Related papers: SQG Point Vortex Dynamics with Order Rossby Correc…
In this paper, we systematically study the existence, asymptotic behaviors, uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds for the generalized surface quasi-geostrophic (gSQG) equation.…
Numerical turbulence simulations typically involve parameterizations such as Large Eddy Simulations (LES). Applications to geophysical flows, especially ocean flows, are further complicated by the presence of complex topography and interior…
In this work, we discuss the long-time behavior of non-rotating quasi-2D viscous flows over topographies. We develop a novel theoretical and numerical framework for the analysis of these flows, derived as a dimensional reduction of the 3D…
The aim of this work is to shed light by revisiting - through the kernel-wave (KW) perspective - the breakdown of a quasi-geostrophic (QG) mixing layer (or vortex strip/filament) in atmosphere under the influence of a background shear. The…
In this paper, we compute the sectional curvature of the quantomorphism group $\mathcal{D}_q(M)$ whose geodesic equation is the quasi-geostrophic (QG) equation in geophysics and oceanography, for flows with a stream function depending on…
Hamiltonian and Lagrangian formulations for the two-dimensional quasi-geostrophic equations linearized about a zonally-symmetric basic flow are presented. The Lagrangian and Hamiltonian exhibit an infinite U(1) symmetry due to the absence…
For settling the problem with rotating turbulence modelling, a quasi-dynamic one-equation subgrid-scale (SGS) model is proposed in this paper. Considering the key role of the joint cascade of kinetic energy and helicity in rotating…
In this paper, the averaging principle for quasi-geostrophic motions with rapidly oscillating forcing is proved, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and…
In this paper, we study the existence of rotating and traveling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation. The solutions are obtained by maximization of the energy over the set of rearrangements of a fixed…
The use of machine learning to represent subgrid-scale (SGS) dynamics is now well established in weather forecasting and climate modelling. Recent advances have demonstrated that SGS models trained via ``online'' end-to-end learning --…
We search for non-trivial relativistic solutions of the hydrodynamic equations with quasi-inertial flows such as in the Bjorken-like models. The problem is analyzed in general and the known results are reproduced by a method proposed. A new…
We study the Boussinesq approximation for rapidly rotating stably-stratified fluids in a three dimensional infinite layer with either stress-free or periodic boundary conditions in the vertical direction. For initial conditions satisfying a…
We use contour dynamics to derive equations of motion for infinite planar surface quasi-geostrophic (SQG) fronts, and show that it leads to the same result as a regularization procedure introduced previously by Hunter and Shu (2018).
We discuss the applicability of quasilinear-type approximations for a turbulent system with a large range of spatial and temporal scales. We consider a paradigm fluid system of rotating convection with a vertical and horizontal temperature…
We prove non-uniqueness of weak solutions to the forced $\alpha$-SQG equation with Sobolev regularity $W^{s,p}$ in the supercritical regime $s < \alpha + \frac{2}{p}$, covering the 2D Euler equation ($\alpha = 0$), the Surface…
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an elaborate scheme for building global quasiperiodic solutions…
The macroscale structure and microscale fluctuation statistics of late-time asymptotic steady state flows in cylindrical geometries is studied using the methods of equilibrium statistical mechanics. The axisymmetric assumption permits an…
We derive statistical equilibrium solutions of the truncated inviscid surface quasi-geostrophic (SQG) equations, and verify the validity of these solutions at late times in numerical simulations of the truncated SQG equations. The results…
We review recent advances in understanding singularity and small scales formation in solutions of fluid dynamics equations. The focus is on the Euler and surface quasi-geostrophic (SQG) equations and associated models.
We propose and analyze numerical schemes for the gradient flow of $Q$-tensor with the quasi-entropy. The quasi-entropy is a strictly convex, rotationally invariant elementary function, giving a singular potential constraining the…