Related papers: Convection in a Single Column -- Modelling, Algori…
The evolution of three-dimensional, cellular convective flows in a plane horizontal layer of a Boussinesq fluid heated from below is well studied. Here we review results from the investigation of this system as well as a number of related…
Buoyancy-induced (Rayleigh-Benard) convection of a fluid between two horizontal plates is a central paradigm for studying the transition to complex spatiotemporal dynamics in sustained nonequilibrium systems. To improve the analysis of…
Clouds play a central role in climate physics by interacting with precipitation, radiation, and circulation. Despite being a fundamental issue in convective organization, the self-aggregation of clouds lacks a theoretical explanation due to…
Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The…
We present a simplified model of the atmosphere of a terrestrial planet as an open two-dimensional system described by an ideal gas with velocity $\vec{v}$, density $\rho$ and temperature $T$ fields. Starting with the Chern-Simons equations…
Our goal is to investigate fundamental properties of the system of internally cooled convection. The system consists of an upward thermal flux at the lower boundary, a mean temperature lapse-rate and a constant cooling term in the bulk with…
Interaction of particles of dust with vortex convective flows is under theoretical consideration. It is assumed that the volume fraction of solid phase is small, variations of density due to nonuniform distribution of particles and those…
We present the results of a very large aspect ratio (42.6) numerical simulation of fully compressible turbulent convection in a polytropic atmosphere, and focus on the properties of large-scale flows. Mesoscale patterns dominate the…
We study an atmospheric column and its discretization. Because of numerical considerations, the column must be divided into two parts: (1) a surface layer, excluded from the computational domain and parameterized, and (2) the rest of the…
The representations of atmospheric moist convection in general circulation models have been one of the most challenging tasks due to its complexity in physical processes, and the interaction between processes under different time/spatial…
We deal with asymptotic analysis for the derivation of partial differential equation models for geophysical flows in the earth's atmosphere with moist process closures, and we study their mathematical properties. Starting with the…
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…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
We are concerned with a one dimensional flow of a compressible fluid which may be seen as a simplification of the flow of fluid in a long thin pipe. We assume that the pipe is on one side ended by a spring. The other side of the pipe is let…
This study proposes introducing convex optimization to find initial perturbations of atmospheric states to realize specified changes in subsequent weather. In the proposed method, we formulate and solve an inverse problem to find effective…
We present high resolution numerical simulations of convection in multiphase flows (boiling) using a novel algorithm based on a Lattice Boltzmann method. We first validate the thermodynamical and kinematical properties of the algorithm.…
The main components of an atmospheric model for numerical weather prediction are the dynamical core, which describes the resolved flow, and the physical parametrisations, which capture the effects of unresolved processes. Additionally,…
We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
In this paper we propose a continuous data assimilation (downscaling) algorithm for a two-dimensional B\'enard convection problem. Specifically we consider the two-dimensional Boussinesq system of a layer of incompressible fluid between two…