Instantaneous Evolution of Kinetic Energy of Perturbations in Barotropic Atmosphere

Seminario del Modelación Matemática de Procesos Atmosféricos

Dr. Yuri Skiba

Abstract

 The barotropic vorticity equation describing the vortex dynamics of viscous and forced incompressible fluid on a rotating sphere is considered. This equation is also used for studying the large-scale dynamics of barotropic atmosphere. A new approach for studying the stability of perturbations to a basic flow is suggested using the equation for instantaneous evolution of the kinetic energy of perturbations. It is shown that this evolution is governed only by the symmetric part of the vorticity equation operator linearized about the basic flow. A relationship between the rate of generation of the kinetic energy of perturbations and the eigenfunctions of this operator is shown. As an illustrative example, the numerical solution of the spectral problem for such operator is discussed in the case when the basic flow is the climatic January circulation.

It should be noted that the Eliassen-Palm flux method is suitable only for analyzing special types of ideal basic flows like the climatic January circulation. Unlike this, the new stability method based on the solution of spectral problem can be applied to arbitrary steady basic state and takes into account all dissipative processes. Therefore, it is a convenient and effective tool for the instability study of stationary flows in the barotropic atmosphere.

Biographical notes Dr. Yuri Skiba

Yuri Skiba was awarded the degree of Doctor of Physics and Mathematics in 1979. He worked at the Computer Center of the USSR Academy of Sciences in Novosibirsk (1971-1985), Computer Center of the State Committee for Science and Technology, USSR Council of Ministers, Moscow (1985-1987), and Institute of Numerical Mathematics, USSR Academy of Sciences, Moscow (1987-1994). In 1989 he was awarded the scientific and educational title «Senior Scientific Researcher of the USSR». From 1988 to 1990, he worked at the Indian Institute of Technology (New Delhi), Indian Institute of Science (Bangalore) and Indian Institute of Tropical Meteorology (Pune).
Since 1992 he has worked as the Head of the laboratory of Mathematical Modeling of Atmospheric Processes at the Center for Atmospheric Sciences, UNAM University, Mexico City. He is a specialist in applied mathematics (partial differential equations, fluid dynamics, numerical methods, and pollution control). His publications include 128 articles, 9 books, 25 chapters in books, 53 articles in the proceedings of scientific conferences and 203 reviews published in Mathematical Reviews (USA). He has delivered more than 250 presentations at various international conferences and congresses. He is the member of the National System of Researchers (CONACYT, Mexico) and various scientific societies.