Volume 33, No. Although these wave parameters are realistic (e.g.,Garwood etal., 2020), examples are provided for illustrative purposes only. }e# Cite this article. Google Scholar. High KESDIT was rarely found below 153m during Event 1 and between 53 and 360m in August between Events 1 and 2. 1dh), implying that wave-wave interaction processes were in action despite there being no local energy source (only remote). of gravity waves. Leichter, J.J., B. Helmuth, and A.M. Fischer. Are any coastal internal tides predictable? These are treated separately below. In our heuristic weakly nonlinear internal wave example, passive plankton at 5 m were displaced a maximum of 2.3 m downward, which reduced their total irradiance exposure by 18.7% over a period of 16.7 minutes. However, one thing which is not discussed in the text is that these winds can often be periodic. between the mountain top and the tropopause.
PDF Chapter 7 Linear Internal Waves - University of California, San Diego 50, 11211135 (2020). Oceanogr. Air is forced to oscillate, and a wave propagates away, as the corrugation forces its To preserve the phase, the filter was applied forward and backward, and the defined bands were not overlapped. 80, 19751978 (1975). region shown by the horizontal bar at the base of the diagram, but the things The layers have a sharp interface with a jump in buoyancy frequency approximately modeling the tropopause. Scientific Reports (Sci Rep) 41, 12971307 (2011). Leichter, J.J., G. Shellenbarger, S.J. McPhee-Shaw, P. Chua, E. Kingsley, M. Denny, R. Phillips, S.J. Climate process team on internal wave-driven ocean mixing. temperature minima, and the red lines represent phase fronts of termperature maxima. Journal of Physical Oceanography 48(1):123143, https://doi.org/10.1175/JPO-D-17-0045.1. However, how far individual organisms will be transported will depend on wave nonlinearity: net transport will be limited in linear internal waves (Franks, 1997), whereas organisms in nonlinear internal waves may be displaced large distances (Figures 2 and 3c,f). Whereas the reduced gravity is the key variable describing buoyancy for interfacial internal waves, a . Res. The role of submesoscale currents in structuring marine ecosystems. Ann. 2015. 8, 95123 (2016). Observations on internal waves in shallow water. We defined this to be the time between an organism encountering two adjacent, identical wave phases (e.g.,crest to crest, or trough to trough). Ocean Model. Res. For example, for passive and depth-keeping plankton initially located at 5 m, total horizontal transport in our weakly nonlinear internal waves was, respectively, ~30 m and ~50 m in the direction of wave propagation. can generate sound by blowing steadily on the reed of a flute - you set up Weakly nonlinear internal gravity waves are treated in a two-layer fluid with a set of nonlinear Schrodinger equations. Zeidberg, and W.F. Note that although organisms may be moved vertically by internal waves, which will affect their total solar irradiance, the vertical profile of solar irradiance itself is not modified by the waves (Figure 5b). 2006.
JMSE | Free Full-Text | Triads and Rogue Events for Internal Waves in Kim, D. J., Nam, S. H., Kim, H. R., Moon, W. M. & Kim, K. Can near-inertial internal waves in the East Sea be observed by synthetic aperture radar? Part II: Energetics and results from PolyMode. 2016. 2c,d). The characteristic slope of internal waves was calculated as70: where wave frequency is set to M2 to compare the characteristic slope of SDITs with the bottom slope at the shelf break in the north of the Korea Strait. If a fluid's potential density decreases continuously with height then it can support internal waves that, like interfacial waves, move up and down due to buoyancy forces but which are not confined to an interface: they can move vertically through the fluid. Although diurnal ITs are mostly trapped in the southern Ulleung Basin near the generation area, northern slope of the Korea Strait (red hatched area in Fig. Article Zhao, Z., Alford, M. H., Girton, J. 1dg, Table2). Images, animations, videos, or other third-party material used in articles are included in the Creative Commons license unless indicated otherwise in a credit line to the material. 