Remarks on computing the ℋ2 norm of incompressible fluids using descriptor state-space formulation

This paper utilizes descriptor state-space formulation for computation of energy amplification in incompressible channel flows. The dynamics of velocity and pressure fluctuations in these flows are described by a system of partial differential-algebraic equations. Typically, the evolution model is obtained by projecting the velocity fluctuations on a divergence-free subspace which eliminates pressure from the equations. This procedure results into a standard state-space representation and the problem of quantifying receptivity of velocity fluctuations to stochastic exogenous disturbances is solved using well-known ℋ₂ formalism. In this paper, however, it is shown how energy amplification can be computed directly from the original system of the linearized Navier-Stokes and continuity equations. This approach avoids the need for finding the evolution model which is advantageous in many applications.