Grooves on a wetted surface is an effective and in-expensive way to control the hydrodynamic stability, requiring, however, to know dependencies of the flow stability characteristics (the linear end energy critical Reynolds numbers and the maximum amplification of mean kinetic energy density of disturbance) on groove parameters. In this monograph, using Poiseuille flow in a streamwise grooved channel as a prototype, the mathematical statement of the computational problems of the stability characteristics is given for flows over streamwise grooved surfaces and numerical algorithms for their solution are described and justified. Computed stability characteristics at different values of groove parameters are given and discussed. Theoretical explanation of their difference from the ones for flow in plane channel is given. The monograph is directed for engineers and scientific researchers, specialists in hydrodynamic and numerical mathematics. It may be used as an additional material for traditional courses on hydrodynamic stability and on numerical methods for studying of stability of autonomic systems.
Keywords:
stability of shear flows, Poiseuille flow, grooves, critical Reynolds numbers, maximum amplification of disturbance energy
