Moist-convective thermal rotating shallow water model

Abstract

We show how the moist-convective rotating shallow water model, where the moist convection and the related latent heat release are incorporated into the standard rotating shallow water model of the atmosphere, can be improved by introducing, in a self-consistent way, horizontal gradients of potential temperature and changes of the latter due to the condensation heating, radiative cooling, and ocean-atmosphere heat fluxes. We also construct the quasi-geostrophic limit of the model in mid-latitudes and its weak-gradient limits in the equatorial region. The capabilities of the new model are illustrated by the examples of convection-coupled gravity waves and equatorial waves produced by the relaxation of localized pressure and potential temperature anomalies in the presence of moist convection.

Equatorial modons in dry and moist-convective shallow-water systems on a rotating sphere

“…We should stress that the realism of mcRSW models can be augmented by including horizontal variations of temperature (Kurganov et al. 2020) and/or precipitable water (Rostami & Zeitlin 2018) in the models. The representation of thermodynamical phenomena and cloud-radiative feedbacks can be, correspondingly, ameliorated.…”

“…Zeitlin 2018). (The latter hypothesis can be relaxed (Kurganov, Liu & Zeitlin 2020), but we will not do it in what follows). A formulation of the primitive equations with the help of pseudo-height isobaric coordinates in the vertical (Hoskins & Bretherton 1972) is used for this purpose.…”

Shallow‐water equations with complete Coriolis force: Group properties and similarity solutions

“…Shallow‐water equations are a set of hyperbolic nonlinear partial differential equations, known also as the Saint‐Venant equations, which describe a thin layer of inviscid fluid with a free surface. There are various applications of the shallow‐water equations in physical science; for some recent results, we refer the reader to previous studies 1‐5 and references therein. In general, hyperbolic equations are of special interest for the study of flows.…”

Carriers of \emph{Sargassum} and mechanism for coastal inundation in the Caribbean Sea

“…This is based on the proposition of a minimal model for Caribbean Sea vortex dynamics, whose properties are discussed in the Appendix. The model builds on an old recipe, which used to be very common in ocean dynamics [Ripa, 1993] and is regaining momentum [Kurganov et al, 2020;Beron-Vera, 2021b,d,a;Holm et al, 2020], to include thermodynamics in the two-dimensional rotating shallow-water model. The paper is closed with a summary and some concluding remarks in Section 5.…”