Author(s): F. C. Chan; M. S. Ghidaoui
Linked Author(s): Mohamed S. Ghidaoui
Keywords: No Keywords
Abstract: Experimental and theoretical researches have shown that high Reynolds number shallow shear flows such as shallow wakes and shallow jets are reminiscent to their counterparts in low Reynolds number unbounded flows. The large-scale two-dimensional coherent structures in shallow flows are the end-products of hydrodynamic instabilities. Stability analyses are found to produce results that are generally consistent with experimental data. This paper uses a nonlinear shallow water-based model to investigate the growth of instabilities near the transition point and assess the validity of weakly nonlinear analysis. The results support the use of Landau’s equation to describe the growth of flow instabilities near the critical conditions. In addition, the analysis shows that the oscillation frequency in the island wake appears to be governed by the period-doubling mechanism. We solve for the wake in two ways: (i) by solving for the flow around a cylinder and (ii) by replacing the cylinder by the velocity at aft of the cylinder which we obtained in (i) (i. e., the velocity is used as an upstream boundary condition). The wake structures obtained with and without cylinder are similar but the oscillation frequency and amplitude are different. Although this result is preliminary and needs further scrutiny, it is potentially significant since it appears to challenge the well accepted approach that one can investigate the stability of shallow wakes by taking a base flow which implicitly reflects the presence of a blunt body through a velocity defect law, but does not reflect the details of the separation point.