Modeling flow statistics using convex optimization

A method is proposed to estimate the covariance of disturbances to a stable linear system when its state covariance is known and a dynamic model is available. This is an issue of fundamental interest for estimation and control of fluid mechanical systems whose dynamics is described by the linearized Navier–Stokes equations. The problem is formulated in terms of a matrix norm minimisation with linear matrix inequality constraint, and solved numerically by means of alternating convex projection. The method is tested on covariance estimation in a low Reynolds number channel flow.