1. Introduction
Internal waves play an important role in the ocean’s energy balance by distributing significant amounts of heat and momentum through wave breaking (Ferrari and Wunsch 2009; Kunze 2017). As they propagate away from their generation sites, internal waves exchange energy with each other (wave–wave interactions), or with the mean flow (wave–mean interactions), or dissipate as turbulent mixing (MacKinnon and Winters 2005; Zhao and Alford 2009; Meyer et al. 2015, hereafter MR15; Waterman et al. 2021, hereafter WR21). Because internal waves are a major link in the forward energy cascade in the ocean, an understanding of the sources, subsequent propagation, and eventual dissipation of these waves is crucial in understanding the ocean’s role in global climate (Whalen et al. 2020).
The Southern Ocean (SO), with its strong frontal jets and energetic mesoscale eddy field, is a cradle of internal waves from various sources. It is a hotspot for energy flux into near-inertial motions from wind (Alford 2003; Whalen et al. 2018), lee waves from fronts and mesoscale eddies (Nikurashin and Ferrari 2010), and internal tides from barotropic tides over topographic features (Egbert and Ray 2000). Internal waves are also generated spontaneously at near-surface fronts in association with frontogenesis (Alford et al. 2013). Recent observations strongly suggest that the distribution of turbulent dissipation and mixing in the Southern Ocean interior is determined by internal wave breaking (Waterman et al. 2013; Sheen et al. 2013; Brearley et al. 2013; Cusack et al. 2017). Yet, our understanding of the energy pathways between internal wave generation and dissipation through wave breaking is far from complete.
The Antarctic Circumpolar Current (ACC) is the largest ocean current in the world, flowing from west to east unblocked by continents and connecting all the ocean basins. In regions of topographic obstacles to the flow, the deep-reaching ACC jets and eddies interact with the bottom topography to generate baroclinic Rossby waves (Hughes et al. 1998). Rossby waves with westward phase speed equal to the eastward flow of the ACC are arrested (Hughes 2005), resulting in the generation of standing meanders (Hughes et al. 1998). Many of the key physical processes central to the SO heat and momentum balance are concentrated in such standing meanders near topographic features (Rintoul 2018). The high eddy activity (Chelton et al. 2007; Martínez-Moreno et al. 2021) in these hotspot regions makes the ACC’s transport barrier “leaky” (Naveira Garabato et al. 2011) allowing poleward transport of heat (Foppert et al. 2017; Meijer et al. 2022) and biogeochemical tracers (Dufour et al. 2015; Patel et al. 2020). Both baroclinic and barotropic instabilities play a key role in the energy budget of the standing meanders (Youngs et al. 2017). Moreover, the standing meanders are regions of enhanced surface ventilation (Dove et al. 2021), vertical momentum transport (Thompson and Naveira Garabato 2014), interior upwelling of Circumpolar Deep Water (Tamsitt et al. 2017), and subduction (Bachman and Klocker 2020; Llort et al. 2018).
Our study is focused on the ACC standing meander between the southeast Indian Ridge and the Macquarie Ridge, which we call the Macquarie meander. The purpose of this paper is to quantitatively characterize the internal wave field in and around the Macquarie meander, including their interactions with the ACC flow and eddies. This work builds upon that of Cyriac et al. (2022, hereafter CR22) which analyzed the variability of diapycnal mixing in this region by applying a shear-strain parameterization to high-resolution profiles collected from Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats. The mixing analysis suggests that the interaction of frontal jets and mesoscale eddies with upward propagating internal waves is a major source of turbulent mixing in this region. We extend this earlier study by quantifying the characteristics of internal waves identified as coherent features in the same dataset. We follow the analysis used in MR15 which characterized the internal wave field in the upper ocean using EM-APEX float data collected from Kerguelen Plateau, also a region of ACC–topography interactions. We diagnose the various processes that affect the wave evolution by characterizing their dynamical time scales following WR21. Furthermore, we examine the energy exchange between the mean flow and the internal waves and discuss the possible sources of the internal waves.
2. Data
a. EM-APEX floats
The EM-APEX float is a combination of an absolute velocity profiler (Sanford et al. 1978) and Argo profiler (Roemmich et al. 2004). In addition to the standard Argo components for measuring temperature, salinity and pressure, the EM-APEX float includes an electromagnetic subsystem with compass, accelerometer, electrodes and external fins. The pitched fins make the instrument rotate as it moves vertically, and the two sets of electrodes independently measure the motionally induced electric fields from which the ocean’s horizontal velocity relative to a depth-averaged reference velocity is estimated at every 3–4 m. The temperature, salinity, and pressure measurements at every 2–3 m are obtained from a Sea-Bird Electronics SBE-41 CTD. Each time the float surfaces, the location of the float is identified from the GPS mounted on the instrument. Details of the float data quality control and data calibration can be found in Phillips and Bindoff (2014) and Cyriac et al. (2021).
