QG-DL: Dynamics of a diabatic layer in the quasi-geostrophic framework

Quasi-geostrophic (QG) theory describes the dynamics of synoptic scale flows in the trophosphere that are balanced with respect to both acoustic and internal gravity waves. Within this framework, effects of (turbulent) friction near the ground are usually represented by Ekman Layer theory. The troposphere covers roughly the lowest ten kilometers of the atmosphere while Ekman layer heights are typically just a few hundred meters. However, this two-layer asymptotic theory does not explicitly account for substantial changes of the potential temperature stratification due to diabatic heating associated with cloud formation or with radiative and turbulent heat fluxes, which, in the middle latitudes, can be particularly important in about the lowest three kilometers. To address this deficiency, this paper extends the classical QG–Ekman layer model by introducing an intermediate, dynamically and thermodynamically active layer, called the “diabatic layer” (DL) from here on. The flow in this layer is also in acoustic, hydrostatic, and geostrophic balance but, in contrast to QG flow, variations of potential temperature are not restricted to small deviations from a stable and time independent background stratification. Instead, within the diabatic layer, diabatic processes are allowed to affect the leading-order stratification. As a consequence, the diabatic layer modifies the pressure field at the top of the Ekman layer, and with it the intensity of Ekman pumping seen by the quasi-geostrophic bulk flow. The result is the proposed extended quasi-geostrophic three-layer QG-DL-Ekman model for mid-latitude (dry and moist) dynamics

Coastal Tropical Convection in a Stochastic Modeling Framework

Recent research has suggested that the overall dependence of convection near coasts on large-scale atmospheric conditions is weaker than over the open ocean or inland areas. This is due to the fact that in coastal regions convection is often supported by meso-scale land-sea interactions and the topography of coastal areas. As these effects are not resolved and not included in standard cumulus parametrization schemes, coastal convection is among the most poorly simulated phenomena in global models. To outline a possible parametrization framework for coastal convection we develop an idealized modeling approach and test its ability to capture the main characteristics of coastal convection. The new approach first develops a decision algorithm, or trigger function, for the existence of coastal convection. The function is then applied in a stochastic cloud model to increase the occurrence probability of deep convection when land-sea interactions are diagnosed to be important. The results suggest that the combination of the trigger function with a stochastic model is able to capture the occurrence of deep convection in atmospheric conditions often found for coastal convection. When coastal effects are deemed to be present the spatial and temporal organization of clouds that has been documented form observations is well captured by the model. The presented modeling approach has therefore potential to improve the representation of clouds and convection in global numerical weather forecasting and climate models.Comment: Manuscript submitted for publication in Journal of Advances in Modeling Earth System

Models for tropical climate dynamics: waves, clouds, and precipitation

This book is a survey of the research work done by the author over the last 15 years, in collaboration with various eminent mathematicians and climate scientists on the subject of tropical convection and convectively coupled waves. In the areas of climate modelling and climate change science, tropical dynamics and tropical rainfall are among the biggest uncertainties of future projections. This not only puts at risk billions of human beings who populate the tropical continents but it is also of central importance for climate predictions on the global scale. This book aims to introduce the non-expert readers in mathematics and theoretical physics to this fascinating topic in order to attract interest into this difficult and exciting research area. The general thyme revolves around the use of new deterministic and stochastic multi-cloud models for tropical convection and convectively coupled waves. It draws modelling ideas from various areas of mathematics and physics and used in conjunction with state-of-the-art satellite and in-situ observations and detailed numerical simulations. After a review of preliminary material on tropical dynamics and moist thermodynamics, including recent discoveries based on satellite observations as well as Markov chains, the book immerses the reader into the area of models for convection and tropical waves. It begins with basic concepts of linear stability analysis and ends with the use of these models to improve the state-of-the-art global climate models. The book also contains a fair amount of exercises that makes it suitable as a textbook complement on the subject

Modélisation asymptotique pour la simulation aux grandes échelles de la combustion turbulente prémélangée

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur

Unification of the mathematical model of elastic perfectly plastic solids: a convex analysis approach

A new mathematical formulation for the constitutive laws governing elastic perfectly plastic materials is proposed here. In particular, it is shown that the elastic strain rate and the plastic strain rate form an orthogonal decomposition with respect to the tangent cone and the normal cone of the yield domain. It is also shown that the stress rate can be seen as the projection on the tangent cone of the elastic stress tensor. This approach leads to a coherent mathematical formulation of the elasto-plastic laws and simplifies the resulting system for the associated flow evolution equations. The cases of one or two yields functions are treated in detail. The practical examples of the von Mises and Tresca yield criteria are worked out in detail to demonstrate the usefulness of the new formalism in applications