2 since it has a finer resolu-. The buoyancy frequency is assumed to be constant: N (z) = N = \operatorname {const} . Res. Effect of internal waves on near-surface chlorophyll concentration and primary production in the Nazar Canyon (west of the Iberian Peninsula). However, highly energetic nonlinear internal waves can also transport larvae away from productive areas and expose them to mechanical stress, resulting in energy loss and lower survival (Ruvalcaba-Aroche etal., 2019). Nash, J., E. Shroyer, S. Kelly, and M. Inall. grey area will be a region of high pressure. The areas of maximum and minimum plankton concentrations will be offset from the areas of maximum convergence and divergence and will occur above wave troughs and crests, respectively. Rainville, L. & Pinkel, R. Propagation of low-mode internal waves through the ocean. 1a), and diurnal ITs (D1) rarely propagate into the interior of the East Sea as f > D1, SDITs often propagate poleward freely as f < M2. In Monterey Bay, California, high-frequency internal waves cause intrusions of low oxygen, low pH waters in coastal ecosystems (Booth etal., 2012; Walter etal., 2014). This work is part of the projects Deep Water Circulation and Material Cycling in the East Sea (20160040) and Construction of Ocean Research Stations and their Applications in Studies funded by the Ministry of Oceans and Fisheries (MOF), Republic of Korea. Gonzlez-Gordillo, and F. Echevarra. Garrett, C. What is the Near-inertial band and why is it different from the rest of the internal wave spectrum? Lett. Shcherbina, A. Y., Talley, L. D., Firing, E. & Hacker, P. Near-surface frontal zone trapping and deep upward propagation of internal wave energy in the Japan/East sea. large amplitude because it is moving along with the air, and eventually gets so big that Because density has been found by others to be largely dependent on tem- Liu, and J.J. Tsai. (e) Hovmller diagram of the energy transfer efficiency in logged colour scale shown in the right at 131.43E (longitude of EC1) as functions of time and latitude where dashed lines indicate the effective Coriolis frequency normalised by f at the surface (contour interval: 0.02f). buoyancy frequency and w the wave frequency. Park, J. J., Kim, K. & Crawford, W. R. Inertial currents estimated from surface trajectories of ARGO floats. Similar to sessile organisms, depth-keeping plankton encounter a range of along-isopycnal properties throughout internal waves. decreases with height. 98, 24292454 (2017). Farmer, D.M., and J.D. Introduction The common view is that the seasonal vertical stratification in density inhibits vertical turbulent exchange of nutrients in shelf seas such as the North Sea, thereby hampering the growth of phytoplankton in summer. & McIntyre, M. E. Wave capture and wave-vortex duality. Oliver, R.L. Then, the relative importance of total strain and relative vorticity was diagnosed with the Okubo-Weiss parameter69, defined as \({\alpha }^{2}=({S}_{n}^{2}+{S}_{s}^{2}-{\zeta }^{2})/4\). Although hidden from sight, the interior of the ocean is just as turbulent as its surface. Fluid Mech. 32, 1120 (2013). In all cases, wave-induced horizontal transport will occur along the same axis as internal wave propagation (Lamb, 1997), and while this may be in the cross-shore direction for many coastal internal waves (e.g.,Lee, 1961; Shroyer etal., 2011; Richards etal., 2013; Colosi etal., 2018; Sinnett etal., 2018), some coastlines favor along-shore displacements (Livana MacTavish etal., 2016). 5 depict the impact of the mesoscale circulation on enhanced internal waves from near-inertial to buoyancy frequencies in several different ways. Ocean. from publication: Mean and Turbulent . Stokes drift of plankton in linear internal waves: Cross-shore transport of neutrally buoyant and depth-keeping organisms. 122, 56455651 (2017). are called gravity waves. O ]Y`h3Rq+ KC7sz~V<6K3b7c{Y358\yN(8
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Danioux, E. et al. While fluid properties such as temperature or nutrient concentrations can change slowly in time due to mixing, buoyant fluxes, and biological activity, they generally follow isopycnals. 4a,b). At the bottom of its motion, the parcel of air is warmer (and less 103, 75797591 (1998). Stud.
Late summer stratification, internal waves, and turbulence in the 67, 13351350 (2017). pressure. Garrett, C. & Kunze, E. Internal Tide Generation in the Deep Ocean. J. Phys.
