1. Introduction
The surface and upper layers of the subpolar North Atlantic (SPNA) are characterized by ubiquitous mesoscale and submesoscale variabilities (e.g., Mahadevan et al. 2012; Zhao et al. 2018a). These variabilities have significant implications for deep convection (Tagklis et al. 2020; Le Bras et al. 2022), water mass transformation (Zhao et al. 2018b), and biogeochemistry of the upper ocean (Mahadevan et al. 2012; Omand et al. 2015). Previous studies concerning these variabilities primarily concentrated on documenting the horizontal and vertical structure (Martin et al. 1998; Hátún et al. 2007; Zhao et al. 2018a), frequency of occurrence (Fan et al. 2013), and impacts (Rieck et al. 2019). Such information helped us to understand their spatial and temporal scales but provided limited insights on the underlying dynamic processes. On the other hand, wavenumber spectrum is a useful metric and widely adopted to infer the dominant dynamics for ocean changes (e.g., Stammer 1997; Le Traon et al. 2008; Sasaki and Klein 2012). The characteristics of wavenumber spectra in the subpolar North Atlantic were only diagnosed using model results (Ajayi et al. 2020; Xu et al. 2022). However, the corresponding observational evidence is still lacking, making it difficult to assess the reliability of model simulations in this region.
Unprecedented observational evidence is expected to be provided by the new generation satellite altimeter mission, Surface Water and Ocean Topography (SWOT). With designed horizontal resolution of 10–15 km, the sea surface height (SSH) data collected by SWOT can significantly improve our understanding of oceanic variations, particularly within mesoscale and submesoscale ranges (Fu and Ubelmann 2014; Morrow et al. 2019). It is well known that SSH variability is induced by both geostrophically balanced and unbalanced motions (Zaron and Rocha 2018). The unbalanced motions such as inertia-gravity waves cannot be simply separated from the balanced motions. This is because their frequency (from hours to days) and spatial scale ranges are similar to the submesoscale balanced motions (McWilliams 2016; Savage et al. 2017). In addition, energy in the unbalanced motions is comparable and sometimes overtakes balanced motions at the submesoscale range (Torres et al. 2018). Thus, to interpret SWOT data, a comprehensive understanding of the energy partition between balanced and unbalanced changes is essential.
In addition to SWOT data, shipboard acoustic Doppler current profiler (SADCP) has been a valuable source for fine-scale observations. The SADCP velocity was utilized to derive kinetic energy (KE) and its wavenumber spectrum in the upper ocean (e.g., Callies et al. 2015; Rocha et al. 2016a; Soares et al. 2022). These measurements were combined with high-resolution modeling results to investigate balanced and unbalanced motions (Rocha et al. 2016b; Qiu et al. 2017; Chereskin et al. 2019). The spectral intensities for both motion types are compared to diagnose the leading processes over different scales. In high eddy kinetic energy (EKE) regions, such as the western boundary currents and the Antarctic Circumpolar Current, geostrophically balanced motions prevail over broader spatial scales of the wavenumber spectra (Qiu et al. 2017; Rocha et al. 2016a). In contrast, in the equatorial region and on the eastern side of ocean basins with lower EKE, the balanced motions appear to be weak, with unbalanced motions dominating the KE spectra at scales smaller than 100–200 km (Soares et al. 2022). The scale at which the two types of motions are equal is usually defined as the transition scale (Qiu et al. 2017). The transition scale is widely adopted to reflect the regime change between the geostrophic and ageostrophic dominance (e.g., Qiu et al. 2017; Torres et al. 2018; Soares et al. 2022).
These studies also shed light on the governing processes for balanced and unbalanced motions. Enhanced submesoscale balanced motions often correlate with active changes in the mixed layer, whereas submesoscale unbalanced motions are mainly influenced by stratification strength and local winds (Rocha et al. 2016b). This can account for the seasonal evolution of wavenumber spectra intensity across different spatial scales (Sasaki et al. 2017; Qiu et al. 2018).
The overall goal of this study is to present the wavenumber spectra in the subpolar North Atlantic based on sustained long-term SADCP measurements. Our results show that geostrophic balanced flow dominates the oceanic variability at scales from 50 to 150 km. The KE spectral characteristics of these processes exhibit seasonal variations and regional dependence. The transition scale provides a critical marker to infer the dominant motions at each scale. The paper proceeds with descriptions of the methods and datasets in section 2, followed by the main results in section 3. The summary and discussion are presented in section 4.