We use data collected from three EM-APEX floats deployed in the Macquarie meander from R/V Investigator voyage IN2018_V05 from October to November 2018 (CR22). The float mission was designed to resolve the inertial cycle (15.2 h at 52°S) and provide six profiles per day. The floats were deployed downstream of the Southeast Indian Ridge on the absolute dynamic topography (ADT) contour of the mean Polar Front (PF, −0.65 m as defined in CR22), at the time of the deployment (Fig. 1). The floats profiled the upper 1600 m of the water column within the standing meander and its eddies for about 6 months, sampling the PF, Subantarctic Front (SAF), and several mesoscale eddies. We use data from the first part of the float record, which was a rapid sampling mode, after which the floats went into a park-profile mode. During rapid sampling, the floats returned data during up and down profiling, allowing absolute velocity to be determined following Phillips and Bindoff (2014). The identification of internal wave-like coherent features uses 810 profiles of temperature, salinity, and absolute velocity sampled during rapid sampling (period of continuous up and down profiles), which are presented in section 3.
The tracks of EM-8489 (cyan), EM-8492 (yellow), and EM-8493 (magenta) are plotted over the mean absolute dynamic topography (ADT) from satellite altimetry (shading) during the float rapid sampling period (October–December 2018). Red stars represent the location of each float deployment. Gray circles are shipboard stations, and black circles are the ship stations that are used in this study. Gray contours are bathymetry at 1000, 2000, 3000, 4000, 5000, and 6000 m. The thick white line is the ADT contour of −0.65 m representing the PF. The thick dashed ADT contours of 0.2 and −0.4 m represent the northern and southern branches of the SAF, respectively. The inset figure shows the location of the survey on the map.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
b. Supporting data
The voyage survey (IN2018_V05) consisted of 77 shipboard conductivity–temperature–depth/lowered acoustic Doppler current profiler (CTD/LADCP) stations along nine transects across the PF that spanned 3/4 of a wavelength of the standing meander. These transects were oriented so that they were perpendicular to the PF at the start of each transect, and are approximately perpendicular to the float tracks. Nineteen full-depth CTD/LADCP profiles from the first three transects are used in this study (Fig. 1). Details of their processing and calibration are available from https://mnf.csiro.au/en/MNF-Data.
Daily sea level anomaly (SLA) and absolute surface geostrophic velocities are obtained from Copernicus Marine Environment Monitoring Service (CMEMS) on a 0.25° × 0.25° spatial grid (https://marine.copernicus.eu/).
To represent the background flow in which the waves evolve, we use the satGEM dataset (Meijers et al. 2011), a gravest empirical mode (GEM) full-depth, circumpolar climatology of temperature and salinity on a longitude, dynamic height, and neutral density grid. The dynamic height coordinate follows the energetic movement of fronts and eddies so that averaging does not smear the cross-front gradients, as is the case for averaging on a latitude grid. The static GEM climatology is combined with SLA data to create time-evolving temperature, salinity, and geostrophic velocity fields on a longitude, latitude, and pressure grid. The GEM data are available from http://portal.sf.utas.edu.au/thredds/catalog/satgem/catalog.html.
The ocean bathymetry used in our analysis is the General Bathymetric Chart of the Oceans (GEBCO) topography data with a 30-arc-s grid (https://www.gebco.net/). The 6-hourly ERA5 reanalysis wind data are obtained from the Asia-Pacific Data-Research Centre on a 0.25° × 0.25° spatial grid (http://apdrc.soest.hawaii.edu/data/data.php?discipline_index=1).
3. Fronts and water masses in the meander
We identify the front positions and bin the float profiles into regions of fronts and mesoscale eddies (Fig. 2) as described in CR22. The PF position is indicated by the northernmost extent of the 2°C contour at a depth of 200 m (Orsi et al. 1995). This coincides with the −0.65 m ADT contour in our region (Figs. 1 and 2a,f,k). The southern branch of the SAF (sSAF) is identified as a temperature of 4°–6°C at a depth of 300–400 m (Sokolov and Rintoul 2002), which coincides with the −0.4 m ADT contour. The northern branch of the SAF (nSAF) is marked by a peak in surface geostrophic and subsurface velocity along the 0.2-m ADT contour. The location of the eddies encountered along the float trajectories are identified using animations of daily SLA maps from CMEMS (not shown). The binned profiles amount to 94% of the 810 profiles collected during rapid sampling: 22% were identified as being in the PF, 14% in anticyclonic eddies, 36% in cyclonic eddies, and 22% in the SAF.
