Internal Tide Dissipation at Topography: Triadic Resonant Instability Equatorward and Evanescent Waves Poleward of the Critical Latitude

The disintegration of the equatorward-propagating K1 internal tide in the South China Sea (SCS) by parametric subharmonic instability (PSI) at its critical latitude of 14.52&#186;N is investigated numerically. The multiple-source generation and long-range propagation of K1 internal tides are successfully reproduced. Using equilibrium analysis, the internal wave field near the critical latitude is found to experience two quasi-steady states, between which the subharmonic waves develop constantly. The simulated subharmonic waves agree well with classic PSI theoretical prediction. The PSI-induced near-inertial waves are of half the K1 frequency and dominantly high modes, the vertical scales ranging from 50 to 180 m in the upper ocean. From an energy perspective, PSI mainly occurs in the critical latitudinal zone from 13&#8211;15&#186;N. In this zone, the incident internal tide loses ~14% energy in the mature state of PSI. PSI triggers a mixing elevation of O(10-5&#8211;10-4 m2/s) in the upper ocean at the critical latitude, which is several times larger than the background value. The contribution of PSI to the internal tide energy loss and associated enhanced mixing may differ regionally and is closely dependent on the intensity and duration of background internal tide. The results elucidate the far-field dissipation mechanism by PSI in connecting interior mixing with remotely generated K1 internal tides in the Luzon Strait.

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The Latitudinal Dependence of Shear and Mixing in the Pacific Transiting the Critical Latitude for PSI

Journal of Physical Oceanography ◽

10.1175/jpo-d-11-0107.1 ◽

2013 ◽

Vol 43 (1) ◽

pp. 3-16 ◽

Cited By ~ 38

Author(s):

J. A. MacKinnon ◽

M. H. Alford ◽

Rob Pinkel ◽

Jody Klymak ◽

Zhongxiang Zhao

Keyword(s):

Turbulent Mixing ◽

Statistical Significance ◽

Internal Tide ◽

Latitudinal Dependence ◽

The Pacific ◽

Thorpe Scale ◽

Mixing Rates ◽

The Pacific Ocean ◽

Parametric Subharmonic Instability ◽

Critical Latitude

Abstract Turbulent mixing rates are inferred from measurements spanning 25°–37°N in the Pacific Ocean. The observations were made as part of the Internal Waves Across the Pacific experiment, designed to investigate the long-range fate of the low-mode internal tide propagating north from Hawaii. Previous and companion results argue that, near a critical latitude of 29°N, the internal tide loses energy to high-mode near-inertial motions through parametric subharmonic instability. Here, the authors estimate mixing from several variations of the finescale shear–strain parameterization, as well as Thorpe-scale analysis of overturns. Though all estimated diffusivities are modest in magnitude, average diffusivity in the top kilometer shows a factor of 2–4 elevation near and equatorward of 29°N. However, given intrinsic uncertainty and the strong temporal variability of diffusivity observed in long mooring records, the meridional mixing pattern is found to be near the edge of statistical significance.

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Parametric Subharmonic Instability of the Internal Tide at 29°N

Journal of Physical Oceanography ◽

10.1175/jpo-d-11-0108.1 ◽

2013 ◽

Vol 43 (1) ◽

pp. 17-28 ◽

Cited By ~ 66

Author(s):

J. A. MacKinnon ◽

M. H. Alford ◽

Oliver Sun ◽

Rob Pinkel ◽

Zhongxiang Zhao ◽

...

