Related papers: Convection in a Single Column -- Modelling, Algori…
We study a single column model of moist convection in the atmosphere. We state the conditions for it to represent a stable steady state. We then evolve the column by subjecting it to an upward displacement which can release instability,…
A single-column model run under the weak temperature gradient approximation, a parameterization of large-scale dynamics appropriate for the tropical atmosphere, is shown to have multiple stable equilibria. Under conditions permitting…
Raylaigh-Benard convection is one of the most well-studied models in fluid mechanics. Atmospheric convection, one of the most important components of the climate system, is by comparison complicated and poorly understood. A key attribute of…
Condensable species are crucial in shaping planetary climate. A wide range of planetary climate systems involve understanding non-dilute condensable substances and their influence on climate dynamics. There has been progress on large-scale…
Mesoscale convection covers an intermediate scale range between small-scale turbulence and the global organization of the convection flow. It is often characterized by an order of the convection patterns despite very high Rayleigh numbers…
A mathematical model is developed to describe column adsorption when the contaminant constitutes a significant amount of the fluid. This requires modelling the variation of pressure and velocity, in addition to the usual…
Multi-fluid models have recently been proposed as an approach to improving the representation of convection in weather and climate models. This is an attractive framework as it is fundamentally dynamical, removing some of the assumptions of…
The effect caused by the presence of a number of distinct time scales in a simple stochastic model for the Earth's atmosphere temperature fluctuations is studied. The model is described by a dissipative dynamics consisting of a set of…
Starting from the balance equations of mass, momentum and energy we formulate an integral 1D model for a poly-disperse mixture injected in the atmosphere. We write all the equations, either in their most general formulation or in the more…
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…
Despite all advances in multi-dimensional hydrodynamics, investigations of stellar evolution and stellar pulsations still depend on one-dimensional computations. The present work devises an alternative to the mixing length theory or…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
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 study shallow moist Rayleigh-Benard convection in the Boussinesq approximation in three-dimensional direct numerical simulations. The thermodynamics of phase changes is approximated by a piecewise linear equation of state close to the…
Downscaling aims to link the behaviour of the atmosphere at fine scales to properties measurable at coarser scales, and has the potential to provide high resolution information at a lower computational and storage cost than numerical…
In order to explore the effects of climate change on atmospheric convection and the water cycle, we develop and analyse an extension of the Rainy-B\'enard model, which is itself a moist version of the Rayleigh-B\'enard model of dry…
The Boussinesq system for buoyancy driven fluids couples the momentum equation forced by the buoyancy with the convection-diffusion equation for the temperature. One fundamental issue on the Boussinesq system is the stability problem on…
Recently linear dissipative models of the Boltzmann equation have been introduced. In this work, we consider the problem of constructiing suitable hydrodynamic approximations for such models where the mean velocity and the temperature of…
Operational weather forecasting models have advanced for decades on both the explicit numerical solvers and the empirical physical parameterization schemes. However, the involved high computational costs and uncertainties in these existing…
This paper presents a comprehensive mathematical model of a servopneumatic system, aimed at its consolidation in literature. The work exploits system's friction forces, temperature and pressure evolution, heat transfer, leakage between…