The evolution of (a) dynamic height (DHT) at 100 dbar corresponding to 800 dbar (green) and sea level anomaly (SLA) (red), (b) Conservative Temperature, (c) Absolute Salinity, (d) current speed, and (e) buoyancy frequency squared along the track of float EM-8489 during the rapid sampling period. (f)–(j),(k)–(o) As in (a)–(e), but for floats EM-8492 and EM-8493, respectively. The light gray lines on all the panels are isopycnals with an interval of 0.2 kg m−3. The evolution of the mixed layer depth along each float track is also marked (blue line on Conservative Temperature for each float). The vertical colored lines represent different dynamic regions: thin black vertical dashed lines show when each float left the PF; pairs of magenta lines show the profiles in the SAF; cyan (red) lines indicate regions of cyclonic (anticyclonic) eddies along the float tracks. Each region is marked on the top panels of each float. The numbering of the eddies is independent for each float.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
The PF subsurface temperature minimum can be seen at the beginning of all float tracks (Figs. 2b,g,l). The isopycnals are flat in this part of the tracks and salinity increasing monotonically from fresh at the surface to saltier at depth (Figs. 2c,h,m). The PF was comparatively quiescent during the sampling period with a moderate mean surface current speed of 0.18 m s−1 (Figs. 2d,i,n). The sudden deepening of isopycnals immediately after the PF marks the beginning of the SAF in the float tracks. The floats later profiled through several cyclonic and anticyclonic eddies. Most of the float profiles were sampled between the northern and southern SAF and in eddies (Fig. 1).
4. Coherent feature analysis
a. Identification of internal waves
Internal waves are ubiquitous in the ocean and yet their intermittent nature makes them very difficult to observe. Here, we identify internal waves as coherent wave-like features observed in consecutive anomaly profiles of horizontal velocity (Fig. 3a). The anomaly profiles are obtained by removing a vertically smoothed profile from each of the individual horizontal velocity profiles corresponding to the feature (Figs. 3b,c). The smoothed profile is the result of a sliding second-order polynomial regression with an increasing vertical fit window length at different depth levels (MR15). The vertical fit window length ranges from ∼100 m at the surface to ∼560 m at the bottom of the profile, and the window length increases by 3 m every 9 m in between. By subtracting the smoothed profile, we remove the signature of the large-scale features such as the front to focus on the smaller scales that are the signatures of internal waves. Density anomaly profiles are derived in the same way.
An example of identification of coherent features from velocity anomalies. (a) Consecutive horizontal velocity anomaly profiles, both zonal (red) and meridional (black) components, corresponding to the coherent feature 92 (gray shading) from float EM-8493. The absolute (b) zonal and (c) meridional velocity profiles and the corresponding smoothed velocity profiles (light red and gray lines, respectively).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
From the velocity and density anomaly profiles, we estimate the energy density spectra of kinetic energy (KE), potential energy (PE), and the clockwise (ECW) and counterclockwise (ECCW) rotary spectra of horizontal velocity profiles corresponding to each coherent feature. If the KE, PE, and any of the polarized component spectra (depending on the direction of propagation) have a distinct peak at a certain vertical wavenumber, we look for a matching peak in the spectral coherence between the polarized component of horizontal velocity and buoyancy perturbations at the same wavenumber. If there is a corresponding peak in spectral coherence, the wave-like feature is classified as an internal wave (Müller et al. 1986; Polzin 2008; MR15; WR21). In this way, we identified 112 coherent features each spanning, on average, over four consecutive profiles. This method reliably identifies high-amplitude, low-frequency waves from velocity and density profiles (WR21). A more detailed description of identification of features from EM-APEX float data is given in MR15.
b. Internal wave properties
By interpreting the coherent features as internal waves, we can estimate their properties using linear wave theory. We follow the approach of MR15 and briefly summarize their method here. The profiles are Wentzel–Kramers–Brillouin (WKB) scaled before estimating the wave properties (e.g., Leaman and Sanford 1975). The vertical wavenumber at which both energy density and rotary spectra peak, is identified as the wavenumber of the internal wave, m, and the vertical wavelength of the internal wave as λz = 2π/m. The intrinsic frequency of the wave is estimated as
c. Time scales of wave evolution in the mean flow
Using the radiative balance equation (Polzin and Lvov 2011) describing the transfer of energy in spatial and spectral domains, we investigate processes that influence the evolution of a wave as it propagates through a background flow. We examine the relative importance of wave–mean interactions, wave–wave interactions, and dissipation by estimating the characteristic time scales associated with these processes from the wave properties, the characteristics of the background flow, and the stratification.
