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

Abstract

Motivated by recent observations of coherent dipolar cyclone-anticyclone structures in the ocean, the modons, and their signature in the surface temperature field, we demonstrate that the classical modon solutions of the barotropic quasigeostrophic equations can be generalized to include buoyancy or temperature as an active tracer. The properties of such "thermal" modons, and especially their ability to carry heat anomaly over long distances, depend on the relative sign of the associated vorticity and buoyancy anomalies. We show using numerical simulations with the thermal shallow water equations, and their quasi-geostrophic version, that the evolution of the modons is consistent with the observations.

Coherent magnetic modon solutions in quasi-geostrophic shallow water magnetohydrodynamics

“…Our experience with TRSW and TQG modons (Lahaye et al. 2020) shows that they may be subject to small-scale convective-type instabilities, which are known for vortex solutions in this model (Gouzien et al. 2017).…”

“…Ribstein, Gula & Zeitlin 2010; Lahaye et al. 2020). To check if this is the case with MQG, numerical simulations with the full MRSW, which would accurately resolve both inertia-gravity and Alfvèn waves, as well as discontinuities of the magnetic field and eventual sharp fronts (shocks), are needed.…”

“…As we know, the modon solutions in 'ordinary' QG and in TQG, which are, respectively, the asymptotic limits of RSW and TRSW equations, survive, albeit slightly distorted, if considered within the parent models (RSW and TRSW, correspondingly, cf. Ribstein, Gula & Zeitlin 2010;Lahaye et al 2020). To check if this is the case with MQG, numerical simulations with the full MRSW, which would accurately resolve both inertia-gravity and Alfvèn waves, as well as discontinuities of the magnetic field and eventual sharp fronts (shocks), are needed.…”

“…As previously mentioned, the MRSW (respectively MQG) model is structurally close to TRSW (respectively TQG). Our experience with TRSW and TQG modons (Lahaye et al 2020) shows that they may be subject to small-scale convective-type instabilities, which are known for vortex solutions in this model (Gouzien et al 2017). To check whether this is also the case with MQG modons, and also to see whether sharp gradients of the magnetic fields engender new instabilities, we performed a set of numerical simulations of the MQG equations using a doubly periodic pseudo-spectral code based on the Python library Dedalus (Burns et al 2020), with modon solutions as initial conditions.…”

“…With the help of direct numerical simulations with the Dedalus code (Burns et al 2020), which we adapted to the MQG simulations, we show that these solutions can be stable or unstable, depending on the intensity of the magnetic field inside and outside the dipole. The construction of the modon solutions follows the lines of that used recently (Lahaye, Zeitlin & Dubos 2020) to obtain similar solutions in the quasi-geostrophic limit of the rotating shallow water model with horizontal density and/or temperature gradients, the so-called thermal rotating shallow water (TRSW, which becomes TQG in the quasi-geostrophic limit). It is a generalization of the classical procedure of building the modon solutions of the 'ordinary' quasi-geostrophic (QG) equations, first obtained by Larichev & Reznik (1976) following the idea of construction of the Lamb's dipole in two-dimensional (2-D) hydrodynamics.…”