Plenary
Lecture
Linear and Weakly Nonlinear Instability of Fluid Flows
Professor Andrei Kolyshkin
Department of Engineering Mathematics
Riga Technical University
Latvia
Email:
andrejs.koliskins@rbs.lv
Abstract: Linear stability theory is widely used
in fluid mechanics to predict when a particular base
flow becomes unstable. The critical values of the
parameters of the problem (for example, the critical
Reynolds numbers) are usually calculated by solving the
corresponding linearized eigenvalue problem. The
structure of the critical motion which takes place just
above the threshold can also be analyzed by means of the
linear stability theory. However, the evolution of the
most unstable disturbance above the threshold cannot be
described by the linear theory.
Weakly nonlinear theories are used in such cases to
derive an amplitude evolution equation (or a system of
evolution equations). The coefficients of such equations
(one example is the complex GinzburgLandau equation)
can be calculated by means of the method of multiple
scales.
In this plenary talk we discuss both linear and weakly
nonlinear models of fluid motion in detail. Two examples
are considered: stability of shallow water flows and
stability of transient rapidly decelerated flow in a
circular pipe. The results of joint work with Prof. M.S.
Ghidaoui are discussed.
Brief Biography of the Speaker:
Andrei Kolyshkin received his undergraduate degree in
Applied Mathematics in 1976 at the Riga Technical
University. In 1981 he received a Ph.D in differential
equations and mathematical physics at the University of
St. Petersburg. Andrei Kolyshkin is currently a full
professor at the Department of Engineering Mathematics
at the Riga Technical University. His current research
interests include investigation of stability problems in
fluid mechanics with applications to openchannel flows
and transient flows in hydraulic systems and
mathematical models for eddy current testing. He is the
coauthor of three monographs published by Academic
Press and CRM. Andrei Kolyshkin has participated in more
than 30 international conferences and has published more
than 50 papers in refereed journals since 1990. As a
visiting professor and visiting researcher he spent a
few years at the University of Ottawa and Hong Kong
University of Science and Technology.