2. Data and method
a. Data
1) Ocean velocity data
Upper-ocean velocity is observed by an acoustic Doppler current profiler (ADCP) mounted on the vessel Nuka Arctica. The ADCP datasets consist of two parts. The first is a 150-kHz ADCP operation profiled currents to 400-m depth between 1999 and 2002. The ship commutes on a 3-week schedule between Greenland and Scotland, sometimes making stops in Iceland. Its data processing and quality control are described in Knutsen et al. (2005), Chafik et al. (2014), and Childers et al. (2015). The second dataset is acquired by a 75-kHz ADCP from late 2012 to 2019. Its velocity profiles extend from near surface to about 800 m. Rossby et al. (2017) combined these ADCP datasets with independent hydrographic profiles and obtained poleward volume, heat, and freshwater flux in the eastern subpolar North Atlantic.
The ADCPs measure water velocity relative to the ship. To obtain geographically referenced water velocities, ship motion must be subtracted. The ship’s movement (vessel speed and heading) is determined from GPS navigation and a GPS-based compass. The accuracy of water velocity depends directly upon accurate ship speed for the along-track direction and ship heading for the across-track component. Further details on the instrument installation and data acquisition can be found in Chafik et al. (2014). Despite frequent inclement weather in the subpolar North Atlantic, the ADCP data are found to be of high quality (Chafik et al. 2014; Rossby et al. 2017). Two factors are crucial: the deep (8 m) draft of the vessel, and the deep and small bow thruster opening that minimizes the down-scooping of air when the bow breaches the surface in severe weather. Chafik et al. (2014) provides detailed descriptions of the ADCP uncertainties estimations. Following their method, the effective uncertainties for the shipboard ADCP data are estimated to be 5–9 cm s−1. This is much larger than the uncertainties in Wang et al. (2010), Soares et al. (2022), and Rocha et al. (2016a). The magnitude of uncertainties in winter is close to the eddy signals of interest. We urge caution in interpreting these results.
The typical speed for Nuka Arctica is about 16 kt (8 m s−1), allowing it to cover 5 km in about 11 min, or ∼3.5 h to sample 100 km. A 5-min bin average of the ADCP records yields a spatial resolution of ∼2.5 km. To mitigate potential noise at smaller scales, we apply moving windows both vertically (40 m) and horizontally (3 km) to average the ADCP data. For each transect, we use a Hanning window and compute the discrete Fourier transform. Our results agree with Rocha et al. (2016a) in that the resulting spectra are not sensitive to the choice of window. We renormalize all postprocessing data to correct the spectra value.
Potential rapid processes in ADCP measurements may include internal gravity waves. To estimate wave velocities, we utilize data from the World Ocean Atlas (WOA) climatology (https://www.ncei.noaa.gov/access/world-ocean-atlas-2023/bin/woa23.pl?parameter=t). Within the track coverage area in the upper ocean, the climatological average buoyancy frequency is approximately 7.5 × 10−6, translating to a period of roughly 5 h for free internal gravity waves. For such waves with wavelengths under 50 km, their propagation speed is slower than the ship’s speed. Further analysis on mode-1 internal tides, obtained through eigenfunction, yield phase speed of around 1.6 m s−1 in this region—again, slower than the ship’s velocity. Thus, our work aligns with the fast-tow assumption (Soares et al. 2022; Rocha et al. 2016a).
To minimize impact of weather, the ships do not commute along an exactly repeating route. Chafik et al. (2014) and Rossby et al. (2017) only utilized the transits within a narrow band bracketing 59.5°N, so that the measurements can be projected onto the same latitude to study the seasonal and temporal changes. Our focus is on spectral properties, and our analysis assumes isotropy, so we include all available ADCP transects. Considering the internal tide might have enhanced energy in shallow waters, we retain only the ADCP observations in deep ocean (>1200-m water depth). We screen the original data to select the mostly uninterrupted, gap-free, or small gap (no more than 5 km) transects. Linear interpolation is used to fill small gaps. Each transect in the Irminger Sea and Iceland Basin is at least 500 km long. The final quality-controlled dataset includes 176 transects in the Iceland Basin and 127 transects in the Irminger Sea. All are utilized to obtain averaged spectra. It is worth noting that the number of transects varies significantly between months, but each season does have more than 20 samplings and there is no major gap within each season (Fig. 1).
