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Numerical simulation of rotating convection in plane layers with free slip boundaries show that the convective flows can be classified according to a quantity constructed from the Reynolds, Prandtl and Ekman numbers. Three different flow…
In its broadest sense the term bent wave rays hints at light or electromagnetic waves bending in a strong gravitational field or in their progress through a transparent medium of nonuniform index of refraction. However, there are instances…
Patterns of convection in internally heated, self-gravitating rotating spherical fluid shells are investigated through numerical simulations. While turbulent states are of primary interest in planetary and stellar applications the present…
We consider semiclassically scaled, weakly nonlinear Schr\"odinger equations with external confining potentials and additional angular-momentum rotation term. This type of model arises in the Gross-Pitaevskii theory of trapped, rotating…
The appearence of a new type of fast nonlinear traveling wave states in binary fluid convection with increasing Soret effect is elucidated and the parameter range of their bistability with the common slower ones is evaluated numerically.…
The mathematical models and numerical simulations reported here are motivated by satellite observations of horizontal gradients of sea surface temperature and salinity that are closely coordinated with the slowly varying envelope of the…
We use an idealized three-dimensional general circulation model to study condensible-rich atmospheres with an ineffective cold trap on slowly rotating tidally locked terrestrial planets. In particular, we show the climate dynamics in a thin…
Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics…
The surface zonal winds observed in the giant planets form a complex jet pattern with alternating prograde and retrograde direction. While the main equatorial band is prograde on the gas giants, both ice giants have a pronounced retrograde…
The physics of topological insulators makes it possible to understand and predict the existence of unidirectional waves trapped along an edge or an interface. In this review, we describe how these ideas can be adapted to geophysical and…
We consider the problem of waves propagating in a viscoelastic solid. For the material properties of the solid we consider both classical and fractional differentiation in time versions of the Zener, Maxwell, and Voigt models, where the…
Rayleigh-Benard convection in a rotating spherical shell provides a simplified model for convective dynamics of planetary and stellar interiors. In this study, we build more than 200 numerical models of rotating convection in a spherical…
A widely used approach to mathematically describe the atmosphere is to consider it as a geophysical fluid in a shallow domain -- and thus to model it using classical fluid dynamical equations combined with the explicit inclusion of an…
This study investigates three-dimensional, steady-state, and non-Newtonian flows within a very thin porous medium (VTPM). The medium is modeled as a domain confined between two parallel plates and perforated by solid cylinders that connect…
We explore theoretically the complex dynamics and emergent behaviors of spinning spheres immersed in viscous fluid. The particles are coupled to each-other via the fluid in which they are suspended: each particle disturbs the surrounding…
Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…
We show that the phase space of stratified turbulence mainly consists of two slow invariant manifolds with rich physics, embedded on a larger basin with fast evolution. A local invariant manifold in the vicinity of the fluid at equilibrium…
We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom…
Rotating turbulence is ubiquitous in nature. Previous works suggest that such turbulence could be described as an ensemble of interacting inertial waves across a wide range of length scales. For turbulence in macroscopic quantum…
In this paper we study the effect of rotation on nonlinear wave phenomena in weakly dispersive media modeled by the Korteweg-de Vries equation on the real line. It is well known that smoothing in the case of the KdV equation with periodic…