Resolvent-based estimation of space-time flow statistics

Understand

We develop a method to estimate space-time flow statistics from a limited set of known data.

• While previous work has focused on modeling spatial or temporal statistics independently, space-time statistics carry fundamental information about the physics and coherent motions of the flow and provide a starting point for low-order modeling and flow control efforts.
• The method is derived using a statistical interpretation of resolvent analysis.
• The central idea of our approach is to use known data to infer the statistics of the nonlinear terms that constitute a forcing on the linearized Navier-Stokes equations, which in turn imply values for the remaining unknown flow statistics through application of the resolvent operator.