PDF Buoyancy frequency profiles and internal semidiurnal tide - SJTU Various mathematical functions, including cnoidal functions, can be used to capture the wide range of weakly nonlinear wave shapes (see review by Apel, 2002). Ocean. Abstr. The enhanced total strain supports the possibility of efficiently transferring mesoscale or subinertial energy into NIWs as further evidenced below. MathSciNet Nonlinear internal waves of depression, for instance, induce wave velocities that are constantly in the direction of wave propagation above the pycnocline, driving net transport in the direction of the waves propagation, and vice versa at depth (Apel etal., 1985; e.g.,Figure 2b,c). If the environmental laspe rate is unstable, 1e, 2be and 4e). Use the Previous and Next buttons to navigate three slides at a time, or the slide dot buttons at the end to jump three slides at a time. Slicks, surface films and internal waves. Small amplitude similarity solutions are obtained for two-dimensional and axisymmetric waves. Lavn, J.J. Leichter, J.A.
Maximum buoyancy frequency anomaly in each layer (a) and - ResearchGate Macas, D., R. Somavilla, J.I. Throughout this manuscript, we consider three categories of marine organisms: (1) those, such as coral reefs, that are anchored to a substrate and are not moved by internal waves, (2) planktonic organisms, such as non-swimming phytoplankton, that are moved by internal wave velocities both horizontally and vertically, and (3) planktonic organisms, such as strong swimming larvae, that are moved horizontally by internal wave velocities but that perfectly oppose wave vertical velocities in order to maintain a fixed depth (Figure 1). Limnology and Oceanography 6(3):312321, https://doi.org/10.4319/lo.1961.6.3.0312. Xie, J. H. & Vanneste, J. Lucas, G. Pawlak, and E. Terrill. The rate at which these fronts appear to move is called Their interactions, interaction with background field, and resulting internal waves at higher frequencies beyond the near-inertial and tidal frequencies have rarely been reported despite its importance on ocean mixing and circulation of energy and materials. Res. the density variation as a function of height as a step, with high density Oceanogr. Article 1974. and exist because of the restoring force of gravity. McManus, M.T. Shanks, A.L. Swimming against the flow: A mechanism of zooplankton aggregation. Internal waves at higher frequencies (0.090.50 cph), defined here as continuum frequency waves (CFWs), have long been described by the classical Garrett-Munk (GM) spectrum37 and believed to arise from nonlinear wave-wave interactions transferring energy out of the NIWs and ITs into the broadband continuum3,38,39. Recent studies noted that the strain of mesoscale flow fields plays an important role in NIW and mesoscale energy exchange via the wave capture process, allowing nonlinear interaction between NIWs and the mesoscale field, e.g., drawing NIW energy from the mesoscale flow17,18,19,27. Pilot whales follow internal solitary waves in the South China Sea. Plankton patchiness in high-frequency internal waves. Res. Significantly high correlations were also found between KECFW and KENIW+SDIT except 77m for Event 4 (Fig. Internal Wave Simulations . Correspondence to as indicated by the short arrow at the top of the diagram. 1fh). Moum. Oceanogr. c) they can trigger convection (b) Dispersion relation (angular frequency vs wave number k) for surface and . Nash. The linear limit of the cnoidal function is associated with a cosine-squared wave (Equation4), while the most nonlinear limit is associated with a hyperbolic secant wave (Equation5), also known as a solitary wave or soliton: where c is the crest elevation. Lucas, A.J., J.D. Our study suggests the significant impact of mesoscale circulation on the variability of internal waves from near-inertial to buoyancy frequencies through multiple pathways.
