Numerical investigation of shallow wake behind a patch of rigid emergent vegetation

The shallow water flow through and around a patch of rigid emergent vegetation was investigated numerically. The mean flow field and turbulent structures were studied, especially their dependence on the solid volume fraction (SVF) of the patch and the bed friction. Two streamwise velocity scales, U-1s at the starting point of the steady wake and U-1e at the downstream end of the steady wake, and the length of the steady wake L-1 were used to describe the steady wake behind the patch. U-1s was found to be related to SVF only. However, U-1e and L-1 were influenced by both the SVF and the wake stability parameter S. For a sparse patch, U-1e was equal to U-1s, and L-1 decreased with the increase of S. For a mid-dense patch, U-1e was always smaller than U-1s, and it increased with S and gradually approached U-1s. The increase of U-1e reduced the lateral velocity difference between the flows inside and outside the wake, which resulted in the increase of L-1. For a highly dense patch, U-1e and L-1 did not increase unless S was larger than a critical value. A new parameter, r, was proposed to represent the development rate of the steady wake. The numerical results showed that r increased monotonously with S for mid-dense patches.