The term (u + Cgh) ⋅ ∇rA(r, p) represents the time rate of change of wave action due to translation of the waves in an advective background flow. We can estimate an upper bound of characteristic time scale by assuming a horizontal length scale of the local first baroclinic Rossby radius of deformation, LRo = 20 km at around 50°S (Chelton et al. 1998). We can thus estimate a propagation time scale,
The propagation of internal waves can be influenced by the mean flow through the Doppler shift, which is a change in frequency of a wave due to the relative motion between the wave source and observer. In a steady background flow, the intrinsic frequency (ω0) is a function of the Eulerian frequency (σ) of the wave and the Doppler shift which is proportional to the mean flow speed (
These four time scales give insights into the relative importance of propagation, advection, wave–mean interactions, and dissipation processes in the evolution of internal waves. The process with the smallest time scale is likely to dominate the wave’s dynamics: an internal wave with a dissipation time scale smaller than advection and wave–mean time scales is likely to dissipate locally; if the advection time scale is smaller than the dissipation time scale, the wave is most likely to dissipate elsewhere.
5. Results
a. Internal wave characteristics
Following the criteria presented in section 4a, we identified 112 internal waves from the float data among which 77 were propagating upward and 35 were propagating downward (Fig. 4). These waves are distributed along the float trajectories at different depths, some within mesoscale eddies and some within frontal jets. The direction of propagation of the waves identified in this study is in agreement with the polarization ratio (CCW/CW rotary shear variance) estimates in CR22 using the same dataset (not shown). The downward propagating features have a median depth of 1500 m whereas the upward propagating features have a shallower median depth of 650 m (Fig. 5a). This is in contrast to MR15 where they found that the upward propagating waves were deeper than the downward propagating waves.
Location of the identified internal waves propagating upward (cyan circles) and downward (red crosses) along the float tracks at different depths. The color shading and the gray contours are potential density. The black thick line is the mixed layer depth along the float tracks.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
Properties of the identified internal waves including the (a) distribution in pressure of internal wave frequency ω normalized by Coriolis frequency f, (b) relationship between horizontal group velocity Cgh and the period T, (c) aspect ratio of the waves shown as the relationship between horizontal λh and vertical λ wavelengths, and (d) relationship between horizontal Cgh and vertical Cgz group velocities with pressure indicated in color. The circles represent upward features and crosses represent downward features.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
The mean and 90% confidence intervals for the properties of the upward and downward propagating internal waves are summarized in Table 1. The confidence intervals are estimated as
Mean and 90% confidence intervals of internal wave properties identified from the EM-APEX data: vertical wavelength (λ), vertical wavenumber (m), horizontal wavelength (λh), intrinsic frequency over Coriolis frequency f (ω0/f), Doppler shift over f, horizontal group velocity (Cgh), vertical group velocity (Cgz), background mean flow, phase (ϕ), and horizontal azimuth (φ).
b. Spatial distribution
The internal waves are scattered along the float tracks at different depths and in different dynamic environments of the PF, SAF, cyclonic (CE), and anticyclonic (AE) eddies (Fig. 4). The highest number of waves are observed in the PF (33%) and the smallest number are observed in the AE (15%) (Table 2). The majority of downward propagating waves are in the SAF (34%) and the least are in the AE (14%). On average, the waves in the SAF have faster vertical propagation while the waves in the CE propagate slower in the horizontal and vertical directions. Internal waves are on average deepest in regions of the AE and shallowest in regions of the CE.
Mean and 90% confidence intervals of internal wave properties within different dynamic regions.
c. Temporal evolution
To investigate the relative role of various processes in the evolution of internal waves, we compare the corresponding time scales of these processes as described in section 4c. The time scale estimates presented in Fig. 6 and Table 3 are the ratio of time scales for dissipation to wave–mean interaction as a function of the ratio of time scales for dissipation to advection (Fig. 6a) and as a function of the ratio of time scales for dissipation to wave propagation (Fig. 6b). These results suggest that advection, propagation and wave–mean flow interactions are all important to the evolution of the internal waves. For the majority of the waves, advection and wave–mean interaction time scales have the same order of magnitude suggesting their combined role in the wave dynamics. The time scales for dissipation are longer than advection time scales for almost all waves (Fig. 6a), indicating that most of the waves are advected away before dissipation takes place. This is the case for both upward and downward propagating waves (Table 3). In Fig. 6b, most of the waves have dissipation time scales longer than propagation time scales. Of the waves that may dissipate locally, having dissipation time scale shorter than advection and propagation time scales, most are upward propagating waves (Figs. 6a,b). These results suggests that very few waves dissipate locally and most are advected by the mean flow or propagate away.