Keyword(s):

Phase Locking ◽

Internal Tide ◽

Observational Evidence ◽

Transfer Rates ◽

The Pacific ◽

The Pacific Ocean ◽

Psi Theory ◽

Parametric Subharmonic Instability ◽

Critical Latitude ◽

Do So

Abstract Observational evidence is presented for transfer of energy from the internal tide to near-inertial motions near 29°N in the Pacific Ocean. The transfer is accomplished via parametric subharmonic instability (PSI), which involves interaction between a primary wave (the internal tide in this case) and two smaller-scale waves of nearly half the frequency. The internal tide at this location is a complex superposition of a low-mode waves propagating north from Hawaii and higher-mode waves generated at local seamounts, making application of PSI theory challenging. Nevertheless, a statistically significant phase locking is documented between the internal tide and upward- and downward-propagating near-inertial waves. The phase between those three waves is consistent with that expected from PSI theory. Calculated energy transfer rates from the tide to near-inertial motions are modest, consistent with local dissipation rate estimates. The conclusion is that while PSI does befall the tide near a critical latitude of 29°N, it does not do so catastrophically.

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Impact of a Mean Current on the Internal Tide Energy Dissipation at the Critical Latitude

Journal of Physical Oceanography ◽

10.1175/jpo-d-16-0197.1 ◽

2017 ◽

Vol 47 (6) ◽

pp. 1457-1472 ◽

Cited By ~ 13

Author(s):

O. Richet ◽

C. Muller ◽

J.-M. Chomaz

Keyword(s):

Large Scale ◽

Internal Tide ◽

Internal Tides ◽

Small Scale ◽

Latitudinal Dependence ◽

Propagating Waves ◽

Parametric Subharmonic Instability ◽

The Impact ◽

Mean Current ◽

Critical Latitude

AbstractPrevious numerical studies of the dissipation of internal tides in idealized settings suggest the existence of a critical latitude (~29°) where dissipation is enhanced. But observations only indicate a modest enhancement at this latitude. To resolve this difference between observational and numerical results, the authors study the latitudinal dependence of internal tides’ dissipation in more realistic conditions. In particular, the ocean is not a quiescent medium; the presence of large-scale currents or mesoscale eddies can impact the propagation and dissipation of internal tides. This paper investigates the impact of a weak background mean current in numerical simulations. The authors focus on the local dissipation of high spatial mode internal waves near their generation site. The vertical profile of dissipation and its variation with latitude without the mean current are consistent with earlier studies. But adding a weak mean current has a major impact on the latitudinal distribution of dissipation. The peak at the critical latitude disappears, and the dissipation is closer to a constant, albeit with two weak peaks at ~25° and ~35° latitude. This disappearance results from the Doppler shift of the internal tides’ frequency, which hinders the nonlinear transfer of energy to small-scale secondary waves via the parametric subharmonic instability (PSI). The new two weak peaks correspond to the Doppler-shifted critical latitudes of the left- and right-propagating waves. The results are confirmed in simulations with simple sinusoidal topography. Thus, although nonlinear transfers via PSI are efficient at dissipating internal tides, the exact location of the dissipation is sensitive to large-scale oceanic conditions.

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Subharmonic Energy Transfer from the Semidiurnal Internal Tide to Near-Diurnal Motions over Kaena Ridge, Hawaii

Journal of Physical Oceanography ◽

10.1175/jpo-d-12-0141.1 ◽

2013 ◽

Vol 43 (4) ◽

pp. 766-789 ◽

Cited By ~ 25

Author(s):

Oliver M. Sun ◽

Robert Pinkel

Keyword(s):

