Analogy between electro-magnetic waves in cold unmagnetized plasma and shallow water inertio-gravity waves in geophysical systems

The fundamental dispersion relation of transverse electro-magnetic waves in a cold collisionless plasma is formally equivalent to the two-dimensional dispersion relation of inertio-gravity waves in a rotating shallow water system, where the Coriolis frequency can be identified with the plasma frequency, and the shallow water gravity wave phase speed plays the role of the speed of light. Here we examine this equivalence and compare between the propagation wave mechanisms in these seemingly unrelated physical systems.

Instability of Lenticular Vortices: Results from Laboratory Experiments, Linear Stability Analysis and Numerical Simulations

The instability of surface lenticular vortices is investigated using a comprehensive suite of laboratory experiments combined with numerical linear stability analysis as well as nonlinear numerical simulations in a two-layer Rotating Shallow Water model. The development of instabilities is discussed and compared between the different methods. The linear stability analysis allows for a clear description of the origin of the instability observed in both the laboratory experiments and numerical simulations. While global qualitative agreement is found, some discrepancies are observed and discussed. Our study highlights that the sensitivity of the instability outcome is related to the initial condition and the lower-layer flow. The inhibition or even suppression of some unstable modes may be explained in terms of the lower-layer potential vorticity profile.

Wave-Vortex Interactions in the Submesoscale

<p>The Surface Water and Ocean Topography (SWOT) mission is the next generation of satellite altimetry, set to launch in early 2022. It will be the first of its kind to provide global sea surface height (SSH) measurements fine enough to begin resolving the submesoscale. In this newly resolvable regime, “slow” flows (jets, vortices…) interact with internal waves by redistributing wave energy to other wave-vectors and frequencies. This introduces the challenge of distinguishing “slow” flows from waves, which is of key importance for inferring ocean circulation, from SSH measurements. I run numerical simulations of the one layer rotating shallow water equations to model the interaction between a single internal tide mode and vortices in (cyclo)geostrophic balance to characterize scattering and map its relevant parameter space. Preliminary results show wave scattering by vortices with Rossby numbers ranging from 0.1-4 that are not explained by the standard methods (frozen-field approximation, ray tracing…) which have been successful in the mesoscale. We find that the Rossby number, the Burger number, and the ratio of the length and velocity scales of the wave and vortex are all necessary to characterize the interaction in submesoscale regimes. Harmonic analysis is used to highlight the direction of the scattered wave energy.</p>