A comparison of the different time scale estimates of the waves showing the relative importance of (a) advection by mean flow and (b) propagation of the wave over dissipation. In both panels, colors represent different dynamic regions, and circles and crosses represent upward and downward features, respectively. The vertical and horizontal dashed lines separate the plot space into regions dominated by processes with the smallest time scale. These regions are labeled by the processes that dominate the wave evolution (i.e., processes that have the smallest time scale).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
Mean and 90% confidence intervals of different time scales associated with propagation (τprop), advection (τadvec), zonal (k), meridional (l), and vertical (m) components of wave–mean interaction (τWM) of upward and downward propagating waves.
d. Energy exchange with the mean flow
(a),(c),(d) The distribution of the energy exchange rate (P) between internal waves and the mean flow and (b) the Okubo–Weiss (OW) parameter as a function of wave frequency normalized by Coriolis frequency. A positive value of P represents energy transfer from the mean flow to the internal waves, and a positive OW parameter suggests horizontal strain dominated flow. The error bars in (a) represent the 90% confidence intervals of P in the 1000 Monte Carlo simulations of instrumental error. The inset panel zooms into the smaller values of P. The distribution of the OW parameter in different dynamic regions for upward (circles) and downward (crosses) propagating features as a function of normalized frequency is shown in (b). The distribution of absolute value of P in different dynamic regions for upward (circles) and downward (crosses) propagating features is shown in (c). The distribution of absolute value of P for each wave, colored by their respective pressure level, is shown in (d).
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
Following Naveira Garabato et al. (2022), we applied a Monte Carlo method to estimate the uncertainties in the energy transfer due to instrumental error in the float measurements of horizontal velocities. We created 1000 random Gaussian values with a mean of zero and a standard deviation of 1 cm s−1, which is the instrument error in velocity (Phillips and Bindoff 2014). We then added these random values to each velocity measurements and accumulated this on each estimate of energy transfer. The 90% confidence intervals calculated from the 1000 samples corresponding to each initial estimate of energy transfer is shown in Fig. 7a as error bars. The error estimation suggests that the uncertainties due to the instrument error does not affect the energy transfer estimates qualitatively and thus provides a robustness to our conclusions.
The energy transfer of individual waves is positive in some cases and negative in others, indicating both energy transfers to and from the mean flow (Fig. 7a). The mean P for the observed waves is (14.3 ± 10.0) × 10−12 m2 s−3, suggesting a net energy transfer from the mean flow to internal waves. The downward propagating waves have a mean energy transfer of −0.42 ± 2.1 × 10−12 m2 s−3 whereas the upward propagating waves have a mean energy transfer of 2.1 ± 1.2 × 10−12 m2 s−3. We do not see a strong relationship between the frequency of the waves and either the rate of energy transfer (Fig. 7a) or the direction of propagation (Fig. 7c). The strongest energy exchange is associated with waves in cyclonic eddies whereas the smallest energy transfer is associated with waves in the PF (Fig. 7c, Table 2).
The OW parameter is negative for just over half (54%) of the waves, suggesting that both relative vorticity and strain of the mean flow are important to the wave dynamics (Fig. 7b). Almost all of the waves (upward and downward) in the PF region (92%) are dominated by background relative vorticity (black circles and crosses in Fig. 7b). In cyclonic eddies and the SAF, 79% and 66% of the waves, respectively, have positive OW parameter, suggesting a dominance of horizontal strain of the background flow in these regions (Fig. 7b). Three out of the five downward propagating waves in anticyclonic eddy regions (red crosses in Fig. 7b) have positive OW suggesting that horizontal strain dominance is leading to wave capture in the anticyclonic eddies as in Polzin (2010).
The mean energy transfer rate from internal waves to the mean flow (P > 0), and from mean flow to internal waves (P < 0), is larger for deeper (>1000 dbar) internal waves than for shallower (<1000 dbar) waves (Fig. 7d). The mean magnitude of P for deeper waves is 7.0 ± 3.5 × 10−11 m2 s−3 whereas that for the shallower waves is 3.2 ± 0.53 × 10−12 m2 s−3. The increase in energy exchange with depth is in agreement with the slower group velocities of the waves observed at depth (Fig. 5d). This suggests that the wave–mean flow interactions for deeper waves are stronger than interactions for shallower waves.
e. Potential sources of internal waves
Possible sources for the generation of internal waves in the meander include wind (near-inertial waves), flow–topography interactions (lee waves), tide–topography interactions (internal tides), and instabilities of the meander. Here, we examine the possibility of wind-generated near-inertial waves and bottom generated lee waves using the clues that we can identify from the data.
1) Wind work and energy flux
Fluctuating wind stress can generate near-inertial oscillations in the mixed layer that can then generate internal waves at near-inertial frequencies at the base of the mixed layer. We compare the wind energy flux going into near-inertial motions with the downward energy flux of the observed downward propagating internal waves.
