Disintegration of the K1 internal tide in the South China Sea due to parametric subharmonic instability

<p>The disintegration of the equatorward-propagating K<sub>1</sub> internal tide in the South China Sea (SCS) by parametric subharmonic instability (PSI) at its critical latitude of 14.52ºN is investigated numerically. The multiple-source generation and long-range propagation of K<sub>1</sub> 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 K<sub>1</sub> 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 13–15ºN. In this zone, the incident internal tide loses ~14% energy in the mature state of PSI. PSI triggers a mixing elevation of O(10<sup>-5</sup>–10<sup>-4</sup> m<sup>2</sup>/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 K<sub>1</sub> internal tides in the Luzon Strait.</p>

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

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°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.

Parametric Subharmonic Instability of the Semidiurnal Internal Tides at the East China Sea Shelf Slope

On the basis of measurements from an observing mooring system, the observational evidence of parametric subharmonic instability (PSI) that transfers energy from semidiurnal internal tides (ITs) to the subharmonic waves at the East China Sea continental shelf slope is presented for the first time. Although the mooring station is very close to the energetic semidiurnal IT generation site, about 76% of the observed shear variance is contained in the near-inertial band, which is found to have comparable upward- and downward-propagating energy components. Bispectra and bicoherence estimates further confirm the occurrence of PSI transferring energy from the low-mode M2 ITs (vertical wavelength of ~1000 m) to high-mode subharmonic waves (vertical wavelength of ~200 m). The calculated energy transfer rate reveals an averaged net value of ~5 × 10−9 W kg−1. Strong temporal variation of is found that is not exactly in phase with the semidiurnal energy flux. After looking into the local vorticity fields, it is strongly suggested that the varying background relative vorticity associated with the evolving Kuroshio has modified the efficiency of PSI at the mooring location through changing the local effective inertial frequency.

Effect of background mean flow on PSI of internal wave beams

An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract energy via resonant triad interactions while in contact with the underlying beam, and the mean flow is assumed to be small so that its advection effect on the perturbations is as important as dispersion, triad nonlinearity and viscous dissipation. In this ‘distinguished limit’, the perturbation dynamics are governed by the same evolution equations as those derived in Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402), except for a mean flow term that affects the group velocity of the perturbations and imposes an additional necessary condition for PSI, which stabilizes very short-scale perturbations. As a result, it is possible for a small amount of mean flow to weaken PSI dramatically.

Parametric subharmonic instability in a narrow-band wave spectrum

Parametric subharmonic instability arising in a narrow-band wave spectrum is investigated. Using a statistical equation that describes weakly nonlinear interactions in a random wave field, we perform analytical and numerical stability analyses for a modulating wave train. The analytically obtained growth rate $\unicode[STIX]{x1D706}=(-\unicode[STIX]{x1D707}+\sqrt{\unicode[STIX]{x1D707}^{2}+4CE_{B}})/2$ agrees favourably with the results from direct numerical experiments, where $\unicode[STIX]{x1D707}$ is the half-value width of the background wave frequency spectrum, $E_{B}$ is the background wave energy density, and $C$ is a constant. This expression has two asymptotic limits: $\unicode[STIX]{x1D706}\sim \sqrt{CE_{B}}$ for $\unicode[STIX]{x1D707}\ll \sqrt{CE_{B}}$ and $\unicode[STIX]{x1D706}\sim CE_{B}/\unicode[STIX]{x1D707}$ for $\unicode[STIX]{x1D707}\gg \sqrt{CE_{B}}$. In the terms of weak turbulence, these two growth rates correspond to the ones occurring in the dynamic and kinetic time scales. In this way, our formulation successfully unifies the two conventional types of parametric subharmonic instability and offers a new criterion to determine the applicability of the classical kinetic equation in three-wave systems.

Geographical Distribution of Diurnal and Semidiurnal Parametric Subharmonic Instability in a Global Ocean Circulation Model

The evidence for, baroclinic energetics of, and geographic distribution of parametric subharmonic instability (PSI) arising from both diurnal and semidiurnal tides in a global ocean general circulation model is investigated using 1/12.5° and 1/25° simulations that are forced by both atmospheric analysis fields and the astronomical tidal potential. The paper examines whether PSI occurs in the model, and whether it accounts for a significant fraction of the tidal baroclinic energy loss. Using energy transfer calculations and bispectral analyses, evidence is found for PSI around the critical latitudes of the tides. The intensity of both diurnal and semidiurnal PSI in the simulations is greatest in the upper ocean, consistent with previous results from idealized simulations, and quickly drops off about 5° from the critical latitudes. The sign of energy transfer depends on location; the transfer is positive (from the tides to subharmonic waves) in some locations and negative in others. The net globally integrated energy transfer is positive in all simulations and is 0.5%–10% of the amount of energy required to close the baroclinic energy budget in the model. The net amount of energy transfer is about an order of magnitude larger in the 1/25° semidiurnal simulation than the 1/12.5° one, implying the dependence of the rate of energy transfer on model resolution.