PDF Fluorescence patches in high-frequency internal waves Rev. Munk, W. & Wunsch, C. Abyssal recipes II: Energetics of tidal and wind mixing. 1a and 3a). 1997. Parcels of air which lie on the
Internal waves in uniformly stratified fluid (Chapter 3) - Internal Shapiro, and T.J. Sherwin. Aerial observations of surface patchiness of a planktonic crustacean. standing waves in the tube of the flute, and by continuing to blow If this is not the case, then the effects of continuous vertical density variations must be considered. In different stratifications, the function of KdV theory can describe the waveforms of ISWs at different depths well. Shanks, A.L., and W.G. Science 111(2874):9194, https://doi.org/10.1126/science.111.2874.91-a. Science 308(5723):860862, https://doi.org/10.1126/science.1107834. The shape of both linear and weakly nonlinear internal waves can be described by analytic expressions that capture the spatial distribution of over time. The mean tidal residuals in the N2 water interior at S2 calculated for two semidiurnal periods of where the squared buoyancy frequency N2 was estimated at ADCP measurements were estimated as b ures N = 0.3 cm/s the same 1-m segments of the smoothed (reordered) and bvres N = 4.6 cm/s, indicating the existence of an along- Please cite this article as: Liu, Z., et al., Late summer . Tang. Chang, who were deeply involved in the last and early version of this manuscript. Marine Ecology Progress Series 10:111117, https://doi.org/10.3354/meps010111. Oceanogr. Pineda, J. To extract three frequency bands, fourth-order Butterworth filters were applied to the hourly time series of the observed horizontal currents (u, v) at each depth. Our model applications with four different cases of input parameters along with the rate of wind work confirmed the surface wind-generated NIWs, at least, during Events 1, 2, and 5 (Fig. Stacey, and J.V. The figure was generated by S. Noh using MATLAB R2019b, http://www.mathworks.com. 2007. Hoecker-Martnez, M.S., and W.D. 1h), were calculated from KENIW and KESDIT, as were the kinetic energies at wave-wave interaction frequencies including higher tidal harmonics within CFW range, such as M2 + f (see Table3). Res. 2003. Okubo, A. Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences. Publishers note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. way through the air. During Event 2, extreme high KENIW generated by the typhoon passage early on may propagate downward vertically, and presumably equatorward horizontally, as low-mode NIWs with a minimum energy loss into CFWs. For example, if you know the envorinmental lapse rate, and the adiabatic lapse rate, you can determine a special period of oscillation called the Brunt-Vaisala period (or sometimes the Vaisala-Brunt Evolution of a shoaling internal solitary wavetrain. Internal waves modulate the immediate environments of marine organisms either by displacing the organisms vertically or by advecting waters with different properties to their depths. Rev. This is true for both linear waves, where horizontal transport is due exclusively to Stokes drift, as well as for weakly nonlinear waves, where transport arises from both nonlinearity and Stokes drift. Temporal variations of SDIT kinetic energy (KESDIT) basically followed a noticeable fortnightly spring-neap tidal cycle (Fig. Prog. of the corrugations, the whole system would appear stationary. why the density variations have this form shortly. With suitable mathematics, it is possible to make even more precise statements. 428, 15962, 2003 W0018 21, 159163 (2003). Gilly. Masters Thesis, Massachusetts Institute of Technology, 78 pp. and S.N. Garwood, J.C., R.C. Although coastal internal waves usually display some degree of nonlinearity, we also include comparisons with linear internal waves (Figure 2a). 2002. Journal of Geophysical Research 118(1):273286, https://doi.org/10.1029/2012JC008154. situation is a bit like the gravity wave's version of a "sonic boom" - the wave grows to very 1fh). These waves lead, of course, to lee-waves Notice that these The WKB factor \({\{N(z,t)/{N}_{0}\}}^{-1/2}\) is less (greater) than unity when and where stratification is stronger (weaker) than the reference (Fig. 1961. In a simple example, where we set the vertical distribution of temperature to match that of density, wave-induced horizontal transport alters the overall water temperatures depth-keeping plankton are exposed to. These parcels will cool as they rise, by adiabatic cooling, so these blue lines will also be regions of To properly assess how vertical motions affect primary production, however, the phasing of internal waves with respect to variable surface irradiance must be taken into account. Genovese, and S.R. Sometimes, they are called This simply arises because the air is most dense when the air is coldest, so we expect that the density will be least when the temperature Lett. by the oscillatory motions of the gravity waves. Marine Biology 91:161171, https://doi.org/10.1007/BF00569432. Then