Related papers: On stability estimates for the inviscid Boussinesq…
In this paper we study the Cauchy problem for the two-dimensional (2D) incompressible Boussinesq equations with fractional Laplacian dissipation and thermal diffusion. Invoking the energy method and several commutator estimates, we get the…
The equations of motion describing buoyant fluids are often simplified using a set of approximations proposed by J. Boussinesq one century ago. To resume, they consist in assuming constant fluid properties, incompressibility and…
In this paper, we consider the Boussinesq equations with magnetohydrodynamics convection in the domain $\mathbb{T} \times \mathbb{R}$ and establishes the nonlinear stability of the Couette flow $(\mathbf{u}_{sh} = (y,0), \mathbf{b}_{sh} =…
The evolution of a localized vortex in stably stratified flow, within the Boussinesq approximation, is analyzed using the fluid impulse concept. The set of equations describing the temporal development of the fluid impulse has an…
In this article we consider weak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group. We examine both the viscous and inviscid cases. For the case of viscous…
Moist stratified turbulence is studied in a two-dimensional Boussinesq system influenced by condensation and evaporation. The problem is set in a periodic domain and employs simple evaporation and condensation schemes, wherein both the…
The main objective of this article is to study the nonlinear stability and dynamic transitions of the basic (zonal) shear flows for the three-dimensional continuously stratified rotating Boussinesq model. The model equations are fundamental…
This paper investigates the stability and large-time behavior of solutions to the rotating Boussinesq system under the influence of a general gravitational potential $\Psi$, which is widely used to model the dynamics of stratified…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
Shear-thinning fluids flowing through pipes are crucial in many practical applications, yet many unresolved problems remain regarding their turbulent transition. Using highly robust numerical tools for the Carreau-Yasuda model, we…
In this paper, we establish linear enhanced dissipation results for the three-dimensional Boussinesq equations around a stably stratified Couette flow, in the viscous and thermally diffusive setting. The dissipation rates are faster…
The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid…
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…
A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…
In this paper, we investigate the instability of the trivial steady states to the incompressible viscous fluid with Navier-slip boundary conditions. For the linear instability, the existence of infinitely many normal mode solutions to the…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
Symmetric instability has broad applications in geophysical and planetary fluid dynamics. It plays a crucial role in the formation of mesoscale rainbands at mid-latitudes on Earth, instability in the ocean's mixed layer, and slantwise…
We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence…
Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial…
New results are obtained for global regularity and long-time behavior of the solutions to the 2D Boussinesq equations for the flow of an incompressible fluid with positive viscosity and zero diffusivity in a smooth bounded domain. Our first…