Multi-point Velocity Research Articles

Statistics of nonlinear dispersive waves II multi-point velocity correlation-functions

A statistical theory of nonlinear dispersive waves is developed on the basis of the Korteweg-de Vries (KdV) equation. The asymptotic expressions of the n(≧3)-point velocity correlation-functions are derived analytically from the given initial velocity distribution. The dependence of various statistical quantities on the initial velocity distribution is investigated in detail. Finally, it is shown that the velocity correlation-functions obtained are exact stationary solutions of the hierarchy of the moment equations derived from the KdV equation.

Decay of Homogeneous Turbulence from a Given Initial State

The homogeneous turbulence problem is formulated by first specifying the multipoint velocity correlations or their spectral equivalents at an initial time. Those quantities, together with the correlation or spectral equations are then used to calculate initial time derivatives of correlations or spectra. The derivatives are in turn used in time series to calculate the evolution of turbulence quantities with time. When the problem is treated in this way, the correlation equations are closed by the initial specification of the turbulence, and no assumption is necessary for closing those equations. An exponential series, which is an iterative solution of the Navier-Stokes equations, gave much better results than a Taylor power series when used with the limited available initial data. In general, the agreement between theory and experiment was good.

Statistical Theory of Certain Distribution Functions in MHD Turbulent Flow for Velocity and Concentration Undergoing A First Order Reaction in a Rotating System

Bangladesh J. Sci. Ind. Res. 46(1), 54-59, 2011

Distribution Functions in the Statistical Theory of Turbulence

A hierarchy of coupled equations for multipoint turbulent velocity distribution functions is derived. These equations resemble the Bogoliubov-Born-Green-Kirkwood-Yvon equations of kinetic gas theory. The properties of the distribution functions and the equations are discussed and compared with kinetic theory.