Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Simple System for Moist Convection: the Rainy-Benard Model
71
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 atmospheric convection is the buoyancy source provided by the condensation of water vapour, but the presence of radiation, compressibility, liquid water and ice further complicate the system and our understanding of it. In this paper we present an idealized model of moist convection by taking the Boussinesq limit of the ideal gas equations and adding a condensate that obeys a simplified Clausius--Clapeyron relation. The system allows moist convection to be explored at a fundamental level and reduces to the classical Rayleigh-Benard model if the latent heat of condensation is taken to be zero. The model has an exact, Rayleigh-number independent `drizzle solution in which the diffusion of water vapour from a saturated lower surface is balanced by condensation, with the temperature field (and so the saturation value of the moisture) determined self-consistently by the heat released in the condensation. This state is the moist analogue of the conductive solution in the classical problem. We numerically determine the linear stability properties of this solution as a function of Rayleigh number and a nondimensional latent-heat parameter. We also present a number of turbulent solutions.
rate research
Read More
This study presents a new formulation for the norms and scalar products used in tangent linear or adjoint models to determine forecast errors and sensitivity to observations and to calculate singular vectors. The new norm is derived from the concept of moist-air available enthalpy, which is one of the availability functions referred to as exergy in general thermodynamics. It is shown that the sum of the kinetic energy and the moist-air available enthalpy can be used to define a new moist-air squared norm which is quadratic in: 1) wind components; 2) temperature; 3) surface pressure; and 4) water vapor content. Preliminary numerical applications are performed to show that the new weighting factors for temperature and water vapor are significantly different from those used in observation impact studies, and are in better agreement with observed analysis increments. These numerical applications confirm that the weighting factors for water vapor and temperature exhibit a large increase with height (by several orders of magnitude) and a minimum in the middle troposphere, respectively.
Rayleigh-Benard convection (RBC) is a fundamental problem of fluid dynamics, with many applications to geophysical, astrophysical, and industrial flows. Understanding RBC at parameter regimes of interest requires complex physical or numerical experiments. Numerical simulations require large amounts of computational resources; in order to more efficiently use the large numbers of processors now available in large high performance computing clusters, novel parallelisation strategies are required. To this end, we investigate the performance of the parallel-in-time algorithm Parareal when used in numerical simulations of RBC. We present the first parallel-in-time speedups for RBC simulations at finite Prandtl number. We also investigate the problem of convergence of Parareal with respect to to statistical numerical quantities, such as the Nusselt number, and discuss the importance of reliable online stopping criteria in these cases.
A simple analytical/numerical model has been developed for computing the evolution, over periods of up to a few hours, of the current and temperature profile in the upper layer of the ocean. The model is based upon conservation laws for heat and momentum, and employs an eddy diffusion parameterisation which is dependent on both the wind speed and the wind stress applied at the sea surface. Other parameters such as the bulk-skin surface temperature difference and CO$_2$ flux are determined by application of the Molecular Oceanic Boundary Layer Model (MOBLAM) of Schluessel and Soloviev. A similar model, for the current profile only, predicts a temporary increase in wave breaking intensity and decrease in wave height under conditions where the wind speed increases suddenly, such as, for example, during gusts and squalls. The model results are compared with measurements from the lagrangian Skin Depth Experimental Profiler (SkinDeEP) surface profiling instrument made during the 1999 MOCE-5 field experiment in the waters around Baja California. SkinDeEP made repeated profiles of temperature within the upper few metres of the water column. Given that no tuning was performed in the model, and that the model does not take account of stratification, the results of the model runs are in rather good agreement with the observations. The model may be suitable as an interface between time-independent models of processes very near the surface, and larger-scale three-dimensional time-dependent ocean circulation models. A straightforward extension of the model should also be suitable for making time-dependent computations of gas concentration in the near-surface layer of the ocean.
We describe and illustrate a mechanism whereby convective aggregation and eastward propagating equatorial disturbances, similar in some respects to the Madden--Julian oscillation, arise. We construct a simple, explicit system consisting only of the shallow water equations plus a humidity variable; moisture enters via evaporation from a wet surface, is transported by the flow and removed by condensation, so providing a mass source to the height field. For a broad range of parameters the system is excitable and self-sustaining, even if linearly stable, with condensation producing convergence and gravity waves that, acting together, trigger more condensation. On the equatorial beta-plane the convection first aggregates near the equator, generating patterns related to those in the Matsuno--Gill problem. However, the pattern is unsteady and more convection is triggered on its eastern edge, leading to a precipitating disturbance that progresses eastward. The effect is enhanced by westward prevailing winds that increase the evaporation east of the disturbance. The pattern is confined to a region within a few deformation radii of equator because here the convection can best create the convergence needed to organize into a self-sustaining pattern. Formation of the disturbance preferentially occurs where the surface is warmer and sufficient time (a few tens of days) must pass before conditions arise that enable the disturbance to reform, as is characteristic both of excitable systems and the MJO itself. The speed of the disturbance depends on the efficiency of evaporation and the heat released by condensation, and is typically a few meters per second, much less than the Kelvin wave speed.
Calculations of entropy fluxes and production rate have been evaluated with some success to study atmospheric processes. However, recurring questions arise as to how best to take into account entropy flux due to radiation, for example. This article raises another kind of question: how to define the entropy of the atmosphere itself, which is composed of variable proportions of dry air (nitrogen, oxygen, argon, etc.) and water (vapour, liquid, ice). The specific values of the entropy for such a variable composition system depend on the reference values of its components. Most of the current definitions are based on entropies set at zero for dry air and liquid water at zero degrees Celsius. Differently, the third law of thermodynamics assumes that the entropy of all species cancels out for the more stable solid state at the zero of absolute temperatures. In this paper, we analyze the possible consequences of this absolute definition of entropy of moist air on the calculation of entropy fluxes. The impacts of moisture are significant and these new calculation methods seem to be able to modify the budgets of atmospheric entropy, with possible impacts on the nature of the equilibrium of the atmosphere resulting from entropic imbalances induced by radiations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
