322 research outputs found
Passive Tracer Dispersion with Random or Periodic Source
In this paper, the author investigates the impact of external sources on the
pattern formation and long-time behavior of concentration profiles of passive
tracers in a two-dimensional shear flow. It is shown that a time-periodic
concentration profile exists for time-periodic external source, while for
random source, the distribution functions of all concentration profiles weakly
converge to a unique invariant measure (like a stationary state in
deterministic systems) as time goes to infinityComment: LaTeX file, 9 page
Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations
The article is devoted to the study of non-autonomous Navier-Stokes
equations. First, the authors have proved that such systems admit compact
global attractors. This problem is formulated and solved in the terms of
general non-autonomous dynamical systems. Second, they have obtained conditions
of convergence of non-autonomous Navier-Stokes equations. Third, a criterion
for the existence of almost periodic (quasi periodic,almost automorphic,
recurrent, pseudo recurrent) solutions of non-autonomous Navier-Stokes
equations is given. Finally, the authors have derived a global averaging
principle for non-autonomous Navier-Stokes equations.Comment: J. Dynamics and Diff. Eqns., in press, 200
Ergodicity of Stochastically Forced Large Scale Geophysical Flows
We investigate the ergodicity of 2D large scale quasigeostrophic flows under
random wind forcing. We show that the quasigeostrophic flows are ergodic under
suitable conditions on the random forcing and on the fluid domain, and under no
restrictions on viscosity, Ekman constant or Coriolis parameter. When these
conditions are satisfied, then for any observable of the quasigeostrophic
flows, its time average approximates the statistical ensemble average, as long
as the time interval is sufficiently long
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