Optimal Control Design for Fluid Mixing: from Open-Loop to Closed-Loop

The question of what velocity fields effectively enhance or prevent transport and mixing, or steer a scalar field to the desired distribution, is of great interest and fundamental importance to the fluid mechanics community. In this talk, we mainly discuss the problem of optimal mixing of an inhomogeneous distribution of a scalar field via active control of the flow velocity, governed by the Stokes or the Navier-Stokes equations.

Data Assimilation for Discontinuous State Variables

Data assimilation is a method for combining available observations with a background from numerical model, to find the best estimate of the system, which is crucial for improving environmental variable prediction. However, commonly used Gaussian distribution assumption could introduce biases for state variables with discontinuous profiles, such as sea ice thickness with sharp features. In this talk, we focus on the design of non-Gaussian prior based on various statistics of the state variables.