Influence of velocity shear on character of flow of incompressible stratified fluid around obstacle

The flow of a fluid around an obstacle in the case of identical boundary conditions but with different velocity profiles of the oncoming flow was examined. It is assumed that flow velocity does not change sign and the conditions in the incident flow are stipulated. It is revealed that an increase in horizontal velocity shear and the introduction of vertical shear intensifies wave formation with some decrease in the amplitudes of the perturbations. The same occurs with disruption of the symmetry of flow. It indicated that the presence of vertical and horizontal improves conditions for the formation of leeward trapped waves. A possibility of the existence of several stationary regimes with one and the same form of the obstacle and the very same structure of the oncoming flow is shown. The vertical plane passing through the crest indicates the direction where the waves have the greatest amplitude. A jump or zone of static instability arises in this direction in currents with a vertical velocity shear. The introduction of a horizontal velocity shear eliminates the jump and exerts a smoothing effect on the waves, decreasing their amplitude. The least perturbed vertical section is the plane situated at a distance of 1/4 of the width of the obstacle from the axial plane. It is suggested that such a direction is favorable for the flights of aircraft when an isolated mountain or peak is rising above a range.