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The aim of this communication is to present a simplified, yet rigorous, deduction of the Boussinesq approximated governing equations for buoyant flows. In order to carry out the core deduction procedure, a simplified version of the manifold…
This short note provides explicit solutions to the linearized Boussinesq equations around the stably stratified Couette flow posed on $\mathbb{T}\times\mathbb{R}$. We consider the long-time behavior of such solutions and prove inviscid…
The mixed convection flow in a plane channel with adiabatic boundaries is examined. The boundaries have an externally prescribed relative velocity defining a Couette-like setup for the flow. A stationary flow regime is maintained with a…
Vertical loads acting on the surface of a half-space made of discrete and elastic particles are supported by a network of force chains that changes with the specific realization of the packing. These force chains can be transformed into…
In this manuscript, we consider the $3$D Boussinesq equations for stably stratified fluids with the horizontal viscosity and thermal diffusivity and investigate the large time behavior of the solutions. Making use of the anisotropic…
Microscopic instability and macroscopic flow pattern resulting from colliding plasmas are studied analytically in support of laboratory experiments. The plasma flows are assumed to stream radially from two separate centers. In a…
We consider a class of time-homogeneous diffusion processes on $\mathbb{R}^{n}$ with common invariant measure but varying volatility matrices. In Euclidean space, we show via stochastic control of the diffusion coefficient that the…
The present study examines the linear instability characteristics of double-diffusive mixed convective flow in a vertical channel with viscosity stratification. The viscosity of the fluid is modelled as an exponential function of…
The quasi-geostrohpic (QG) equation has been used to capture the asymptotic dynamics of the rotating stratified Boussinesq flows in the regime of strong stratification and rapid rotation. In this paper, we establish the invalidity of such…
A multiscale reduced description of turbulent free shear flows in the presence of strong stabilizing density stratification is derived via asymptotic analysis of the Boussinesq equations in the simultaneous limits of small Froude and large…
We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model, and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic…
We present a complete analysis of the problem of convection-diffusion in low Re, 2-dimensional flows with distributions of singularities, such as those found in open-space microfluidics and in groundwater flows. Using Boussinesq…
We probe the diffusive motion of particles in slowly sheared three dimensional granular suspensions. For sufficiently large strains, the particle dynamics exhibits diffusive Gaussian statistics, with the diffusivity proportional to the…
A low diffusive flux difference splitting based kinetic scheme is developed based on a discrete velocity Boltzmann equation, with a novel three velocity model. While two discrete velocities are used for upwinding, the third discrete…
The stability of density-stratified viscous Taylor-Couette flows is considered using the Boussinesq approximation but without any use of the short-wave approximation. The flows which are unstable after the Rayleigh criterion (\hat \mu<\hat…
The influence of a small relative density difference on the displacement of two miscible liquids is studied experimentally in transparent 2D networks of micro channels. Both stable displacements in which the denser fluid enters at the…
This paper develops a two-stage stochastic model to investigate evolution of random fields on the unit sphere $\bS^2$ in $\R^3$. The model is defined by a time-fractional stochastic diffusion equation on $\bS^2$ governed by a diffusion…
We consider a two-dimensional, incompressible, inviscid fluid with variable density, subject to the action of gravity. Assuming a stable equilibrium density profile, we adopt the so-called Boussinesq approximation, which neglects density…
A novel deep learning technique called Physics Informed Neural Networks (PINNs) is adapted to study steady groundwater flow in unconfined aquifers. This technique utilizes information from underlying physics represented in the form of…
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…