The vertical energy flux of the observed waves is estimated as Fz = HKE × Cgz where horizontal kinetic energy,
The mixed layer slab model we use (Pollard and Millard 1970) is forced with ERA5 reanalysis winds with a constant mixed layer depth of 70 m (mean value from the float data) and a damping constant of 0.15f, where f is the mean Coriolis frequency along the float tracks (Alford and Gregg 2001). The damping parameter represents the downward radiation of near-inertial oscillations out of the mixed layer. The wind energy flux into near-inertial motions is then estimated as Π = τU, where τ(τx + iτy) is the wind stress and U(u + iυ) is the mixed layer velocity estimated from the slab model (Alford 2003; Silverthorne and Toole 2009).
We calculate a vertical propagation time scale (τz = depth of the wave/Cgz) to account for the generation and subsequent propagation of the waves from the base of the mixed layer to the depth where the wave is observed. To investigate the possibility of wind generation, we first compare the vertical propagation time scale with the dissipation time scale τE of each downward propagating wave (Fig. 8). If the vertical propagation time scale is smaller than τE, the wave packet is likely to be wind generated. The slab model we use does not have a varying background flow and so does not take into account how the waves are affected by wave–mean and/or wave–wave interactions during their downward propagation. About half of the downward propagating waves have smaller or comparable magnitudes of dissipation time scale and vertical propagation time scale (shaded area in Fig. 8a). All but one of the waves in the SAF region have comparable dissipation and vertical propagation time scales. Thus, we conclude that internal waves in the SAF region are more likely to be wind generated. A small fraction of waves in the other dynamic region may also be wind generated.
(a) Comparison of dissipation time scale and vertical propagation time scale of downward propagating waves. The colors represent different dynamic regions. The black dashed 1:1 line is for visual comparison of the dissipation time scales and vertical propagation time scales. The shaded area corresponds to waves with comparable dissipation and propagation time scales. (b) The ratio of wave flux to wind energy flux from a slab layer model for the waves in the shaded area in (a). The size of the circles in (b) is proportional to the dissipation time scale of the waves in the shaded area. A ratio less than 1 indicates that the wind energy flux is larger than the vertical energy flux of the wave.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
We can estimate an approximate generation time for each of the waves that have comparable dissipation and vertical propagation time scales (shaded area in Fig. 8a). Combining the vertical propagation time scale and date of observation of the wave allows an estimate of the time of generation of the wave. We then estimate the wind work at this time as a temporal and spatial average to account for the strong and frequent atmospheric storms in this region. The wind work is a 3-day average (±1 day around the estimated generation time) over 1° × 1° boxes around float profiles corresponding to each of these waves. We compare the vertical energy flux of these waves with that of their corresponding wind work in Fig. 8b. The mean wind work corresponding to downward propagating waves is 2.2 × 10−3 W m−2. This result is one order larger than the mean vertical energy flux estimated for the downward propagating waves of 1.6 × 10−4 W m−2. This means that for all but one of these waves, the wind energy flux is sufficient to generate the waves, thus confirming that most of these waves could be wind generated (Fig. 8b).
2) Lee waves
The predominance of upward propagating waves in the data suggests that the flow–topography interactions are a major source of internal waves. Since the floats do not sample close to the ocean bottom, we use the CTD and LADCP data from this voyage to estimate the predicted lee wave vertical wavelength based on the stationary lee wave theory. Using bottom speed (Ubot) and stratification (Nbot), we get an estimate of the lee wave vertical wavelength as λlee = 2πUbot/Nbot (Waterman et al. 2013). The bottom speed and stratification are defined as the average in the lower 500 m following Waterman et al. (2013) and Nikurashin and Ferrari (2011). We estimate the predicted lee wave vertical wavelength in the three westernmost cruise transects which intercepted the float trajectories (Fig. 1). The predicted lee wave vertical wavelength varies from 200 to 1500 m (Fig. 9). The values of λlee are smaller in the PF compared to that in the SAF where the current speeds are higher. Observed vertical wavelengths of the upward propagating internal waves identified in the float data vary from 200 to 500 m (Fig. 5), in agreement with the predicted lee wave vertical wavelengths for the PF. In addition, the numerical simulations of Zhang and Nikurashin (2020) show the presence of internal lee waves extending all the way to near the ocean surface in the Macquarie meander. This suggests that the upward propagating waves observed in the PF could be lee waves generated from flow–topography interactions. The relatively quiescent PF during the float sampling period (mean surface current speed of 0.17 m s−1) with weaker Doppler shift (Table 2) would contribute to allow the lee waves to reach the upper ocean within our study region.