the surface of the corrugation will appear to However, gravity waves are different to many other waves in that they have special laws which Res. By resisting vertical velocities, fixed-depth organisms essentially move in the direction opposite to passive organism displacements, relative to the wave field. Madden, and C.L. Episodic nutrient supply to a kelp forest ecosystem in Southern California. The discussion here focuses on cases in which internal waves influence marine organisms time-integrated environmental conditions, such as irradiance for passive plankton moved vertically, and temperature for depth-keeping and sessile organisms. Pierce, and L.A. Levin. Limnol. Gravity waves can be found in many other instances in the atmosphere- we cannot list them all here. Continental Shelf Research 36:818, https://doi.org/10.1016/j.csr.2012.01.003. the red, grey and Navarro, M.O., G.T. These changes are mainly due to changes of the mesoscale fields (Fig. The rate of energy transfer from the mesoscale field to NIWs was estimated following Jing et al.27, \({\rm{P}}=-\,0.5(\langle uu\rangle -\langle vv\rangle ){S}_{n}-\langle uv\rangle {S}_{s}\), where the angle brackets represent the running mean over three inertial periods. Internal tidal waves in Tiburon Basin (Gulf of California, Mexico) modulate fish larvae aggregations. & Schmitt, R. W. Observation of near-inertial wave reflections within the thermostad layer of an anticyclonic mesoscale eddy. The key sample phase fronts of the wave. Schooling fish may benefit not only from internal wave troughs concentrating vertically swimming zooplankton prey above the pycnocline but also from the waves increasing the vertical space available for schooling and feeding (Bertrand etal., 2008). The two mechanisms are not simple, particularly considering the periods and depths where only NIWs were enhanced without enhancements of SDITs or CFWs (purple box in Fig. it is coolest, and therefore has the lowest density. (This is different to the case of other waves, like ocean waves or sound waves, where the energy On the shape of progressive internal waves. The Sulu Sea internal soliton experiment. Res. J. Phys. Coast. 2018. J. Geophys. Introduction [2] Internal gravity waves reflecting from bottom topography represent an important phenomenon in ocean dynamics. We also They are actually called INTERNAL GRAVITY (or BUOYANCY) waves, to distinguish them from waves which occur at a surface interface. Jaffe, L. DeGelleke, and P.J.S. This can be seen from the expression for the steepness m of wave- energy propagation, where m = tany (with y the angle of the wave-energy propagation direction with respect to the hori- zontal) m w2f2 N2w2 11=2 ; 1 2020. 13, 167182 (1975). Ocean Model. Res. Has data issue: true The Auk 104(1):129133, https://doi.org/10.2307/4087244. 2015. In addition, upward propagating NIWs due to the reflection of downward propagating NIWs back to the surface from the UWE thermostad were observed 19. Zhang, S., M.H. Sci. Franks, P.J.S. Connecting wind-driven upwelling and offshore stratification to nearshore internal bores and oxygen variability. In particular, this shows that the buoyancy frequency is an upper limit of allowed internal wave frequencies. The diagram is not to scale - as a general rule the horizontal wavelengths are Plueddemann, A. J. CAS << /Length 5 0 R /Filter /FlateDecode >> The onshore transport of an oil spill by internal waves. Details on the moored time-series measurements are provided by Kim et al.63 and Noh and Nam64.
Internal wave modes in the open ocean: (a) buoyancy frequency profiles Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. These help to anticipate the dispersion relation that describes internal waves that are not influenced by rotation. These relationships are likely indicative of a reactive process, in which higher trophic levels seek higher concentrations of prey and/or drift algae created by internal wave motions (Kingsford and Choat, 1986; Moore and Lien, 2007; Lvy etal., 2018). Thus, by affecting light penetration in the ocean, internal waves can also increase feeding opportunities for predators that must avoid their own visual predators (Kaartvedt etal., 2012). Our findings are summarised as follows: The local wind-forced, damped slab model well reproduced most of mixed layer NIWs supporting well-known mechanisms of surface generation and downward propagation of NIWs, particularly during typhoon passage (Event 2); Modified slab model explained mixed layer NIWs even with weak wind forcing by considering the amplification due to interaction with the surface background flow field during the generation stage (Event 4); Potentially evident and efficient energy transfer from mesoscale field to internal waves via wave capture accounted for enhanced NIWs at 360m when the total strain exceeds relative vorticity and rates of energy transfer is positive (Events 3 and 4); Remarkable time-depth variations of SDITs in addition to noticeable spring-neap tide cycles were found largely following mesoscale conditions favourable for generating the SDITs at the shelf break in the north of the Korea Strait and eastward refracting of the poleward propagating SDITs toward the observation site in the northern Ulleung Basin (Events 24 and early Event 5); Importance of local and remote wave-wave interaction processes and forward energy cascading from NIWs and SDITs into CFWs was emphasised to account for time-depth patterns of KECFW and the frequency spectrum of horizontal kinetic energy, ruling out the possibility of bottom generation of local CFWs under the condition of small Froude number. 