iceland and Irminger Basins reveal rotary-with-depth velocity profiles that are predominantly counterclockwise-with-depth (upward energy propagation) in late spring to midsummer (Figs. 5, 6, and 7a,b). This contrasts with the upper-ocean predominance of clockwise-with-depth profiles, regardless of season, at lower latitudes (Leaman and Sanford 1975; D’Asaro and Perkins 1984; Pinkel 1985; Waterhouse et al. 2022). So CCW dominance in summer is unusual. Three possible explanations are

  1. interior vertical reflections of wind-forced near-inertial waves from discontinuities in stratification or background shear in the water column (Ghaemsaidi et al. 2016; Thomas et al. 2023, manuscript submitted to Oceanography) with time lags between generation and reflection because of finite vertical group velocities (Fig. 15);

  2. bottom reflection (Eriksen 1982; Müller and Liu 2000) or scattering (Müller and Xu 1992) of wind-forced near-inertial waves with propagation time lags between generation, reflection, and return to the permanent pycnocline; and

  3. semidiurnal internal tide generation by bottom topography with upward propagation into the pycnocline (Althaus et al. 2003; Rudnick et al. 2003; Nash et al. 2006; Garrett and Kunze 2007).

Fig. 15.
Fig. 15.

Schematic illustrating (a) surface-forced internal waves experiencing bottom and internal reflections and (b) bottom-forced internal waves experiencing surface and internal reflections.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Long propagation times between the surface and bottom, as well as multiple surface and bottom reflections of surface- and bottom-forced near-inertial/semidiurnal internal waves, could confound interpretation.

Both wind-forcing and semidiurnal tide–topography interactions contribute to the near-inertial frequency wave band at subpolar latitudes (Figs. 7c, 8c, and 9f; Vic et al. 2021). Inertial wind-work 〈τwv〉, where τw is the wind-stress vector, v is the model inertial velocity vector, and 〈 〉 is a 10-day average, is based on the 6-h, 0.5° latitude–longitude JRA-55 reanalysis wind product of Kobayashi et al. (2015) applied to the Pollard and Millard (1970) slab model with mixed layer depth interpolated along float trajectories and a 3-day decay time; these are doubtless underestimates since even 1-h wind products underestimate inertial wind-work by ∼40% because of unresolved short wind-stress time scales (Klenz et al. 2022). Nevertheless, seasonal maximum of inertial wind-work (Fig. 7c) in August–September at the onset of the stormy season yields the expected upper-ocean near-inertial hke response (Fig. 7a) before the mixed layer becomes too thick (Figs. 3a and 4a) for efficient generation of surface-layer inertial oscillations. Semidiurnal barotropic-to-baroclinic tidal conversion interpolated along float trajectories (Figs. 7c and 9) from a HYCOM OGCM September 2016 monthly mean (Buijsman et al. 2020) should be interpreted as spatial variability as the floats pass over rough topography (Figs. 1 and 8f). Internal tide generation exhibits a peak in summer 2020 (Fig. 7c) as floats encounter Reykjanes Ridge, coincident with CCW-with-depth shear dominance (Fig. 7b). However, no strong upward-propagating near-inertial/semidiurnal hke coincides with the peak in January 2020, at most a slight reduction of CW-with-depth dominance. Likewise, there is no strong tidal forcing during summer 2019 when upward dominance is evidence, though both down- and upgoing shear variances are weak during that season (Fig. 7a). Nevertheless, Fig. 9 supports a connection between CCW-with-depth (upgoing energy propagation) shear variance and the largest semidiurnal barotropic-to-baroclinic tidal conversion associated with the East Greenland continental slope, Reykjanes Ridge, and the west flank of Rockall Plateau (Figs. 1 and 8c,f).

The rich eddy field extending to the bottom in Iceland and Irminger Basins will facilitate more rapid propagation from the surface to the bottom and back (and vice versa) than is possible in a quiescent ocean due to an eddy effective beta βe = (∂/∂x, ∂/∂y)(f + ζ/2) = (0, β) + (∂/∂x, ∂/∂y)ζ/2 (Kunze 1985; Kunze et al. 1995; D’Asaro 1995; Young and Ben Jelloul 1997; Asselin et al. 2020; Raja et al. 2022; Essink et al. 2022), where planetary β = ∂f/∂y. Taking eddy vorticity to vary by Δζ ∼ ±0.1f over 10 km in the region (Thomas et al. 2020), mesoscale vorticity gradients are ∼O(10−9) s−1 m−1, exceeding planetary β by two orders of magnitude though this is likely an upper bound. The horizontal wavevector kh evolves with time t as khβet, refracting near-inertial/semidiurnal waves toward lower fe = f + ζ/2 in anticyclones. For vorticity-trapped waves in low-Ro eddies, the dispersion relation can be expressed ωfe+N2kh2/(2fkz2) (Kunze 1985) and kh2 cannot exceed fζkz2/N2 for trapped waves, where kz = /H is vertical wavenumber, n is the mode number, and H is the water depth. Therefore, the vertical group velocity magnitude behaves as
|Cgz|=ωkz=N2kh2fkz3=min{N2H3βe2t2n3π3f,ζHnπ}
and the depth z traveled in time t is
z=Cgzdt=min{N2H3βe2t33n3π3f,ζHtnπ},
so the roundtrip time between the surface and bottom (z = 2H) is
t=max{nπ(6fN2H2βe2)1/3,2nπζ}.
Thus, roundtrip travel times can be reduced by as much as two orders of magnitude compared to planetary β.

