ATTEMPTS AT DERIVATION OF TRANSITION FROM LAMINAR INTO TURBULENT FLOW ALONG A FLAT PLATE.
NEW YORK UNIV N Y COLL OF DENTISTRY
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Research has resulted in the derivation of a numerical scheme for the solution of the complete Navier-Stokes equations for two-dimensional time-dimensional time-independent viscous incompressible flow, as applied to the problem of the development of turbulence in the laminar boundary layer on a flat plate. The basic equations are reduced to a single quasi-linear vorticity-transport equation plus a Poisson equation these are then written in finite-difference form. The solution of the difference system comprises a semi-implicit scheme for the quasi-linear equation together with an extrapolated line-Liebmann iteration method for the linear Poisson analog. Solutions for the two cases investigated very low amplitude linear and very high amplitude nonlinear are presented and discussed. The numerical scheme is demonstrated to be stable and capable of generating solutions which exhibit major theoretical andor experimentally-observable features for each of the two cases. Author