(a) Routes for vessel Nuka Arctica in the subpolar North Atlantic. They correspond to the ADCP transects used in this study. The total number of ADCP transects is aggregated into 12 months for (b) the Iceland Basin and (c) the Irminger Sea. The black line in (a) denotes the 1200-m isobath.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
2) Sea surface height
Surface geostrophic velocity fields between 1998 and 2019 are downloaded from the Copernicus Marine and Environment Monitoring Service (CMEMS; https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_L4_MY_008_047/description). The eddy kinetic energy is defined as EKE = (1/2)(u′2 + υ′2), where u′ and υ′ are derived by removing the long-term mean from the total surface geostrophic velocity.
b. Method
1) Inferring one-dimensional horizontal wavenumber spectra
The theoretical framework for kinetic energy spectra is based on two-dimensional isotropic spectra. However, observations used to derive KE spectra are mostly one-dimensional along-track data. According to the conversion relationship between two-dimensional isotropic spectrum and one-dimensional spectrum, if the two-dimensional isotropic spectrum follows a power law of
The slope (n) of the horizontal wavenumber spectrum also reflects important ocean dynamics. Geostrophic balanced motions predominantly exhibit interior quasigeostrophic (QG) and surface quasigeostrophic (SQG) turbulence dynamical characteristics. Within the interior QG theoretical framework, kinetic energy primarily originates from baroclinic instabilities, triggered by changes in the vertical potential vorticity gradient within the ocean interior. For the inertial range smaller than the forcing scale, there is an enstrophy forward cascade, characterized by a −3 slope in the kinetic wavenumber spectra (Charney 1971). In contrast, kinetic energy undergoes an inverse cascade toward larger scales until it is influenced by the β effect. The SQG theory assumes that there are no PV anomalies within the interior, and the surface-intensified flows are driven by buoyancy gradients (Lapeyre and Klein 2006; Wang et al. 2013). According to the SQG theory, the kinetic energy spectra of geostrophic balanced motions exhibit a −5/3 slope. (Blumen 1978; Callies and Ferrari 2013). This flatter spectrum corresponds to reverse energy cascade feature of the submesoscale turbulence, with energy injection at smaller scales (Kraichnan 1967). Both theoretical frameworks coexist in ocean motions, with their relative strengths causing distinct features in the kinetic energy.
The one-dimensional velocity data provides both across-track and along-track KE components. The ratio of across-track to along-track KE components, along with the slope (n) are critical indicators to determine whether the flow is divergent or rotational. If the flow is horizontally nondivergent, the ratio should equal to the power law exponent (n) in its wavenumber spectrum. That is, the across-track component will be n times more energetic than its along-track counterpart. On the other hand, for a purely divergent flow, the along-track component should be n times stronger than the across-track component (Bühler et al. 2014). Motivated by these theoretical conclusions, the slope of the one-dimensional spectrum and the ratios of across- to along-track KE components are taken as two key diagnostics in analyzing the shipboard ADCP observations (e.g., Rocha et al. 2016a; Qiu et al. 2017; Chereskin et al. 2019; Soares et al. 2022).
In this study, we also calculate the one-dimensional KE spectrum and study its characteristics. We use the Bühler et al. (2014) method to perform a Helmholtz decomposition method to partition the KE spectrum into its rotational and divergent components. Such a decomposition method requires that the flows are stationary, homogeneous, and isotropic. In addition, we further use Bühler et al. (2014) method decomposition to separate total KE into vortex and wave components. This latter method operates on the presumption that any divergence is the result of linear internal gravity waves. To be consistent with previous studies on shipboard ADCP analysis, we perform the calculations according to the steps described in Rocha et al. (2016a). Upon assessment, we identify no significant depth dependence for either the shape or amplitude of the spectra. The results presented here represent the depth-averaged spectra between the surface and 300 m.
