Shallow wakes are ubiquitous in nature. Examples include island wakes in ocean and atmosphere. These natural wake flows are characterized by their high Reynolds number ( Re≈10⁶-10⁹) and their large horizontal length scales in comparison to their vertical counterpart. Despite of the high Reynolds number, large-scale two-dimensional coherent structures, which are reminiscent to those typically shown in deep flows at low Reynolds numbers, are observed in shallow wakes. It is believed that the formation of large-scale coherent structures in turbulent flows is associated with the development of hydrodynamic instability, and the coherent structures represent the end product of large-scale flow instability....[ Read more ]

Shallow wakes are ubiquitous in nature. Examples include island wakes in ocean and atmosphere. These natural wake flows are characterized by their high Reynolds number ( Re≈10⁶-10⁹) and their large horizontal length scales in comparison to their vertical counterpart. Despite of the high Reynolds number, large-scale two-dimensional coherent structures, which are reminiscent to those typically shown in deep flows at low Reynolds numbers, are observed in shallow wakes. It is believed that the formation of large-scale coherent structures in turbulent flows is associated with the development of hydrodynamic instability, and the coherent structures represent the end product of large-scale flow instability.

For its paramount significance in engineering analyses and applications, shallow wake is investigated in this thesis through analytical and numerical methods. A two-dimensional shallow water equation-based numerical model is employed. The capabilities and limitations of the BGK model on modeling shallow wakes are explored. The numerical data generated are either incorporated into the stability analysis or compared to the instability predictions. The principle of stability analysis applied on shallow wakes is then reviewed and the instability generation mechanism is investigated. In particular, the importance of blunt body in generating wake instability is explored. It is found from the numerical experiments that the key role of blunt body is to generate shear-inducing wake deficit profiles which initiate wake instability in downstream region. In order to recover the wake oscillation frequency, separation point oscillation should also be simulated. Through comparison between numerical data and instability results in other literatures, the validity of quasi-parallel assumption as well as the good performance of linear stability analysis are revealed. Lastly, the validity of weakly nonlinear stability analysis in describing the convective instability evolution is demonstrated.