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math-ph2019★ 16 cited
Lagrangian averaged stochastic advection by Lie transport for fluids
Theodore D. Drivas, Darryl D. Holm, James-Michael Leahy
We formulate a class of stochastic partial differential equations based on Kelvin's circulation theorem for ideal fluids. In these models, the velocity field is randomly transporte…
math-ph2014
Spontaneous Stochasticity and Anomalous Dissipation for Burgers Equation
Gregory L. Eyink, Theodore D. Drivas
We develop a Lagrangian approach to conservation-law anomalies in weak solutions of inviscid Burgers equation, motivated by previous work on the Kraichnan model of turbulent scalar…