Accession Number : ADP004050

Title :   Secondary Instability of Shear Flows,

Corporate Author : VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF ENGINEERING SCIENCE AND MECHANICS

Personal Author(s) : Herbert,T.

Report Date : JUN 1984

Pagination or Media Count : 13

Abstract : A survey is given on the appearance of secondary instability in shear flows. The mixing layer, the flat-plate boundary layer, and plane Poiseuille flow are considered as prototype flows. The computational and analytical work which produced conceptual enlightenment is discussed. A theory of secondary instability is presented: the (almost) periodic flow that develops in the presence of finite-amplitude traveling waves is used as a basic flow for a linear stability analysis with respect to spanwise periodic, three-dimensional disturbances. The Hill-type stability equations with periodic coefficients allow for various classes of normal modes that are associated with different types of resonance. A numerical method for solving the secondary stability problem is discussed. Results for fundamental and subharmonic modes in plane Poiseuille flow are reviewed briefly. The present scope of the theory and its potential for future extensions are discussed.

Descriptors :   *Boundary layer, *Boundary layer transition, Stability, Steady flow, Pressure gradients, Secondary, Mixing, Traveling waves, Shear properties, Three dimensional flow, Perturbations, Periodic variations, Coefficients, Numerical methods and procedures, Theory

Distribution Statement : APPROVED FOR PUBLIC RELEASE