Predicted lee wave vertical wavelength (λlee) at different shipboard stations (circles) and the vertical wavelengths (λ) of upward propagating waves observed in the float data (triangles). The gray contours are bathymetry at intervals of 1, 2, 3, 3.5, and 4 km from the GEBCO topography data. The average position of the ADT contours representing the PF, nSAF, sSAF during the three transects are marked as in Fig. 1.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
f. Internal waves and mixing
The observed internal waves and their interactions with the mean flow are of particular importance to the standing meander dynamics as a source of turbulent mixing. However, the time scale analysis suggests that the waves are more likely to be advected by the background flow or propagate away, rather than dissipate locally (Table 3). The dissipation rate of turbulent kinetic energy (E) was estimated with a finescale parameterization method applied to the EM-APEX float data in CR22. In Fig. 10 we compare the predicted dissipation rate from CR22 with the ratio of dissipation to propagation time scale. Waves with propagation time scales shorter than dissipation time scales [log10(τE/τprop) > 0], which dissipate remotely, have a wider range of dissipation rates than locally dissipating waves (Fig. 10). Around 25% (47%) of the remotely dissipating waves have higher dissipation rate than the mean (median) of all the waves whereas only 15% (31%) of the locally dissipating waves have dissipation rates higher than the mean (median). These results together suggest that internal waves that propagate downstream are likely to result in higher diapycnal mixing than the waves that dissipate locally.
Scatterplot of the ratio of dissipation time scale (τE) to propagation time scale (τprop) and the corresponding predicted dissipation rate of turbulent kinetic energy (E) using finescale parameterization from CR22. The circles represent upward features and crosses represent downward features. The yellow and magenta stars represent the mean and median values of dissipation rates for all the waves, respectively. Negative values on x axis indicate that the waves dissipate locally whereas positive values suggest remote dissipation.
Citation: Journal of Physical Oceanography 53, 8; 10.1175/JPO-D-22-0157.1
6. Discussion and conclusions
In this study we characterize the internal wave field and wave generation mechanisms in an energetic standing meander near Macquarie Ridge in the Southern Ocean. We identified a total of 112 coherent wavelike features in 810 vertical profiles of temperature, salinity and horizontal velocity collected from rapidly profiling EM-APEX floats. The floats profiled a range of dynamic regions, including the Polar Front, Subantarctic Front, and cyclonic and anticyclonic eddies. Most of these internal waves (69%) were found to be propagating upward. On average, upward propagating waves were observed at shallower depths than downward propagating waves. The characterization of time scales of various processes such as advection, wave–mean interaction, propagation and dissipation provides insight into the dominant dynamics that affect the evolution of the observed internal waves. Our results suggest that the ACC plays an important role in the evolution of the internal waves in this region through advection and wave–mean interactions. The majority of the observed waves are likely to be advected and/or propagate away to dissipate remotely, thereby impacting water-mass transformations downstream. In addition, we found that internal waves with propagation time scales shorter than dissipation time scales, which dissipate remotely, were associated with higher predicted dissipation rates of turbulent kinetic energy than the locally dissipating waves. Thus, we suggest that these remotely dissipating waves with higher dissipation rates might play an important role in setting the stratification of the Southern Ocean. Finally, we found that there is roughly the same amount of energy being transferred from the mean flow to internal waves as there is from the waves to the mean flow in this region.
Our analysis indicates that variable winds and mean flow–topography interactions are plausible generation mechanisms for internal waves in the region of the Macquarie meander. Thus, the downward propagating waves in the SAF are feasibly generated by winds whereas the upward propagating waves in the PF are most likely generated from flow–topography interactions. The intrinsic frequency of the observed internal waves is within the range of near-inertial waves and semidiurnal M2 tides, the latter suggesting the possibility of internal tides generated along the Macquarie Ridge to the east of our study region (Zhao et al. 2018). The Macquarie Ridge has long been identified as a hotspot of M2 tidal energy dissipation (e.g., Egbert and Ray 2000). The recent Tasman Tidal Dissipation Experiment (TTIDE) has shown that the Macquarie Ridge radiates three internal tidal beams into the Tasman Sea (Zhao et al. 2018). This latter work suggests that the generation and propagation of the southern beam is modulated by the ACC. It is possible that some of the upward propagating waves observed in our study are part of the southern tidal beam. This is supported by a brief investigation in CR22 which suggests that the observed turbulent mixing variability in this region from the same dataset is dominated by tidal motions. Future work using numerical simulations and ray tracing will further explore the sources of the internal waves observed in this study.
The internal wave characteristics and their relationship with the background environment identified in this study can be compared with observations in the upper 1600 m along EM-APEX trajectories across the northern Kerguelen Plateau (MR15). There are significant differences between these two regions. In the Macquarie meander, we found that 68% of the waves observed in the upper 1600 m were upward propagating waves. While in MR15, a higher proportion of the waves observed in the upper 1600 m across the Kerguelen Plateau, about 57%, were propagating downward. In the Macquarie meander, waves deeper than ∼1000 m have slower horizontal propagation (Fig. 5c) than shallower waves, whereas at the Kerguelen Plateau (MR15), deeper waves (750–1200 m) had faster horizontal propagation than shallower waves.
