Sparsity-promoting methods for isolating dominant linear amplification mechanisms in wall-bounded flows

Abstract

This work proposes a method to identify and isolate the physical mechanisms that are responsible for linear energy amplification in fluid flows. This is achieved by applying a sparsity-promoting methodology to the resolvent form of the governing equations, solving an optimization problem that balances retaining the amplification properties of the original operator with minimizing the number of terms retained in the simplified sparse model. This results in simplified operators that often have very similar pseudospectral properties as the original equations. The method is demonstrated on both incompressible and compressible wall-bounded parallel shear flows, where the results obtained from the proposed method appear to be consistent with known mechanisms and simplifying assumptions, such as the lift-up mechanism, and (for the compressible case) Morkovin’s hypothesis and the strong Reynolds analogy. This provides a framework for the application of this method to problems for which knowledge of pertinent amplification mechanisms is less established.