U.S.-Switzerland Cooperative Research on Instabilities in Flows with Strongly Temperature Dependent Viscosity

该奖项支持西北大学的Moshe Matalon教授与洛桑联邦理工学院数学系的Philippe Metzener教授合作进行流体动力学研究。他们研究的目标是获得对粘度强烈依赖于温度的液体不稳定性的基本机制的基本理解。他们将详细研究不稳定性的两个重要物理机制：当流体层从下面加热时产生的热不稳定性和剪切不稳定性。合作者在应用数学方面具有互补优势，涉及数学建模，数学分析和数值计算。马塔隆教授的强项是数学分析。他的专长是渐近和摄动方法，这些方法来源于燃烧问题和化学反应流动问题的数学建模。梅策纳教授在研究对流问题方面有着丰富的经验；他和他的研究小组有很强的计算和数值技能。以前关于流体流动不稳定性的大多数工作都假定流体的粘度是恒定的。虽然这产生了有用的基本信息，但人们认识到，如果粘度随温度变化，不稳定性将会改变。从地下岩浆的运动到工业上重要的聚合物的加工，在现实世界的许多系统中都是如此。因此，本研究的成果将具有广泛的应用前景。

This award supports Professor Moshe Matalon of Northwestern University to collaborate in a study of fluid dynamics with Professor Philippe Metzener of the Mathematics Department of the Ecole Polytechnique Federale de Lausanne (EPFL). The goal of their research is to gain fundamental understanding of the basic mechanisms of instability in liquids for which viscosity depends strongly on temperature. They will examine in detail two important physical mechanisms of instability: thermal instability that arises when a fluid layer is heated from below, and shear instability. The collaborators bring complementary strengths in applied mathematics to the proposed research, which involves mathematical modeling, mathematical analysis and numerical calculations. Professor Matalon's strengths are in mathematical analysis. He has expertise in asymptotic and perturbation methods derived from work on combustion problems and the mathematical modeling of chemically reacting flow problems. Professor Metzener has extensive experience studying problems of convection; he and his research group have strong computational and numerical skills. Most previous work on instabilities in fluid flows has assumed a constant viscosity in the fluid. While this has produced useful basic information, it is recognized that instabilities will be modified if the viscosity varies with temperature. Such is the case in many real world systems, ranging from the movement of magma below the surface of the earth to the processing of industrially important polymers. Thus the results of this research will have a broad range of applications.