Related papers: Topology of rotating stratified fluids with and wi…
The rotation of the earth breaks time-reversal and reflection symmetries in an opposite sense north and south of the equator, leading to a topological origin for certain atmospheric and oceanic equatorial waves. Away from the equator the…
Topology sheds new light on the emergence of unidirectional edge waves in a variety of physical systems, from condensed matter to artificial lattices. Waves observed in geophysical flows are also robust to perturbations, which suggests a…
As the Earth rotates, the Coriolis force causes several oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincar\'e modes. It has been demonstrated that the mathematical origin of these…
We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability conditions. We study the flow with Sinus profile in details…
Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is…
Driven by growing momentum in two-dimensional geophysical flow modeling, this paper introduces a general family of "thermal" rotating shallow-water models. The models are capable of accommodating thermodynamic processes, such as those…
Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such systems which appears…
Aims. Qualitative analysis of key (but yet unappreciated) linear phenomena in stratified hydrodynamic Keplerian flows: (i) the occurrence of a vortex mode, as a consequence of strato-rotational balance, with its transient dynamics; (ii) the…
We study the two-dimensional rotating shallow-water model describing Earth's oceanic layers. It is formally analogue to a Schr\"odinger equation where the tools from topological insulators are relevant. Once regularized at small scale by an…
We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. An analytical solution is permitted via integration of the Euler equations.…
Origin of hydrodynamic turbulence in rotating shear flow, e.g. plane Couette flow including the Coriolis force, is a big puzzle. While the flow often exhibits turbulence in laboratory experiments, according to the linear perturbation theory…
Inertial modes are the eigenmodes of contained rotating fluids restored by the Coriolis force. When the fluid is incompressible, inviscid and contained in a rigid container, these modes satisfy Poincar\'e's equation that has the peculiarity…
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary…
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…
Using topology, we unveil the existence of new unidirectional modes in compressible rotating stratified fluids. We relate their emergence to the breaking of time-reversal symmetry by rotation and vertical mirror symmetry by stratification…
Topology is bringing new tools for the study of fluid waves. The existence of unidirectional Yanai and Kelvin equatorial waves has been related to a topological invariant, the Chern number, that describes the winding of $f$-plane shallow…
Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper, we study long linear and weakly-nonlinear ring waves in a stratified fluid in the presence of a…
In the Stokesian limit, the streamline topology around a single neutrally buoyant sphere is identical to the topology of pair-sphere pathlines, both in an ambient simple shear flow. In both cases there are fore-aft symmetric open and closed…
We analyze the linear stability of monoclinal traveling waves on a constant incline, which connect uniform flowing regions of differing depths. The classical shallow-water equations are employed, subject to a general resistive drag term.…
Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows are…