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

该奖项支持西北大学的摩西·马塔隆教授与洛桑联邦理工学院(EPFL)数学系的Philippe Metzener教授合作研究流体力学。他们的研究目标是从根本上了解液体中粘度强烈依赖于温度的不稳定的基本机制。他们将详细研究不稳定的两个重要物理机制：流体层从下加热时产生的热不稳定，以及剪切不稳定。合作者将应用数学方面的优势互补到拟议的研究中，该研究涉及数学建模、数学分析和数值计算。马塔隆教授的长处在于数学分析。他在渐近和微扰方法方面有专长，这些方法来自于燃烧问题和化学反应流动问题的数学建模。梅茨纳教授对对流问题有丰富的研究经验，他和他的研究小组具有很强的计算和数值技能。大多数以前关于流体流动不稳定性的工作都假定流体中的粘度是恒定的。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，不稳定性将被修正。这在许多现实世界的系统中都是如此，从地球表面以下的岩浆运动到具有重要工业意义的聚合物的加工。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.