Related papers: The Boussinesq approximation in rapidly rotating f…
We study the Boussinesq approximation for the incompressible Euler equations using Lagrangian description. The conditions for the Lagrangian fluid map are derived in this setting, and a general method is presented to find exact fluid flows…
The theory of internal waves between two layers of immiscible fluids is important both for its applications in oceanography and engineering, and as a source of interesting mathematical model equations that exhibit nonlinearity and…
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…
A one-dimensional long-wave model of an unsteady three-layer flow of a stratified fluid under a lid is proposed, taking into account turbulent mixing in the intermediate layer. In the Boussinesq approximation, the equations of motion are…
This paper presents a joint theoretical and numerical study of a stochastic version of the compressible Navier-Stokes equations within the location uncertainty (LU) framework, applied to problems related to upper ocean vertical mixing. This…
The existence of outflow in accretion flows is confirmed by observations and magnetohydrodynamics (MHD) simulations. In this paper, we study outflows of accretion flows in the presence of resistivity and toroidal magnetic field. The…
Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…
We present hydrodynamic equations of compressible fluids in gravity as a generalization of those in the Boussinesq approximation used for nearly incompressible fluids. They account for adiabatic processes taking place throughout the cell…
Linear stability analysis has proven to be a useful tool in the analysis of dominant coherent structures, such as the von K\'{a}rm\'{a}n vortex street and the global spiral mode associated with the vortex breakdown of swirling jets. In…
In this paper, we consider dynamics defined by the Navier-Stokes equations in the Oberbeck-Boussinesq approximation in a two dimensional domain. This model of fluid dynamics involve fundamental physical effects: convection, and diffusion.…
This study investigates the dynamics of incompressible fluid flows through quaternionic variables integrated within Sobolev-Besov spaces. Traditional mathematical models for fluid dynamics often employ Sobolev spaces to analyze the…
Considered herein are a number of variants of the Boussinesq type systems modeling surface water waves. Such equations were derived by different authors to describe the two-way propagation of long gravity waves. A question of existence of…
We introduce a continuous (downscaling) data assimilation algorithm for the 2D B\'enard convection problem using vorticity or local circulation measurements only. In this algorithm, a nudging term is added to the vorticity equation to…
A study of convection in a circular two dimensional cell is presented. The system is heated and cooled at two diametrically opposed points on the edge of the circle, which are parallel or anti-parallel to gravity. The latter's role in the…
We solve the two-dimensional hydrodynamic equations of hot accretion flow in the presence of the thermal conduction. The flow is assumed to be in steady-state and axisymmetric, and self-similar approximation is adopted in the radial…
We present the results of numerical integrations yielding the structure of and meridional flow in axisymmetric thin viscous accretion disk models. The solutions are obtained by simplifying and approximating first the equations, using…
By taking into account photon absorption, we investigate the vertical structure of accretion flows with comparable radiation and gas pressures. We consider two separate energy equations for matter and radiation in the diffusion limit. In…
We analyse the tumbling of small non-spherical, axisymmetric particles in random and turbulent flows. We compute the orientational dynamics in terms of a perturbation expansion in the Kubo number, and obtain the tumbling rate in terms of…
Entangled magnetic fields entering into an accretion flow would very soon be stretched into a dominant toroidal component due to strong differentially rotating motion inside the accretion disc. This is particularly true for weakly viscous,…
In this paper we found, by means of numerical simulations, a transition in the oscillatory character of the flow field for a particular combination of buoyancy and spacing in an array of six circular cylinders at a Reynolds number of 100…