Energy Transfer ◽

Resonance Condition ◽

Internal Tide ◽

Resonant Interaction ◽

Ocean Energy ◽

Turbulent Dissipation ◽

Transfer Rates ◽

Energy Transfers ◽

Forward Energy ◽

Critical Latitude

Abstract Nonlinear energy transfers from the semidiurnal internal tide to high-mode, near-diurnal motions are documented near Kaena Ridge, Hawaii, an energetic generation site for the baroclinic tide. Data were collected aboard the Research Floating Instrument Platform (FLIP) over a 35-day period during the fall of 2002, as part of the Hawaii Ocean Mixing Experiment (HOME) Nearfield program. Energy transfer terms for a PSI resonant interaction at midlatitude are identified and compared to those for near-inertial PSI close to the M2 critical latitude. Bispectral techniques are used to demonstrate significant energy transfers in the Nearfield, between the low-mode M2 internal tide and subharmonic waves with frequencies near M2/2 and vertical wavelengths of O(120 m). A novel prefilter is used to test the PSI wavenumber resonance condition, which requires the subharmonic waves to propagate in opposite vertical directions. Depth–time maps of the interactions, formed by directly estimating the energy transfer terms, show that energy is transferred predominantly from the tide to subharmonic waves, but numerous reverse energy transfers are also found. A net forward energy transfer rate of 2 × 10−9 W kg−1 is found below 400 m. The suggestion is that the HOME observations of energy transfer from the tide to subharmonic waves represent a first step in the open-ocean energy cascade. Observed PSI transfer rates could account for a small but significant fraction of the turbulent dissipation of the tide within 60 km of Kaena Ridge. Further extrapolation suggests that integrated PSI energy transfers equatorward of the M2 critical latitude may be comparable to PSI energy transfers previously observed near 28.8°N.

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Disintegration of the K1 Internal Tide in the South China Sea due to Parametric Subharmonic Instability

Journal of Physical Oceanography ◽

10.1175/jpo-d-19-0320.1 ◽

2020 ◽

Vol 50 (12) ◽

pp. 3605-3622

Author(s):

Kun Liu ◽

Zhongxiang Zhao

Keyword(s):

South China Sea ◽

South China ◽

Internal Tide ◽

The South China Sea ◽

Internal Tides ◽

Upper Ocean ◽

The South ◽

China Sea ◽

Parametric Subharmonic Instability ◽

Critical Latitude

AbstractThe disintegration of the equatorward-propagating K1 internal tide in the South China Sea (SCS) by parametric subharmonic instability (PSI) at its critical latitude of 14.52°N is investigated numerically. The multiple-source generation and long-range propagation of K1 internal tides are successfully reproduced. Using equilibrium analysis, the internal wave field near the critical latitude is found to experience two quasi-steady states, between which the subharmonic waves develop constantly. The simulated subharmonic waves agree well with classic PSI theoretical prediction. The PSI-induced near-inertial waves are of half the K1 frequency and dominantly high modes, the vertical scales ranging from 50 to 180 m in the upper ocean. From an energy perspective, PSI mainly occurs in the critical latitudinal zone from 13° to 15°N. In this zone, the incident internal tide loses ~14% energy in the mature state of PSI. PSI triggers a mixing elevation of O(10−5–10−4) m2 s−1 in the upper ocean at the critical latitude, which is several times larger than the background value. The contribution of PSI to the internal tide energy loss and associated enhanced mixing may differ regionally and is closely dependent on the intensity and duration of background internal tide. The results elucidate the far-field dissipation mechanism by PSI in connecting interior mixing with remotely generated K1 internal tides in the Luzon Strait.

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Effects of an along-shelf current on the generation of internal tides near the critical latitude

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.1071 ◽

2021 ◽

Vol 932 ◽

Author(s):

Yangxin He ◽

Kevin G. Lamb

Keyword(s):

Conversion Rate ◽

Internal Tide ◽

Internal Tides ◽

Horizontal Shear ◽

Background Current ◽

Baroclinic Energy Conversion ◽

Internal Wave Generation ◽

Spatially Varying ◽

Beam Patterns ◽

Critical Latitude

The effects of along-shelf barotropic geostrophic currents on internal wave generation by the $K_1$ tide interacting with a shelf at near-critical latitudes are investigated. The horizontal shear of the background current results in a spatially varying effective Coriolis frequency which modifies the slope criticality and potentially creates blocking regions where freely propagating internal tides cannot exist. This paper is focused on the barotropic to baroclinic energy conversion rate, which is affected by a combination of three factors: slope criticality, size and location of the blocking region where the conversion rate is extremely small and the internal tide (IT) beam patterns. All of these are sensitive to the current parameters. In our parameter space, the current can increase the conversion rate up to 10 times.

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