Numerically Modelling Stochastic Lie Transport in Fluid Dynamics

Understand

We present a numerical investigation of stochastic transport in ideal fluids.

• According to Holm (Proc Roy Soc, 2015) and Cotter et al.
• (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a physically meaningful, data-driven approach for decomposing the fluid transport velocity into its drift and stochastic parts, for a certain class of fluid flows.
• In the current paper, we develop new methodology to implement this velocity decomposition and then numerically integrate the resulting stochastic partial differential equation using a finite element discretisation for incompressible 2D Euler fluid flows.