Damping of inertial motions by parametric subharmonic instability in baroclinic currents

Abstract

A new damping mechanism for vertically-sheared inertial motions is described involving an inertia-gravity wave that oscillates at half the inertial frequency, f , and that grows at the expense of inertial shear. This parametric subharmonic instability forms in baroclinic, geostrophic currents where thermal wind shear, by reducing the potential vorticity of the fluid, allows inertia-gravity waves with frequencies less than f . A stability analysis and numerical simulations are used to study the instability criterion, energetics, and finite-amplitude behaviour of the instability. For a flow with uniform shear and stratification, parametric subharmonic instability develops when the Richardson number of the geostrophic current nears Ri PSI = 4/3 + γ cos φ, where γ is the ratio of the inertial to thermal wind shear magnitude and φ is the angle between the inertial and thermal wind shears at the initial time. Inertial shear enters the instability criterion because it can also modify the potential vorticity and hence the minimum frequency of inertia-gravity waves. When this criterion is met, inertia-gravity waves with a frequency f /2 and with flow parallel to isopycnals amplify, extracting kinetic energy from the inertial shear through shear production. The solutions of the numerical simulations are consistent with these predictions and additionally show that finite-amplitude parametric subharmonic instability both damps inertial shear and is itself damped by secondary shear instabilities. In this way, parametric subharmonic instability opens a pathway to turbulence where kinetic energy in inertial shear is transferred to small scales and dissipated.

First Evidence of Coherent Bands of Strong Turbulent Layers Associated with High-Wavenumber Internal-Wave Shear in the Upstream Kuroshio

“…While the wind energy flux to the inertial currents is found to be sufficient to generate an observed amplitude of near-inertial waves, it is not clear how the observed high vertical wavenumber near-inertial internal waves are formed. We speculate that the possible mechanisms are (1) PSI of the M 2 internal tide upstream, which was advected to the observation sites by the Kuroshio flow, (2) local PSI with anomalously lower minimum internal-wave frequency than f due to mean velocity shears, (3) K 1 internal tides generated over rough topography, (4) near-inertial internal waves generated by the Kuroshio over shallow topography in Okinawa Trough and Tokara Strait, (5) spontaneously generated near inertial internal waves by the Kuroshio, and (6) PSI of wind-induced inertial waves to generate high wavenumber anomalously low frequency internal waves of half the Coriolis frequency, f /2 along isopycnal in a strong baroclinic front 31 .…”

“…The near-inertial waves induced by the Kuroshio over the topography cannot be ruled out. Other possibilities, such as the spontaneous generation of the near-inertial waves by the meandering Kuroshio 24 – 28 , and the PSI of wind-induced near-inertial waves 31 are not discussed in the present study due to the limited observation data. More intensive field campaigns, and high-resolution numerical simulations, are necessary to definitively identify the source of these near-inertial waves propagating in the upstream Kuroshio.…”

“…Near the critical latitude, K 1 or O 1 diurnal internal tides generated over the rough topography are also near-inertial internal waves. In a strong baroclinic front, where geostrophic shear allows anomalously low frequency internal waves, a recent theoretical study 31 showed that PSI of wind-driven near-inertial waves could generate high wavenumber internal waves with a frequency of half the local Coriolis frequency f /2. Regardless of their generation mechanism, these propagating near-inertial internal waves can be trapped on the anticyclonic side of the front where the lowest internal wave frequency is decreased by geostrophic lateral and vertical shears 32 – 34 .…”

Seasonality of submesoscale flows in the ocean surface boundary layer

“…Increased variance in R o due to vortex stretching has the effect of revealing vorticity skewness even in the absence of instabilities [ Capet et al , ]. Thus, whether or not the marginally stable state (i.e., f q = 0) is crossed, leading to the suite of instabilities referred to above, and to what degree wind forcing and buoyancy loss at the surface are relevant factors [ Thomas and Lee , ; Thomas , ; Taylor and Ferrari , ; Thomas and Taylor , ; Hamlington et al , ; Whitt and Thomas , ] are questions that we leave for a future study.…”

Geophysical turbulence dominated by inertia–gravity waves

“…Thomas (2017) reviews a wide range of situations in which NIW–front interactions can initiate instabilities, turbulence and dissipation of both the wave and the front. Amongst these different wave–front configurations discussed by Thomas, the investigation undertaken by Thomas & Taylor (2014) is an example where NIWs transfer energy to baroclinic geostrophic currents, this being catalyzed by parametric subharmonic instability.…”