Threedimensional effects of the linear hydrodynamic instability on the plane wake flow
Abstract
The LINEAR hydrodynamic stability for plane shear flows considers planar disturbances superimposed over the main flow. Squire transforms justify the use of disturbances of this kind in order to detect the critical Reynolds number. In this way the behavior of the onset of oscillations of the flow field is well described, especially for flows with a profile of the basic velocity with points of inflexion like wake profile flows. A tentative approach is pursued for the study of the behavior of the flow for a Reynolds number slightly greater than the critical value using the Squire transforms to obtain new solutions of the flow field, with disturbances neither amplified nor damped but of threedimensional character. The twodimensional mode is obtained as an eigenfunction of the OrrSommerfeld equation by an already tested Galerkin procedure. Hence the Poisson equation is solved in order to obtain the pressure field of the disturbance. The presence of more than one mode is analyzed with their influence on the two and threedimensional organized structures of large eddies. Numerical and experimental results are compared.
 Publication:

Archiv of Mechanics, Archiwum Mechaniki Stosowanej
 Pub Date:
 1987
 Bibcode:
 1987ArMeS..39...41M
 Keywords:

 Computational Fluid Dynamics;
 Flow Stability;
 Incompressible Flow;
 Parallel Flow;
 Shear Flow;
 Three Dimensional Flow;
 Galerkin Method;
 NavierStokes Equation;
 OrrSommerfeld Equations;
 Poisson Equation;
 Reynolds Number;
 Wave Functions;
 Fluid Mechanics and Heat Transfer