2) Isotropy verification
To verify the reliability of the one-dimensional Helmholtz decomposition in our analysis, we test the isotropy assumption using three metrics recommended by Bühler et al. (2017) and Soares et al. (2022). The metrics include the expected values of the difference between along-track and across-track components E(u2 − υ2), their correlation E(uυ), and their cross spectrum. Here u and υ denote the along-track and across-track velocity, respectively. As shown in Fig. 2, E(uυ) is close to zero in both the Iceland Basin and the Irminger Sea, suggesting that the along-track velocity has very weak correlation with the across-track one. E(u2 − υ2) satisfies the criteria that its values are less than 10% of its variance, and E(u2 − υ2) ≫ E(uυ). The ratio of E(uυ) to E(u2 − υ2) is O(1 × 10−4), which is much smaller than the results obtained in the eastern tropical Pacific and north tropical Pacific (Bühler et al. 2017; Soares et al. 2022). Note, unlike the results obtained near the Gulf Stream and in the eastern tropical Pacific (Soares et al. 2022), the metrics E(u2 − υ2) in the Iceland Basin and the Irminger Sea exhibit positive values. This is attributed to a more energetic along-track component at large scales. In high latitudes such as our study regions, the deformation scale is relatively small, making the large-scale motions more susceptible to the influence of the β effect. The prevalence of along-track velocity at large scales was also reported in the ACC region (Rocha et al. 2016a).
The metrics E(u2 − υ2), E(uυ), and E(u2 − υ2) for different seasons in (a)–(d) the Iceland Basin and (e)–(h) the Irminger Sea. The u and υ here denote the along-track and across-track velocity, respectively. Red bars are twice the standard error of the mean, and the black bars show the 5%–95% range. The cross-spectra [real (red) and imaginary (blue) components] and spectral coherence squared (γ2; right y axis) for collocated segments for different seasons in (i)–(l) the Iceland Basin and (m)–(p) the Irminger Sea. Shading gives the 95% confidence interval.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
Moreover, cross-spectrum results are not statistically significant across the entire study range from 500 to 10 km. The real part of the cross-spectrum is close to zero at scales below 100 km, and frequently switches between positive and negative values, indicating that there is no significant correlation between the along-track and across-track flow (Figs. 2i–p). Overall, our results support that the isotropy assumption is satisfied in the Iceland Basin and the Irminger Sea.
3. Results
a. Kinetic energy spectra and its Helmholtz decomposition
The spectra from all available ADCP segments are averaged to obtain the representative KE spectra in the Iceland Basin and the Irminger Sea (Fig. 3). From here on, the statistical confidences of across-track and along-track KE spectra are estimated by assuming that the Fourier coefficients are normally distributed and that their magnitudes squared follow a χ2 distribution (Bendat and Piersol 2010). The confidence intervals for the rotational and divergent KE spectra are estimated by propagating the upper and lower bounds of the confidence intervals for the across-track and along-track KE spectra. For further decomposition into vortex and wave components, we employed two statistical methods to estimate the confidence: the χ2 distribution (as presented in this paper) and standard error. Both methods yielded similar magnitude of confidence interval results. At the same time, we would like to emphasize that propagating the upper and lower bounds of the confidence intervals of the rotational and divergent KE spectra to the wave–vortex decomposition results could lead to significantly negative KE spectra signals due to the cumulative unphysical error in statistical results.
Mean spectra of kinetic energy (KE; black lines), the across-track and along-track components, and the Helmholtz decomposition of the KE spectra into rotational and divergent components, for ADCP data collected in (a),(b) the Iceland Basin and (c),(d) the Irminger Sea. Shaded areas denote the 95% confidence intervals.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
The KE spectrum in the Iceland Basin is dominated by the across-track component at scales of 20–300 km, but the along-track component is larger for scales < 20 km and >300 km (Fig. 3a). The slope for KE spectrum is −1.9 ± 0.1 on the scale range of 20–150 km, which is close to the power ratio between the across- and along-track spectra (1.8). Such general consistency indicates that the rotation component dominates at scales > 20 km. In contrast, the flatter slope and the more energetic along-track component suggest an enhancement of divergent motions at scales < 20 km.
In the Irminger Sea, the KE spectrum is slightly weaker than the Iceland Basin. The dominance of across-track component takes place between 40 and 300 km and the across- and along-track components are almost indistinguishable below 40 km. The KE spectrum in the Irminger Sea has a mean slope of −1.7 ± 0.1 for the 30–150-km wavelengths. As a comparison, the power ratio between the across- and along-track components is 1.6 over the same wavelength.