There are also similarities in the impact of the mean flow at both the Macquarie meander and Kerguelen Plateau. The background mean flow has moderate speed in both regions (∼0.2 cm s−1) at the locations and depths where the waves are observed. The waves in the PF have smaller Doppler shift values where the mean flow is weaker (Table 2), whereas the waves in the SAF have stronger flow and higher Doppler shift in both regions. A large Doppler shift results in the filamentation of internal waves where horizontal strain dominates the background relative vorticity (Polzin 2010). We found negative values of OW parameter (vorticity dominates strain) for the PF region at the Macquarie meander (Table 2) and positive values of OW parameter for the SAF region. Thus, in the PF region, relative vorticity of the mean flow influences the wave evolution. On the other hand, horizontal strain of the background flow dominates the waves in the SAF region and large Doppler shift there suggests the waves may be subject to filamentation and smaller angular displacement. Thus, waves with large Doppler shifts, as found in the SAF, are likely to be parallel to the mean flow, whereas waves with smaller Doppler shift, as in the PF, are more likely to be perpendicular to the flow. This is confirmed in our results by the slightly larger mean angular displacement for the PF region and smaller displacement for the waves in the SAF in Table 2.
Our finding that a large fraction of the internal waves we observed in the ACC will dissipate remotely is also found in observations at Kerguelen Plateau (MR15; WR21) and numerical simulations at Drake Passage (Zheng and Nikurashin 2019). From EM-APEX floats in the upper 1600 m of the SAF, MR15 found that very few waves dissipate their energy locally and the majority of the waves propagate away from their generation site to dissipate downstream of the Kerguelen Plateau. The dissipation time scales in the PF and SAF regions are similar (∼20 days) in both Kerguelen Plateau (MR15, their Table 3) and Macquarie meander (Table 2). The propagation time scales for the PF region in the Macquarie meander are larger than those at the Kerguelen Plateau (MR15). Using full-depth cross-frontal CTD and LADCP profiles, the analysis of WR21 complemented the earlier EM-APEX analysis of MR15 for the Kerguelen Plateau region. Comparing the characteristic time scales of different processes that would affect wave evolution, WR21 found that about 67% of the waves are dominated by advection and/or wave–mean interactions. Furthermore, all the waves that are likely to dissipate locally (smallest dissipation time scales compared to that of advection and wave–mean interactions) are found outside of the ACC jets. Zheng and Nikurashin (2019) used realistic topography simulations to investigate the downstream evolution and dissipation of internal lee waves generated by geostrophic flow–topography interactions. They found that about 60%–70% of the energy is advected downstream and dissipated remotely. Our work combined with the aforementioned studies suggest that a local balance between internal wave generation and dissipation is unlikely to hold in standing meander hotspots of the ACC that are associated with topographic features. The waves generated in these regions will be advected downstream by the mean flow where they will continue to evolve through nonlinear wave–mean interactions and eventually dissipate. Thus, the sinks of energy (dissipation) are likely to be more dispersed along the path of the ACC than the sources (internal wave generation), which is likely concentrated in hotspot regions such as the Macquarie standing meander.
Acknowledgments.
We thank the scientists, student volunteers, and crew from the IN2018-V05 voyage on board R/V Investigator. We are grateful to S. Waterman and K. Polzin for valuable suggestions. The observations were funded through grants from the Australian Research Council Discovery Project (DP170102162), which funded AC’s postdoctoral Fellowship, and Australia’s Marine National Facility. AM was supported by the Australian Research Council Discovery Early Career Research Award project DE200100414. AC, HEP, and NLB acknowledge support from the Australian Government Department of the Environment and Energy National Environmental Science Program Climate Systems Hub, the Australian Government as part of the Antarctic Science Collaboration Initiative and the Australian Research Council Special Research Initiative, Australian Centre for Excellence in Antarctic Science (Project Number SR200100008). AC, AM, HEP, and NLB acknowledge support from the Australian Research Council Centre of Excellence in Climate Extremes (CE170100023).
Data availability statement.
The primary data used in this study are collected from three Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats. These data are being prepared to be lodged and publicly available at the Australian Antarctic Data Centre (https://data.aad.gov.au/). The primary data are also available on request from A/Prof. Helen Phillips (h.e.phillips@utas.edu.au). Further details about the data quality control and processing of EM-APEX floats are described in Cyriac et al. (2021). The other datasets are openly available at locations cited in section 2.
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