Wave-induced mean flows in rotating shallow water with uniform potential vorticity

Thomas, Jim; Bühler, Oliver; Smith, K. Shafer

doi:10.1017/jfm.2018.22

Cited by 13 publications

(22 citation statements)

References 20 publications

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“…Future work aims to explore transport and long wave resonance in more realistic detail through including the effects of background rotation (see recent work by Wagner & Young (2016) and Thomas et al (2018)) and allowing for the wavepacket to have finite spanwise extent.…”

Section: Discussionmentioning

confidence: 99%

Lagrangian transport by vertically confined internal gravity wavepackets

2019

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We examine the flows induced by horizontally modulated, vertically confined (or guided), internal wavepackets in a stratified, Boussinesq fluid. The wavepacket induces both an Eulerian flow and a Stokes drift, which together determine the Lagrangian transport of passive tracers. We derive equations describing the wave-induced flows in arbitrary stable stratification and consider four special cases: a two-layer fluid, symmetric and asymmetric piecewise constant (‘top-hat’) stratification and, more representative of the ocean, exponential stratification. In a two-layer fluid, the Stokes drift is positive everywhere with the peak value at the interface, whereas the Eulerian flow is negative and uniform with depth for long groups. Combined, the net depth-integrated Lagrangian transport is zero. If one layer is shallower than the other, the wave-averaged interface displaces into that layer making the Eulerian flow in that layer more negative and the Eulerian flow in the opposite layer more positive so that the depth-integrated Eulerian transports are offset by the same amount in each layer. By contrast, in continuous stratification the depth-integrated transport due to the Stokes drift and Eulerian flow are each zero, but the Eulerian flow is singular if the horizontal phase speed of the induced flow equals the group velocity of the wavepacket, giving rise to a single resonance in uniform stratification (McIntyre, J. Fluid Mech., vol. 60, 1973, pp. 801–811). In top-hat stratification, this single resonance disappears, being replaced by multiple resonances occurring when the horizontal group velocity of the wavepacket matches the horizontal phase speed of higher-order modes. Furthermore, if the stratification is not vertically symmetric, then the Eulerian induced flow varies as the inverse squared horizontal wavenumber for shallow waves, the same as for the asymmetric two-layer case. This ‘infrared catastrophe’ also occurs in the case of exponential stratification suggesting significant backward near-surface transport by the Eulerian induced flow for modulated oceanic internal modes. Numerical simulations are performed confirming these theoretical predictions.

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Section: Discussionmentioning

confidence: 99%

Lagrangian transport by vertically confined internal gravity wavepackets

2019

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“…Several studies demonstrate that interactions arise between NIWs and geostrophic motions due to similar spatial scaling, and produce a frequency shift by the relative vorticity of the geostrophic field (Mooers 1975;Kunze 1985;Young and Ben Jelloul 1997;Whitt and Thomas 2013;Danioux et al 2015;Wagner and Young 2016;Thomas et al 2018). Kunze (1985) shows that the intrinsic frequency v 0 of a NIW is influenced by the horizontal and vertical geostrophic shear as well as the mean flow advection.…”

Section: Introductionmentioning

confidence: 99%

Frequency Shift of Near-Inertial Waves in the South China Sea

Boyer

Alford

Pinkel

et al. 2020

Journal of Physical Oceanography

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Despite sufficient wind forcing, internal waves in the South China Sea do not exhibit the strong near-inertial wave (NIW) peak that is typical in most of the world oceans. Using data from 10 contemporaneous moorings deployed in summer 2011, we show that strong isopycnal vertical tidal displacements transfer most of the near-inertial (NI) kinetic energy (KE) to frequencies higher than the inertial frequency in an Eulerian reference frame. Transforming to an isopycnal-following reference frame increases the KE at NI frequencies, suggesting the presence of NIWs. However, the projection onto a semi-Lagrangian coordinate system still underestimates the expected NI peak. To fully resolve NIWs requires the use of time-dependent vertical wavenumber–frequency spectra because the intrinsic frequency of the NIWs varies substantially, owing to Doppler shifting by lateral mesoscale flows. Here, we show NIW intrinsic frequency variations of ±0.2 cpd within few days, of similar magnitude as the observed variations of relative vorticity associated with the meandering Kuroshio.

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“…In part due to the need to understand pathways for energy transport from large-scale atmospheric and oceanic circulations to small dissipative scales, there have been several studies aiming to examine interactions between near-inertial waves (internal waves with frequency close to f ) and mean flows [6][7][8][9][10][11] . In most of these studies, the focus has been on the excitation of inertial waves by geostrophically balanced flows.…”

Section: Introductionmentioning

confidence: 99%

“…In most of these studies, the focus has been on the excitation of inertial waves by geostrophically balanced flows. Conversely, even relatively large frequency internal waves can put energy into large scale flows due to dissipative processes, such as overturning and breaking [12][13][14][15][16] , as well as non-dissipative processes, such as Eulerian induced flows 6,10,[17][18][19] . It is an investigation of the latter case that guides the work presented herein.…”

Section: Introductionmentioning

confidence: 99%

Flows induced by Coriolis-influenced vertically propagating two-dimensional internal gravity wave packets

2020

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Theory is developed to predict the flows induced by small-amplitude two-dimensional vertically propagating internal wavepackets under the influence of rotation. While the long wave response originally predicted by Bretherton [J. Fluid Mech. 36, 785-803 (1969)] dominates if the influence of background rotation is negligible, the induced waves are found to be evanescent if the Coriolis parameter is sufficiently large. Explicitly, evanescent induced flows dominate if the Coriolis parameter is greater than the forcing frequency, which is set by the ratio of the vertical group velocity of the wavepacket divided by the vertical scale of modulation of the wavepacket. The predicted structure of the induced flow is confirmed by numerical simulations. For an up-and rightward propagating Gaussian wavepacket that dominantly induces a long wave response, the flow is rightward across the upper flank and leftward across the lower flank of the wavepacket. In contrast, the induced flow for a dominantly evanescent response is negative over the middle of the wavepacket. This qualitative change in structure is anticipated to influence the modulational stability of moderately large amplitude wavepackets.

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Wave-induced mean flows in rotating shallow water with uniform potential vorticity

Cited by 13 publications

References 20 publications

Lagrangian transport by vertically confined internal gravity wavepackets

Lagrangian transport by vertically confined internal gravity wavepackets

Frequency Shift of Near-Inertial Waves in the South China Sea

Flows induced by Coriolis-influenced vertically propagating two-dimensional internal gravity wave packets

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