Existence and properties of ageostrophic modons and coherent tripoles in the two-layer rotating shallow water model on the -plane

Abstract

We study formation and properties of new coherent structures: ageostrophic modons in the two-layer rotating shallow water model. The ageostrophic modons are obtained by 'ageostrophic adjustment' of the exact modon solutions of the twolayer quasi-geostrophic equations with the free surface, which are used to initialize the full two-layer shallow water model. Numerical simulations are performed using a well-balanced high-resolution finite volume numerical scheme. For large enough Rossby numbers, the initial configurations undergo ageostrophic adjustment towards asymmetric ageostrophic quasi-stationary coherent dipoles. This process is accompanied by substantial emission of inertia-gravity waves. The resulting dipole is shown to be robust and survives frontal collisions. It contains captured inertia-gravity waves and, for higher Rossby numbers and weak stratification, carries a (baroclinic) hydraulic jump at its axis. For stronger stratifications and high enough Rossby numbers, 'rider' coherent structures appear as a result of adjustment, with a monopole in one layer and a dipole in another. Other ageostrophic coherent structures, such as two-layer tripoles and two-layer modons with nonlinear scatter plot, result from the collisions of ageostrophic modons. They are shown to be long-living and robust, and to capture waves.

Centrifugal, barotropic and baroclinic instabilities of isolated ageostrophic anticyclones in the two-layer rotating shallow water model and their nonlinear saturation

“…The barotropic dipoles are not stable: after ejection of the lower anticyclonic vortex, the dipoles become essentially baroclinic (two-layer cyclone plus upper-layer anticyclone). Such a 'rider modon' was reported in the two-layer shallow water model by Lahaye & Zeitlin (2012). The first-stage barotropic and subsequent baroclinic dipoles do not dissipate PV, while the tripole does (through weak but continuous filamentation of the patches).…”

Coherent dipoles in a mixed layer with variable buoyancy: Theory compared to observations

“…Let us finally mention that the known modon solutions in two-layer QG and RSW models, e.g. Lahaye and Zeitlin (2012a), can be generalized to the thermal counterparts of both models along the same lines as above. Yet, in order to compare such solutions with observations, an information on the deep structure is needed in these latter.…”

Geophysical turbulence dominated by inertia–gravity waves

“…This is a significant advantage for the present study that is attempting to understand the effect of high energy non-breaking dispersive waves on balanced flow. Although RSW models have a clear separation between waves and balanced flow at the linear level, analogous to the decomposition presented in (2.8) and (2.12), nonlinear interactions and subsequent shock formation will result in strong intermittent and localized dissipation, which can in turn generate PV locally (Pratt 1983; Jiang & Smith 2003; Lahaye & Zeitlin 2012 b ). Such shock-induced wave dissipation makes it difficult to maintain a high wave-to-balance energy ratio in the different regimes we are interested in.…”