32, 14 (2005). 1980. Flameling, I.A., and J. Kromkamp. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Life in Internal Waves | Oceanography - The Oceanography Society Moreover, the mechanism of NIWs interacting with ITs and enhancing CFWs remained unanswered. 80, 5973 (2014). Each colour box in (dh) represents enhanced NIWs only with no enhancements of SDITs or CFWs (purple), enhanced CFWs only with no enhancements of NIWs or SDITs (green), enhanced NIWs and CFWs with no SDIT enhancement (black), enhanced SDITs and CFWs with no NIW enhancement (red), and enhanced NIWs, SDITs, and CFWs (blue). Woodson, C.B. Primary writing: S.N. In the above discussions, we consider air flow relative to the ground as a major source Google Scholar. Le Boyer. Internal waves at tidal frequencies are produced by tidal flow over topography/bathymetry, and are . Lee, O.S. We use buoyancy frequency to reveal the mixing effect of the internal waves along the attractor-like trajectory. Journal of Marine Research 32(1):6789. (1983) Tidally generated high-frequency internal wave-packets and their effects on plankton in Massachusetts Bay. Waves of this type exist throughout the atmosphere. In the case of depth-keeping plankton, a similar effect is seen for isopycnal properties. Tidally generated high-frequency internal wave packets and their effects on plankton in Massachusetts Bay. 2010. 68, 427437 (2012). We then contrast time series of these properties as they apply to virtual organisms released in both linear and weakly nonlinear internal waves (Box 1). Close this message to accept cookies or find out how to manage your cookie settings. Our heuristic examples focus on high-frequency internal waves, that is, on internal waves at the local buoyancy frequency, with periods on the order of tens of minutes. While the modelled amplitudes of NIWs are sensitive to both MLD and damping time scale, the timing of enhanced NIWs is consistent among the cases, as described in previous section. please confirm that you agree to abide by our usage policies. in so doing modulate the strong local surface winds. Res. Walter, R.K., C.B. Horizontal currents measured every 30min at the RCMs were subsampled at a 1h interval. 1999. a "propagating wave" is produced. Upslope internal-wave Stokes drift, and compensating downslope Eulerian mean currents, observed above a lakebed. Henderson, S.M. (Horizontal Wavelength)/(Vetical Wavelength) = (Wave Period)/(Brunt-Vaisala Period). We will not discuss all of these sources - but we will note Journal of Geophysical Research 102(C8):18641, https://doi.org/10.1029/97JC00441. Kwan, O. Batalov, C.Y. Annual Review of Marine Science 10(1):421441, https://doi.org/10.1146/annurev-marine-121916-063619. Here, for ease of comparison, we apply the same parameters to both linear and weakly nonlinear internal waves; we set c to 0 m, max to 2.5 m, c to 0.3 m s1, and T to 900 s (15 min). In these shallow water environments, market squid lay their egg capsules directly on the seafloor (Zeidberg etal., 2012); by modulating oxygen, pH, and temperature, internal waves may thus affect squid embryonic development (Navarro etal., 2016). The spectral energies integrated over the continuum frequency band were 2.13 104 and 1.14 104 m2 s2 cph1 (corresponding to ~0.96 and 0.76Jm3 of KECFW) at 360m during Events 3 and 4, and 3.74 105, 2.50 105, and 4.94 105 m2 s2 cph1 (corresponding to ~0.35, 0.34, and 0.51Jm3 of KECFW) at 77m during Events 1, 2, and 5, respectively. Seo, S. et al. The easiest way to physically understand the characteristics of gravity waves is to visualize a Thus this
Design of the FUXING buoyancy-driven system - nature.com Variability in depth-keeping abilities between planktonic prey and predators can lead to differential vertical advection by internal waves and different concentration patterns, both of which will influence trophic interactions (Macas etal., 2010; Greer etal., 2014). 25, 17121719 (2005). Maps of (f,g) surface geostrophic currents derived from satellite altimetry (vectors) and vertical relative vorticity (colours), and (h,i) total strain (colours) and Okubo-Weiss parameters 2 (dotted contours) at 2 1011 (blue), 1 1011 (cyan), 0.0 (black), 1 1011 (orange), and 2 1011 (red) for (f,h) October 22 and (g,i) November 20 corresponding to early Event 3 and late Event 4, respectively.
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