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Shallow Flow Instabilities


Shallow flow past successive cavities is characterized via a technique of high-image-density particle image velocimetry. Highly coherent, self-sustained oscillations arise due to coupling between: the inherent instability of the separated shear layer along the opening of each sequential cavity; and a gravity standing wave mode within each cavity. The globally coupled nature of the flow structure is evident in dominance of the same spectral component in the undulating vorticity layers along each of the successive cavities and the wall pressure fluctuations within the cavities. Unlike coupled phenomena associated with flow past single cavities, optimal coupling for successive cavities requires a defined phase shift between the standing wave patterns in adjacent cavities and, furthermore, an overall phase shift of the undulating shear layer along the cavity openings. The magnitudes of these phase shifts depend on the mode of the gravity standing wave in each cavity, i.e., longitudinal or transverse mode, which are respectively aligned with and normal to the main stream. Such phase shifts result in corresponding displacements of patterns of phase-referenced vorticity concentrations along the cavity openings and change in timing of impingement of these concentrations upon the downstream corners of successive cavities. All of the foregoing aspects are related to the unsteady recirculation flow within the cavity, the time-dependent streamline topology, and concentrations of Reynolds stress along the cavity opening.

Principal Investigator: B. A. Tuna

Fully turbulent shallow flow past a cavity can give rise 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 objective of the present investigation is to attenuate these oscillations by a single geometric perturbation (cylinder) on the bed (bottom surface), which is located near the leading corner of the cavity. The patterns of the flow structure are characterized as a function of height of the cylinder above the bed by using digital particle image velocimetry. 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 layer away from the cavity opening are evident. The 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, which is due to the decreased entrainment demand of the separated shear layer. This decrease in magnitude of the exchange velocity in the presence of the cylinder results in a 50% reduction of the value of mass exchange coefficient between the cavity and the mainstream.

Principal Investigator: B. A. Tuna 

The structure of shallow flow past a cavity is characterized as a function of: elevation above the bed (bottom surface); and the onset of coupling between the separated shear layer along the opening of the cavity and a gravity wave mode within the cavity. A technique of particle image velocimetry is employed to characterize the flow structure. Coherent patterns of vorticity along the cavity opening and at the trailing (impingement) wall of the cavity are related to the streamline topology and associated critical points as a function of elevation above the bed. Associated patterns of normal and shear Reynolds stresses are defined, and related to the exchange velocity and mass exchange coefficient along the cavity opening. Substantial increase of mass exchange between the cavity and the main flow occurs in presence of shear layer-gravity wave coupling for all elevations above the bed.

Principal Investigators: B. A. Tuna & E. Tinar

Related Publication: Shallow flow past a cavity: globally coupled oscillations as a function of depth

Coupling with a Standing Gravity Wave 
Shallow, fully turbulent inflow past a cavity can give rise to highly organized oscillations, due to coupling between: (i) the inherent instability of the separated turbulent layer along the opening of the cavity, and (ii) a gravity standing wave within the cavity. Techniques of particle image velocimetry and pressure measurements are employed to characterize the occurrence of the fully coupled state of the oscillation, relative to its uncoupled state. At a threshold value of inflow velocity, the frequency of the inherent instability of the turbulent separated shear layer locks-on to the frequency of the gravity standing wave. Moreover, the amplitude of the spectral peak of the pressure fluctuation, both at the impingement corner of the cavity and within the cavity, attains maximum values when lock-on occurs. Occurrence of a fully coupled or locked-on state substantially alters the time-averaged flow structure. Enhanced magnitudes of patterns of Reynolds stress and transverse velocity fluctuation occur along the cavity shear layer. Simultaneously, increased flow from within the cavity towards the separated shear layer occurs at a location immediately downstream of separation at the leading-edge of the cavity and, correspondingly, increased flow into the cavity occurs in the impingement region. The influence of the locked-on state is therefore global: both the separated shear layer along the mouth of the cavity and the flow within the cavity are substantially altered. Phase-averaged representations of the flow structure show highly coherent, phase-locked patterns of vorticity along the cavity opening during the locked-on state. These vorticity patterns are associated with large, phase-locked excursions of the transverse component of velocity, within both the separated the shear layer and the cavity. 
Principal Investigators: M. Wolfinger and C. Ozen