Accession Number : AD0718308

Title :   A Numerical Investigation of Finite-Amplitude Disturbances in a Plane Poiseuille Flow.

Descriptive Note : Doctoral thesis,

Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF

Personal Author(s) : O'Brien,George Donoghue

Report Date : JUN 1970

Pagination or Media Count : 208

Abstract : A consistent and stable finite-difference approximation of the vorticity transport equations was applied to a plane Poiseuille flow with spatially periodic disturbances of finite amplitude. By application of the discrete Fourier transform to the solution of a Poisson equation, significant improvements in the speed and accuracy of the calculations were obtained. Numerical tests indicate that the usual iterative schemes are inadequate if a large number of mesh points are employed. The effect of mesh size was determined by extensive calculations based on a consistent second-order representation of the linear eigenvalue problem. The results indicate that a fine mesh is required to accurately represent the behavior of even the large-scale unstable motions. The stability and accuracy of the present formulation was demonstrated, in the linear range, by comparison with the established results of the linear theory. Calculations in the non-linear range, at a moderate value of the Reynolds number, indicate the existence of an equilibrium state. The calculated values of the mean spectral density of kinetic energy are consistent with the exponential law predicted by Kraichnan for two-dimensional turbulence. The program, developed in this investigation, provides a means, of demonstrated accuracy, for the extensive investigation of two dimensional turbulence in a shear flow. (Author)

Descriptors :   (*LAMINAR FLOW, NUMERICAL ANALYSIS), (*TURBULENCE, TWO DIMENSIONAL FLOW), REYNOLDS NUMBER, EQUATIONS OF MOTION, STABILITY, KINETIC ENERGY, SHEAR STRESSES, THESES

Subject Categories : Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE