Shallow Flow Instabilities: Effects of Gravity Standing Wave Coupling

Shallow turbulent shear flows such as shallow mixing layers, jets, or wakes, can exist in environmental flows, e.g., flows in rivers, lakes, estuaries, and coastal regions. These flows frequently have large-scale, highly-coherent, vortical structures with length scales that are much larger than the flow depth. Such vortical structures can arise from either a convective or an absolute instability. Fully turbulent shallow flow past a cavity can lead to highly coherent oscillations, which arise from coupling between the inherent instability of the separated shear layer along the cavity opening and a gravity standing wave within the cavity. The ultimate objectives of this investigation are to: (i) determine the effect of shear layer-gravity standing wave coupling on the flow structure and exchange processes; (ii) control the oscillations and exchange processes; (iii) reveal flow features for different cavity configurations and relate the flow patterns to the characteristics of exchange processes. Techniques of unsteady pointwise pressure measurements and particle image velocimetry (PIV) are used to assess the coherence and basic flow physics of oscillations over the flow domain along both a single cavity and successive cavities. The basic flow features observed for the oscillations were either a transverse or longitudinal gravity standing wave within the cavity, downstream propagation of an organized disturbance or large-scale vortex along the cavity opening, and its impingement on the trailing corner of the cavity. The amplitude of free surface oscillation within the cavity is characterized as a function of inflow velocity via unsteady pressure measurements. Coupled oscillation of the shear layer and the gravity standing wave yields large increases in the time-averaged entrainment and mass exchange coefficients between the cavity and the main flow. Such increases are due to substantial enhancement of turbulent stresses in the separated shear layer during the coupled oscillation, relative to the stresses associated with no coupling. Patterns of the flow structure have been characterized as a function of elevation above the bed (bottom surface) of the shallow flow. At elevations close to the bed, the time-averaged streamlines are deflected inwards towards their center of curvature. This streamline deflection is due to radial migration of flow along the bed, which arises from a radial pressure gradient; this deflection causes skewing of the velocity vectors over the depth and creates streamwise vorticity. In addition, patterns of normal and shear Reynolds stresses are substantially altered as the bed is approached. These changes of stresses with depth are, in turn, associated with degradation of coherent, phase-averaged patterns of vortex formation in the separated shear layer. Coupled oscillations of the shear layer and the gravity standing wave can be attenuated by a single geometric perturbation (cylinder) on the bed (bottom surface), which is located near the leading corner of the cavity. Reduced amplitude of the coupled oscillation can be attained for values of cylinder diameter and height nearly an order of magnitude smaller than the water depth. The reduction of oscillation amplitude is associated with an increased width of the separated shear layer along the opening of the cavity, even at elevations above the bed much larger than the height of the cylinder. Near the bed, a vorticity defect in the separated shear layer and deflection of the vorticity layer away from the cavity opening are evident. Attenuation of the oscillation amplitude is associated with: a major decrease in the peak values of the normal and shear Reynolds stresses in the separated shear layer; degradation of coherent, phase-averaged patterns of vortex formation; and decreased scale of the coherent vortical structures that propagate downstream along the cavity opening. These changes in the stresses and the flow structure are, in turn, directly correlated with lower values of exchange velocity along the opening of the cavity due to the decreased entrainment demand of the separated shear layer and, as a result, reduction of the value of mass exchange coefficient in presence of passive control device (cylinder). In addition to shear layer-gravity standing wave coupling for a single cavity, shallow flow past successive cavities can also give rise to self-sustained oscillations, due to coupling between: the inherent instability of the separated shear layer along the opening of each cavity; and a gravity standing wave mode within the cavity. As the flow velocity is varied, this coupling is associated with different orientations of the gravity standing wave, i.e., it can occur in either the transverse or the streamwise direction. Correspondingly, a defined phase shift exists between the coupled oscillations of adjacent cavities; the flow structure and mass exchange process along each of the sequential cavities can be altered depending on the orientation of the gravity standing wave within each cavity, that is, a streamwise-oriented versus a transversely-oriented gravity standing wave, as well as the phase shift between the standing waves in adjacent cavities. In presence of the transversely-oriented gravity standing wave, the oscillation amplitude of the coupled shear layer instability-cavity mode is larger, as indicated by the amplitude of deflection of the free-surface, and enhanced coherence and scale of the phase-averaged vortex formation occurs in the separated shear layer along the opening of each cavity. This coherent vortex formation results in a large increase in the magnitude of the turbulent shear stress in the separated shear layer and, as a consequence, an increase of the time-averaged exchange velocity and mass exchange coefficient along the opening of each cavity