It should be noted that the KE spectral slopes become flatter at scales 200 km in Iceland and 100 km in the Irminger Sea, deviating from the predictions of geostrophic turbulence (−3 or −5/3). The different deviating scales are associated with difference in the maximum radii of mesoscale eddies of the two basins (Zhao et al. 2018a; Fan et al. 2013). In the Iceland Basin, the observed mesoscale eddy radius can reach up to 70 km, while in the Irminger Sea, the maximum mesoscale eddy radius is 20 km. Further, in the two basins, the along-track components surpass the across-track components at wavelengths > 300 km. Similar behavior was also found in the Southern Ocean as reported by Rocha et al. (2016a). Indeed, the ocean motions at large scales no longer satisfy isotropic assumptions due to the influence of the β effect.
The Helmholtz-decomposed spectra indicate that the rotational component distinctly exceeds the divergent component for scales > 30 km in the Iceland Basin, and >40 km in the Irminger Sea (Fig. 3). The rotational component in component regions account for more than 90% of the total KE. In the Iceland Basin, the spectrum of the rotational component appears to roll off as k−3 between 40 and 100 km. Its mean slope is −2.7 in the 40–150-km range. On the other hand, In the Irminger Sea, the rotational component is between k−3 and k−2 at scales of 30–100 km This slope is slightly less steep compared to that for the Iceland Basin.
Note that caution should be taken for the spectra at scales < 40 km whose slopes are too flat and do not seem to be supported by plausible physical mechanisms. As we will show later that the spectra have substantial uncertainties during some seasons, likely attributed to underway biases from adverse weather conditions. This raises concerns about the reliability of data collected during winter, some parts of fall, and early spring, which may exhibit significant along-track velocity variance. Unfortunately, postprocessing cannot eliminate these biases without introducing gaps in the transects. More details will follow in subsequent sections.
Based on the analysis presented above, we focus on the 50–150-km range. Within this range, observational biases are minimized, and the spectral slope adheres to the QG and SQG theory. We conducted integrations of both the total kinetic energy and the rotational component within this scale range to analyze their seasonality. Indeed, the choice of integration range does not affect the seasonal variation characteristics. The seasonal cycles for KE at 50–150 km are similar in both regions and both are featured with higher values in spring and weaker in fall. As shown in Fig. 4, the seasonal variances of total KE predominantly stem from its rotational components.
The kinetic energy (KE) in ADCP data is aggregated over different scale ranges for both (a) the Iceland Basin and (b) the Irminger Sea. This is obtained by integrating the spectral values in 50–150 km for both the total KE and its rotational component. The January data are not included due to too few high-quality data points. The eddy kinetic energy (EKE; green lines) is calculated using geostrophic velocity, derived from the satellite altimetry data, that is selected according to the timing and location of shipboard ADCP data. Their uncertainties are denoted by vertical bars and shading. The climate mean EKE (dashed gray lines) is derived using all (1998–2019) geostrophic velocity data for the area shown in Fig. 5. Note: the ranges of the y axis in (a) and (b) differ to better illustrate seasonal changes.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
We compare these findings with EKE derived from satellite altimetry (Fig. 5) to pinpoint the sources of their seasonal variations. The satellite results include two calculations: only using data that matches with SADCP measurement in time and location (green line in Fig. 4) and using all data during the SADCP period (1998–2019, gray dashed line). The latter reflects the long-term mean of surface geostrophic EKE in both regions. In the Iceland Basin, the two EKE estimates align with the seasonality of the total kinetic energy calculated from spectrum integration. This suggests that the seasonal variations in total kinetic energy in the Iceland Basin are primarily driven by mesoscale eddies and can represent the typical seasonal characteristics of this region. This perspective aligns with Zhao et al. (2018a), who showed that the SSH data in this region adeptly encapsulates the dynamics of mesoscale eddies.
Seasonal mean geostrophic EKE in the subpolar North Atlantic. They are calculated from the satellite altimetry sea surface height measurement.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
On the contrary, SSH results in the Irminger Sea deviate considerably from the values obtained from the spectrum integration. Among these, the seasonal variance of satellite EKE corresponding to the SADCP time and location (green line in Fig. 4b) shows slightly better agreement with total KE and its rotational component. The primary difference appears during the period of March–May when both total kinetic energy and rotational energy reach their peaks. This discrepancy may be attributed to the small size of mesoscale eddies in this region. Their diameters of about 10–20 km cannot be fully captured by the satellite altimetry (Fan et al. 2013). Note that the long-term area averaged EKE does not exhibit pronounced seasonality. This implies that the SADCP data are collected during energetic motions or periods, and the seasonality from SADCP might overestimate the true seasonal changes in the Irminger Sea.