In Iceland Basin, water depth H ∼ 3000 m, depth-average buoyancy frequency N ∼ 1.5 × 10−3 rad s−1 below 600-m depth (Fig. 16), and Coriolis frequency f = 1.23 × 10−4 rad s−1. Using these values and the above effective βe, the unrestricted roundtrip can be as short as ∼8 days for mode 8, which are the longest waves (lowest modes) resolved with the 800-m float profiles, and ∼15 days for mode 16 (Fig. 17). Taking eddy vorticities to be ∼−0.3f (Rossby number Ro = 0.3), which is not unreasonable for anticyclones recently spun off the North Atlantic Current (Kunze 1985; Kunze et al. 1995), more realistic vorticity-limited maximum roundtrip travel times are ∼17 days for mode 8 and 1 month for mode 16 (Fig. 17). These can be compared to 1–2-yr roundtrip travel times under planetary β. Roundtrip travel times can be shorter if lower-mode downgoing waves are scattered to higher resolved wavenumbers upon bottom reflection from topographic roughness. Refraction by effective βe also allows mixed layer inertial oscillations to penetrate to 800-m depth in 4–8 days (Fig. 17) compared to 1 year under planetary β. This is consistent with the rapid observed energization of the permanent pycnocline following energization of surface-layer inertial oscillations (Figs. 3d,e and 4d,e). For comparison, dissipation time scales hke/ε ∼ 15 days (Fig. 17), where inertial/semidiurnal wave energy hke ∼ 10−3 m2 s−2 (Fig. 2a) and turbulent dissipation rates ε ∼ 10−9 W kg−1 below 400-m depth (Fig. 13b) where the rotary-with-depth analysis (Figs. 59) was conducted. This dissipation time scale allows a single full-depth roundtrip but prevents multiple roundtrips. This may be an underestimate because it does not account for other sources of dissipation than the measured near-inertial/semidiurnal hke (Figs. 3d,e and 4d,e), i.e., higher-frequency internal waves. But since near-inertial waves dominate the vertical shear, they seem the most likely source of turbulence production.

Fig. 16.
Fig. 16.

Average buoyancy frequency N profile in Iceland and Irminger Basins (52°–62°N, 16°–40°W) from WOCE/CLIMOD hydrography. Below 200-m depth, it lies between 10−3 and 2 × 10−3 rad s−1. Horizontal dotted lines mark the base of the remnant winter mixed layer at 600-m depth and the 800-m depth range of the finescale profiles.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

Fig. 17.
Fig. 17.

Propagation times t from the surface to the bottom (H = 3000 m) and back (or vice versa) (3) as a function of mode number n for both unlimited effective β refraction (βe ∼ 100β, black dots) and limited by anticyclonic vorticity extremum (|ζ| ∼ 0.3f, blue dots), and from the surface to 800-m depth (red triangles) for surface-forced inertial waves. For resolved modes 8–16 (λz = 400–800 m), surface-forced inertial waves can reach 800-m depth in 4–8 days and make the roundtrip from the surface to the bottom and back in less than a month. The dotted horizontal line is the dissipation time scale hke/ε.

Citation: Journal of Physical Oceanography 53, 12; 10.1175/JPO-D-22-0231.1

The short propagation, dissipation, and replenishment times (Fig. 17; Vic et al. 2021) imply that inertial/semidiurnal variability will be local in time and space. Thus, different seasons (Figs. 59) will be independent of each other, and seasonal variability of rotary-with-depth behavior (Figs. 6 and 7a,b) can be attributed to month-by-month competition between surface wind and bottom tidal forcings in the near-inertial internal-wave band. This is consistent with CW- and CCW-with-depth shear variances tending to increase and decrease together (Fig. 7a), likely due to bottom reflection of downgoing seasonal storm-forced waves acting to increase the upgoing (CCW) component [(i) or (ii)]. Fall and winter storm-forced waves will not persist into spring and summer, excluding bottom reflection of wind-forced near-inertial waves (ii) as a plausible explanation for the upgoing (CCW) predominance in late spring and early summer (Figs. 57). Most likely appears to be recent semidiurnal internal tide generation (iii), which is supported by the tendency for CCW-with-depth dominance over CW to line up with internal tide generation by the East Greenland continental slope, Reykjanes Ridge, and western slope of Rockall Plateau (Figs. 8f and 9). Although internal reflection from discontinuous stratification or shear in the water column (i) cannot be absolutely ruled out, the rotary-with-depth analysis (Figs. 68) was conducted in the permanent pycnocline below the base of the remnant winter mixed layer which Thomas et al. (2023, manuscript submitted to Oceanography) identified as a reflection surface for downgoing wind-forced waves.

