Experimental study of plane turbulent wakes in a shallow water layer

Shallow two-dimensional turbulent wake flows have been studied experimentally on a large water table. In the experiments, the ambient Reynolds number Re_h = U_aH/ν, in which U_a is the depth-averaged ambient velocity, H the water depth, and ν the kinematic viscosity, is large, well above a lower critical value of the order of 500 for open-channel flows so that the ambient base flow is fully turbulent. Different types of blunt bodies extending over the full depth are inserted in that base flow, including cylinders and flat solid and porous plates oriented transversely to the ambient flow. In all cases, the transverse body dimension D greatly exceeds the water depthy, D/H ≫ 1. With that condition, the wake Reynolds number Re_d = U_aD/ν is very large, greater than 10⁴. The shallow near-wake characteristics of plane wakes from blunt bodies extending over the full water depth have been found to fall into one of three classes: (i) the vortex street (VS) type with an oscillating vortex shedding mechanism, (ii) the unsteady bubble (UB) wake type with flow instabilities growing downstream of a recirculating bubble attached to the body, and (iii) the steady bubble (SB) wake type with an attached bubble followed by a turbulent wake that contains no growing instabilities. When Re_h > 1500, the flow classification is uniquely dependent on a shallow wake parameter, S = c_fD/H in which c_f is a quadratic law friction coefficient. For circular cylindrical bodies the VS-UB transition is characterized by a critical value, S_ca ≈ 0.2, and the UB-SB transition by S_cc ≈ 0.5. Solid plates, oriented transversely, differ by a factor of 1.25.

The shallow far-wake behavior has been investigated with a special variable porosity wake device that reduces the wake velocity deficit and completely suppresses the VS instabilities in the near-field. Thus, only UB and SB wake types are found in that case. Furthermore, the shallow plane wake is obsserved to "stabilize" for large downstream distances, x/H, in the sense that the growth and maintenance of the large scale structures in the wake flow become suppressed and the wake collapses into a more ordered flow that, however, still contains small scale (of scale H) turbulence. This wake stabilization is controlled by two factors: first, the usual evolution in a turbulent wake that reduces the velocity deficit while increasing the wake parameter S, and secondly, the exponential loss of the momentum deficit flux in the wake due to bottom friction.