In accordance with the time variability of KE, its spectra in different seasons are aggregated and compared (Fig. 6). In the Iceland Basin, large uncertainties in winter make it difficult to distinguish energy levels between the across- and along-track components. Furthermore, the spectra exhibit a slope of about −1 at wavelengths < 40 km, which does not conform to the predictions of known physical processes. Therefore, we believe that the winter results are largely influenced by observational biases. In spring, the across-track component tends to be more energetic than the along-track component on scales of 350–40 km. The scales range dominated by across-track components shift to 150–10 km in summer and 100–20 km in fall. The change in the dominant scale range at larger scales appears to be influenced by the intensity of EKE, as shown in Fig. 4. The relative magnitudes of the across-track and along-track components reflect the relative importance of the divergent and rotational components. In spring, summer, and fall, the scales dominated by the rotational components are similar to those dominated by the across-track components.
Mean spectra of kinetic energy in the Iceland Basin using ADCP data collected in (a) winter (December–February), (b) spring (March–May), (c) summer (June–August), and (d) fall (September–November). Each panel illustrates the across-track (blue), along-track (red) components, and the Helmholtz decomposition of the KE spectra into rotational (yellow) and divergent (green) components. Shaded areas denote the 95% confidence intervals.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
The winter results in the Irminger Sea are similar to those in the Iceland Basin with large uncertainties and an overly flat slope. The dominance of across-track spans 150–20 km in spring and 120–10 km in summer (Fig. 7). In fall, the across-track dominance is observed within a narrower range (20–80 km), and it is indistinguishable from the along-track for scales below 20 km. The dominance of the across-track components is largely shaped by the rotational component. Additionally, the spectral slopes of the rotational components in both basins exhibit seasonal variations. However, as they include signals related to both balanced and unbalanced motions, we will further discuss them in the subsequent sections based on the results of wave–vortex decomposition.
As in Fig. 6, but for the Irminger Sea.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
b. Wave and vortex components
1) Wave–vortex decomposition
The wave–vortex decomposition requires separating the energy contributions from wave (unbalanced motions) and vortex (balanced motions) components. As detailed in Bühler et al. (2014) and Soares et al. (2022), estimations of wave energy depend on a critical ratio
Due to considerable observational errors in the winter results, we decide not to include the decomposition results for this season in Fig. 8. In the Iceland Basin (Figs. 8a–c), the vortex is the leading component at scales > 40 km in spring, 200–10 km in summer, and 150–30 km in fall. The spectra of vortex components closely follow the k−3 power law at scales of 80–10 km in spring and summer, but get flattened at scales of 200–80 km. The results in the range of 80–10-km scales are consistent with the predictions of isotropic, interior-QG theory, dominated by the entropy forward cascade. In fall, the spectrum of balanced flow becomes flattened, with a −2 slope, which obeys the SQG theory.
Mean spectra of kinetic energy in the Iceland Basin using ADCP data collected in winter (December–February), spring (March–May), summer (June–August), and fall (September–November). (a)–(d) The total KE (including both along- and across-track component) and its decomposition into wave (blue) and vortex (red) components. (e)–(h) The vortex (black) component and its projections into along-track (blue) and across-track (red) directions. Shaded areas denote the 95% confidence intervals.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
The decomposition results in the Irminger Sea show a similar picture (Figs. 8d–f): the geostrophic flow prevails at scales of 200–40 km in spring, 200–10 km in summer, and 100–30 km in fall. For the two basins, the spectral slopes of vortex components are similar in summer and fall. While the vortex spectra in spring have slopes of about −2 and are even flatter than those in the Iceland Basin.
The wave energy dominates the spectra in winter, spring, and fall at small scales (<40–50 km). In this regime the ratio
We also attempt to improve the wave–vortex decomposition following Soares et al. (2022) by adopting a constant parameter
The ratios of
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
Wave–vortex decomposition based on constant
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
2) Transition scale
Motivated by Qiu et al. (2018) and Soares et al. (2022), we define the transition scale as the wavelength at which the vortex and wave spectra intersect. It represents the shift of dominance between balanced and unbalanced motions. To avoid possible interference from large-scale flows, we only search the transition scale within the range of 10–150 km. Limited by the number of observations, spectral uncertainties in individual months can lead to complicated identification of transition scales (e.g., multiple wave–vortex intersections). A 3-month moving average is applied to smooth the monthly spectra. In instances of multiple crossovers, where we deem the wave and vortex as comparable over these scales, we select the middle points between the first and last crossover scales. In addition, visual examinations are also carried out to make sure the transition scale reasonably reflects the regime shift. Furthermore, winter results are not included due to large errors mentioned above. Due to these limitations and uncertainties, our focus is on the seasonal distinction rather than the specific values.