Some caveats apply. CW-with-depth dominance persists for 8 months after the strong forcing of late summer–early fall, seemingly at odds with dissipation time scales. It is possible that the near-inertial shear in the permanent pycnocline is a superposition of rapidly propagating waves under the influence of eddy effective βe, and slower waves outside eddies that experience only planetary β refraction, but these slower waves would also have to experience weaker dissipation to reach pycnocline depths. There may also be vorticity-trapping of downgoing near-inertial waves in upper-ocean anticyclones (Fig. 2; Kunze et al. 1995; Zhai et al. 2005; Elipot et al. 2010; Voet et al. 2023, manuscript submitted to Oceanography) which we have not been able to reliably identify because of the incoherent temporal sampling. Near-inertial waves have nearly horizontal propagation |Cgh/Cgz||kz/kh|N/(ω2f2)1/210, so semidiurnal internal wave energy can radiate laterally more than 30 km from bottom sources as it propagates into the upper ocean if not corralled by vorticity.

Iceland and Irminger Basins are regions of elevated near-inertial band internal waves (Figs. 3, 4 and 6; Vic et al. 2021) and turbulence (Figs. 1013), particularly during late summer to early spring. Both wind and semidiurnal tides are sources for near-inertial wave energy at this latitude (Figs. 7c, 8c,f, and 9; Vic et al. 2021). Winter storms will drive seasonal variability while tide/topography interactions are spatially heterogeneous. Interactions with the effective βe = |[∂(ζ/2)/∂x, ∂(ζ/2)/∂y]| of the mesoscale eddy field as described by (1)(3) will facilitate transformation of surface-layer inertial oscillations into pycnocline near-inertial waves (Kunze 1985; D’Asaro 1995; Young and Ben Jelloul 1997; Asselin et al. 2020; Thomas et al. 2020; Raja et al. 2022; Essink et al. 2022) that can propagate rapidly from the surface to the bottom and back (and vice versa for semidiurnal internal tides) on time scales of weeks (Figs. 3, 4, and 17). As a general result, this implies that time scales for energizing the pycnocline with storm-forced near-inertial fluctuations may be orders-of-magnitude shorter in eddy-rich parts of the ocean, such as western boundary currents and the Antarctic Circumpolar Current, than from planetary β dispersion in more quiescent parts of the ocean (Anderson and Gill 1979; D’Asaro 1989; Garrett 2001) although, even in the relatively quiescent northeastern North Pacific, effective beta appears to be active (D’Asaro 1995). The dissipation time scale associated with elevated turbulent dissipation rates ε (Fig. 10) is 1–2 weeks (Fig. 17) as are replenishment times (Vic et al. 2021). This compares to 24 weeks at midlatitudes (Garrett and Munk 1979), implying that multiple bottom and surface reflections, and basin-scale propagation, are unlikely, localizing variability in time and space for the modes exceeding 8 measured here. Thus, CW-with-depth (downward-propagating energy) variance can be attributed to surface forcing and CCW-with-depth (upgoing energy) to bottom forcing. Therefore, the dominant CW-with-depth shear variance of late summer to early spring in the 500–800-m permanent pycnocline (Figs. 57) can be attributed to the atmospheric low pressure systems which are more prevalent in late summer through early spring (Vic et al. 2021). During late spring and early summer, Vic et al. (2021) reported that internal tide generation at Reykjanes Ridges was 2–3 times inertial wind-work, so the dominance of CCW-with-depth shear variance (Figs. 57) is likely due to semidiurnal barotropic-to-baroclinic tide conversion along the East Greenland continental slope, Reykjanes Ridge, and western flank of Rockall Plateau (Figs. 69; Buijsman et al. 2020).

Seasonal near-inertial/semidiurnal cycles were clear in both shear and rotary-with-depth variability (Figs. 57) while the only repeatable feature in turbulence variability was a minimum in diapycnal diffusivity K in early August (Fig. 12), pointing to the need for more, longer, and deeper microstructure time series to establish the seasonal and interannual variability of turbulent dissipation and mixing in these basins.

Acknowledgments.

We thank engineers Avery Snyder and Ryan Newell, as well as chief scientist Luc Rainville, and the captain and crew of the R/V Neil Armstrong for their valiant service during the challenging pandemic period. Anne Takahashi is thanked for valuable discussions about microstructure interpretation. This research was funded by ONR Grants N00014-18-1-2598 and N00014-18-1-2801 under the NISKINE DRI. In memory of James Ledwell for answering and raising important questions about ocean mixing, and as an exemplary colleague, mentor, and leader.

Data availability statement.

EM-APEX profiling float data used in this paper are available at the University of Washington ResearchWorks Archive (http://hdl.handle.net/1773/49493). Wind data for the wind-work calculation can be found at the NCAR/UCAR Research Data Archive (https://rda.ucar.edu/datasets/ds628.0/).

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