A Cross-Over in the Enstrophy Decay in Two-Dimensional Turbulence in a Finite Box

The numerical simulation of two-dimensional decaying turbulence in a large but finite box presented in this paper uncovered two physically different regimes of enstrophy decay. During the initial stage, the enstrophy, generated by a random Gaussian initial condition, decays as t^{-gamma} with gamma approximately 0.7-0.8. After that, the flow undergoes a transition to a gas or fluid composed of distinct vortices. Simultaneously, the magnitude of the decay exponent crosses over to gamma approximately 0.4. An exact relation for the total number of vortices, N(t), in terms of the mean circulation of an individual vortex is derived. A theory predicting that N(t) is proportional to t^{-xi} and the magnitudes of exponents gamma=2/5 and xi=4/5 is presented and the possibility of an additional very late-time cross-over to gamma=1/3 and xi=2/3 is also discussed.Comment: 11 pages, 7 figure

New classes of exact solutions of three-dimensional Navier-Stokes equations

New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are obtained. The general physical interpretation and classification of solutions is given.Comment: 11 page

Mechanics of liquids and gases

Mechanics of Liquids and Gases, Second Edition is a 10-chapter text that covers significant revisions concerning the dynamics of an ideal gas, a viscous liquid and a viscous gas.After an expanded introduction to the fundamental properties and methods of the mechanics of fluids, this edition goes on dealing with the kinetics and general questions of dynamics. The next chapters describe the one-dimensional pipe flow of a gas with friction, the elementary theory of the shock tube; Riemann's theory of the wave propagation of finite intensity, and the theory of plane subsonic and supersonic flows