The seasonal evolution of transition scale exhibits a similar pattern in both regions (Fig. 11). The transition scale reaches its maximum in March and April with values of ∼30 km in the Iceland Basin and 40 km in the Irminger Sea. The minimum transition scale takes places in June–August at scales of ∼15 km. There is a slight increase to ∼20 km after September. Such seasonal variations are jointly determined by the strength of vortex and wave components. The vortex component, primarily governed by the rotational element, sees an increase in intensity during spring (Fig. 4).
The (a),(b) vortex and (c),(d) wave spectra calculated using ADCP data collected in (left) the Iceland Basin and (right) the Irminger Sea. Black lines denote the transition scale which is the largest wavelength for crossover between the vortex and wave spectra. Error bars correspond to 95% confidence intervals.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
4. Summary and discussion
This study examines the spectral properties of currents on scales ranging from 10 to 500 km, using ADCP measurements collected in the Iceland Basin and the Irminger Sea. To our knowledge, this is the only observational estimate of KE wavenumber spectra in the subpolar North Atlantic. Following the decomposition method proposed by Bühler et al. (2014) and other relevant studies about KE spectra using SADCP data (e.g., Callies and Ferrari 2013; Rocha et al. 2016a,b; Qiu et al. 2017, 2018; Chereskin et al. 2019; Soares et al. 2022), we obtain the rotational and divergent components and subsequently partition the KE spectra into wave and vortex components to infer the balanced and unbalanced motions.
The KE spectra in both basins are predominantly influenced by the rotational components. In the Iceland Basin, for instance, the integrated results of the total KE and the rotational components within the 50–150-km range closely resemble each other. They both display noticeable seasonal variations. These variations align well with the seasonal changes of EKE derived from satellite reanalysis data, suggesting that upper-ocean motions are largely driven by mesoscale eddies. In contrast, in the Irminger Sea, there is less agreement, particularly during March–May when the total KE reaches its peak within the 50–150-km scale range. This discrepancy might stem from the smaller scale of mesoscale eddies that are often present in the Irminger Sea but are too small to be adequately captured by traditional satellite altimetry. The KE spectra are segmented by season. The energy levels of both rotational and divergent components exhibit seasonal variations, but the seasonality is scale dependent. In spring and summer, the dominance of the rotational component extends to larger scales, approximately 200–10 km. However, in fall, its influence narrows to scales between 100 and 20 km. The winter results in both basins show unusually flat spectra with slope close to −1. Such a behavior does not match predictions from recognized physical processes, suggesting it might arise from observational errors.
To obtain more insights on the possible governing factors, we employed wave–vortex decompositions on the seasonal data. The summer spectra for geostrophic balanced motions roll off as the k−3 power law in both basins, suggesting that the summer fields are ruled by the interior QG turbulence. In contrast, the spectral slopes in fall season approach −2, consistent with the SQG theory. The spectra in spring differ in two basins: the spectral slope is close to −3 in the Iceland Basin but shifts toward −2 in the Irminger Sea. On the other hand, the unbalanced motions are enhanced in spring and fall over the 10–50-km scale range. They are strong enough to render the KE spectra to be flatter.
The transition scales mark the crossover between the wave and vortex components and indicate the distinct scales dominated by balanced versus unbalanced motions. In spring, this scale expands to approximately 30–40 km and decreases to a minimum of about 15 km in summer. Our results are consistent with the study in high latitudes of the Southern Ocean. For instance, Rocha et al. (2016a) documented that the transition scale over the Drake Passage is less than 40 km. In contrast, in low-latitude areas, a transition scale exceeding 200 km is observed near the North Equatorial Current region (Qiu et al. 2017). Additionally, transition scales between 65 and 240 km are noted in the eastern equatorial Pacific (Soares et al. 2022).
