Complementary modes of impulse generation for flow past a three-dimensional obstacle

A Lagrangian model for viscous incompressible flow past a stationary solid obstacle is developed in terms of the creation over successive instants of time of fluid impulse at the obstacle's bounding surface. Upon creation this compactly supported vector field actively evolves into the flow interior according to its equation of motion. At the wall, distinct creation modes can be identified by specifying two exterior Poisson problems, distinguished from each other by complementary gradient boundary conditions. We demonstrate how in each case the relevant Poisson problem is to be solved numerically. Impulse generation is modeled in Lagrangian terms for each mode in turn for the case of flow past a sphere. (In the spherical geometry we exploit image theory to simplify some aspects of the computation.) We argue that the concurrent existence of these two distinct modes provides an insight into the complex phenomenology of turbulent wake formation.