Analysis of turbulence based on resolvent analysis for time dependent mean flow*

A fundamental distinction exists between the mechanism of perturbation growth by extracting

energy from the time-independent time mean flow and the mechanism of perturbation growth

by extracting energy from the time-dependent streamwise mean flow. In the former case, the mechanism is transient growth associated with the non-

normality of the structurally invariant eigenvectors of the time mean flow. In the latter case,

perturbation growth can be attributed to contributions to growth arising from two distinct non-

normal processes: growth of each covariant Lyapunov vector in isolation and growth resulting

from non-normal interaction among the covariant Lyapunov vectors. Both of the mechanisms participate in producing perturbation growth and they work together to

determine the excitation of the streamwise mean flow arising from perturbation perturbation nonlinearity. Resolvent analysis is extended to time dependent streamwise mean flow of a turbulent Couette flow at low and moderate Reynolds numbers to analyze and separate these two components of the mechanism of perturbation growth in time dependent flow.