Analyses of SADCP spectra in both the Gulf Stream (Wang et al. 2010) and the Pacific Ocean (Qiu et al. 2017; Soares et al. 2022) indicate that the summer spectrum is consistent with interior QG turbulence. Our observations in the Iceland Basin and the Irminger Sea corroborate this conclusion. In fall, the flatter spectra of balanced motions suggest an enhancement in submesoscale energy. Given that the mixed layer in this region starts to deepen in September (de Jong et al. 2012), the submesoscale energy can be fueled by mixed layer instability. However, other processes such as wind/eddy-driven frontogenesis can also contribute to the conversion of potential energy to kinetic energy at the submesoscale range (Zhang et al. 2021; Thompson et al. 2016). On the other hand, the unbalanced motions are also strengthened in fall with energy equal to the energy level of balanced motions at scales < 40 km. The processes of balanced and unbalanced decomposition depend on identification of the source of divergence. Although we have examined the decomposition methods of NIW and GM and concluded that they do not affect the results, submesoscale instabilities can still generate vertical velocities, creating divergent signals. Therefore, the source of divergence in the fall will be a focus of our future work.
Interestingly, the spectra in two regions exhibit different properties in spring, with a k−3 power law in the Iceland Basin but closer to k−2 in the Irminger Sea. In spring, mixed layer is quite deep in the Irminger Sea due to deep convection events (de Jong and de Steur 2016; de Jong et al. 2018). This might foster active mixed layer instabilities to flatten the spectra. However, mesoscale eddies are quite active in the Iceland Basin, and the surface geostrophic eddy kinetic energy is strongest in spring and summer (Fig. 5). Those eddies were documented to have radii ranging between 40 and 70 km (Martin et al. 1998; Read and Pollard 2001; Shoosmith et al. 2005; Zhao et al. 2018a). As a comparison, eddies in the Irminger Sea, such as the Irminger Rings, display much smaller radii (less than 20 km; Fan et al. 2013). To further demonstrate the possible impact of mesoscale eddies, we examine the satellite altimetry data and select the ADCP transects when eddies can be visually found in sea surface height. The geostrophic spectra in the two scenarios are compared in Fig. 12. Evidently, the spectral slope is closer to −3 when eddies are present but becomes flatter when eddies do not exist or very weak. Thus, the active eddy activities in spring might be an important player to shape the spectra in the Iceland Basin.
Mean spectra of the vortex component in the Iceland Basin using SADCP data when eddies are found (red) and absent (blue) in the satellite altimetry data along the SADCP transects.
Citation: Journal of Physical Oceanography 54, 1; 10.1175/JPO-D-22-0247.1
The transition scale between the balanced and unbalanced motions is more relevant to the new generation altimeters, with the designed 15-km spectral resolution for the SWOT mission (Fu and Ubelmann 2014). Our findings indicate that near-surface currents in the Iceland Basin are primarily governed by geostrophic balanced motions. The current data derived from satellite altimeters is reliable for scales greater than 20 km, which can be extended to 15 km in summer. In the Irminger Sea, these scales are larger: 40 km in spring and 25 km in summer. Existing satellite data products seem to lack the capability to accurately resolve the strength of mesoscale eddies in the Irminger Sea. The improvement in the resolution of SWOT data has the potential to further address this issue.
In the end, we want to emphasize that our results are based on the Helmholtz decomposition that is widely used in prior studies (e.g., Bühler et al. 2014; Rocha et al. 2016a; Qiu et al. 2017; Chereskin et al. 2019; Soares et al. 2022). The method invokes assumptions of stationarity, homogeneity, and horizontal isotropy of the flow, but they do not always hold in the real ocean (Cao et al. 2019; Pearson et al. 2020). While we characterize the divergent flow using the Garrett–Munk spectrum, other processes such as the mixed layer instability, wind/eddy-driven frontogenesis, near-inertial waves, and internal tides might also energize the ageostrophic motions in fall and winter. Further investigation is ongoing to promote our understanding of the submesoscale dynamics in the subpolar North Atlantic.
Acknowledgments.
Constructive comments from reviewers made important contributions to improve this paper. Junwei Chai is supported by the National Natural Science Foundation of China (41925025 and 92058203). We are grateful to the captain and crew of the Nuka Arctica for their excellent technical and logistical support on data acquisition. We are profoundly grateful to Ms. S. Fontana for her careful editing, processing, and archival of all Nuka Arctica ADCP data. The ADCP data are kindly provided by Henrik Søiland.
Data availability statement.
Surface geostrophic velocity fields are downloaded from the Copernicus Marine and Environment Monitoring Service (CMEMS) (https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_L4_MY_008_047). The calculated KE spectra in this study can be obtained from the corresponding author upon reasonable request.
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