Vortex Stability in a Large-Scale Internal Wave Shear

Abstract

The effect of a large-scale internal wave on a multipolar compound vortex was simulated numerically using a 3D Boussinesq pseudospectral model. A suite of simulations tested the effect of a background internal wave of various strengths, including a simulation with only a vortex. Without the background wave, the vortex remained apparently stable for many hundreds of inertial periods but then split into two dipoles. With increasing background wave amplitude, and hence shear, dipole splitting occurred earlier and was less symmetric in space. Theoretical considerations suggest that the vortex alone undergoes a self-induced mixed barotropic–baroclinic instability. For a vortex plus background wave, kinetic energy spectra showed that the internal wave supplied energy for the dipole splitting. In this case, it was found that the presence of the wave hastened the time to instability by increasing the initial perturbation to the vortex. Results suggest that the stability and fate of submesoscale vortices in the ocean may be significantly modified by the presence of large-scale internal waves. This could in turn have a significant effect on the exchange of energy between the submesoscale and both larger and smaller scales.

Stability of three-dimensional Gaussian vortices in an unbounded, rotating, vertically stratified, Boussinesq flow: linear analysis

“…Several other studies (Smyth & McWilliams 1998;Brunner-Suzuki et al 2012;Dritschel & Mckiver 2015;Tsang & Dritschel 2015) have shown numerically that the stability properties and some aspects of the dynamics of vortices in rotating, stratified flows are not very sensitive to the specific value of f /N as long as this value is small. Here, we show numerically that the eigenvectors and eigenvalues of Gaussian vortices (with N 2 c > 0), when properly scaled, are nearly independent of f /N for small f /N .…”

“…Like many other studies, for most cases we have used f /N = 0.1, rather than f /N = 0.01 (which is a better representative of the mid-latitude oceans, see Chelton et al (1998); ), because small values of f /N are computationally expensive to tackle (see, e.g., Brunner-Suzuki et al 2012;Tsang & Dritschel 2015). However in this paper, we use the semi-analytic method of Barranco & Marcus (2006), which allows us to compute flows efficiently for a wide range of f /N , including the more physically relevant value of 0.01.…”

“…Only few studies have used the full Boussinesq equations, and even those have focused on very different vortex models such as barotropic Taylor columns (Smyth & McWilliams 1998), evolving (out-of-equilibrium) 3D vortices interacting with large-scale internal waves (Brunner-Suzuki et al 2012), out-of-equilibrium, ellipsoidal 3D vortices with discontinuous PV profiles (Tsang & Dritschel 2015), and 3D equilibrium vortices with Gaussian angular velocity (Yim et al 2016). Here we focus on the latter, because the main difference between our analysis and that of Yim et al (2016) is in the vortex model:…”

Upscale Energy Transfer by the Vortical Mode and Internal Waves

“…Additional structural details of mixed patches can be inferred from our figures (see section 3), but these are not our main focus. The interested reader is referred to Lelong and Sundermeyer (2005) and Brunner-Suzuki et al (2012). In our primary simulations (Table 2, runs A-E), mixed patches are assumed fully mixed at their centers (i.e., DN /N 2 5 1), yielding a time-and volume-averaged energy dissipation rate of approximately 8 3 10 28 W kg 21 .…”

“…An S vortex is unstable by itself, owing to vertical variations of its meridional PV (Flierl 1988;Morel and McWilliams 1997) as well as its horizontal PV (Kloosterziel and Carnevale 1999;Beckers et al 2003). Furthermore, when perturbed by a large-scale internal wave, an S vortex will break into dipoles, with time to breakup decreasing with increasing internal wave strength (Brunner-Suzuki et al 2012). Resulting dipoles have smaller horizontal diameter than the original S vortex, indicating a downscale energy transfer, counter to the canonical vortexinduced upscale transfer.…”