On the causes of instability along the shifting plunge line of a sediment-laden density inflow, Lillooet Lake, Canada
Previous field work at Lillooet Lake, British Columbia, has revealed a transitory, pulsing, nature to the position of the plunge line, where regions of the scallop-shaped plunge line advance and retreat with a period of c. 4 minutes. Field measurements with acoustic Doppler current profilers have shown how this shifting plunge line generates discontinuous density underflows that may progress down the delta slope into the lake, or become buoyant as interflows when the lake is temperature stratified. Here, we present new observations on these plunge-line dynamics and an analysis that suggests the pulsing behavior may be explained as a turbulent Rayleigh-Taylor (RT) instability, which together with the momentum of the flow as it enters the lake, produces a shift in the position of the lobes along the plunge line and hence pulsing underflows. This paper will present new details of these underflows and a simple analysis that examines their period as RT fingers that penetrate into the ambient lake water.
Generation of Internal Waves by a Supercritical Stratified Plume
The generation of internal waves by a propagating river plume is studied in the framework of a fully-nonlinear non-hydrostatic numerical model. The vertical fluid stratification, parameters of tide, river discharge and the bottom topography were taken close to those observed near the Columbia River mouth. It was found that in the beginning of the ebb tidal phase the river water intruding into the sea behaves as a surface jet stream. It collides with the stagnant shelf waters and sinks down in the area of the outer plume boundary forming a head of the gravity current. In supercritical conditions which are normally realized at the first stage of the ebb tidal phase, internal waves are arrested in the head of the gravity current because their phase speed is smaller than the velocity of the plume. They are released and radiate from the plume when the speed of the decelerating front becomes smaller than the internal wave phase speed. This mechanism of the wave generation is sensitive to the stratification of the ambient shelf waters. It was found that dramatic decay of the buoyancy frequency profile from the surface to the bottom provides the most favourable conditions for the efficient disintegration of the head of the gravity current into a packet of internal waves and their fast separation from the plume. In the case when the fluid stratification on the shelf is close to monotonous, the disintegration of the head of the gravity current into a packet of solitary internal waves is not expected. NERC project NE/E01030X/1.
Mixed Region Collapse in Stratified Ambients
Compared with the substantial body of theoretical, experimental and computational work examining the evolution of gravity currents in uniform ambient fluids, relatively little is known about intrusions in stratified environments. Most lock-release laboratory experiments have focused upon one of two symmetric circumstances: in one the ambient is a two-layer fluid with equal-depth upper and lower layers; in the other, the ambient is uniformly stratified. In both these cases, the intrusion density is the average ambient fluid density and is observed to propagate long distances at mid-depth with approximately constant speed. If symmetry is broken, experiments reveal qualitatively different behaviour. The intrusion propagates a much shorter distance and large-amplitude internal waves are excited. These studies are extended to examine asymmetric intrusions in uniformly stratified fluids resulting both from a full-depth lock-release experiment and also from a localized mixed patch in rectilinear and axisymmetric geometries.
Turbulent Mixing and Dispersion in a Laboratory Gravity Current
Turbulent mixing and dispersion occurs when a wall-bounded stably-stratified gravity current generates sufficient shear to destabilized the layer. The instability of such a flow is described by the Richardson number, Rig = N2/S2, where N is the local Brunt-Vaisala frequency and S is the local mean shear rate. The Kelvin- Helmholtz instability that occurs for low Rig < 0.25 causes vigorous vertical mixing. Such instabilities are important in the mixing and entrainment of the gravity currents occurring in oceanic overflows. We present high-resolution velocity and density measurements of the development of a stably-stratified gravity current on a smooth plane, inclined at 10° with respect to horizontal. The velocity and density fields are measured simultaneously using particle image velocimetry and planar laser induced fluorescence. As opposed to many measurements of gravity currents where the current itself is laminar, our gravity current is turbulent with Reynolds number Re ≈ 5000. From the measured velocity/density fields we compute the energy dissipation ε ≈ 1 cm2/ s3, the mean shear rate S ≈ 1.5 s-1, and the average N ≈ 0.4 s-1. We then compute the vertical turbulent transport of momentum and density by directly evaluating the vertical Reynolds stress, ReT = u' w' and the buoyancy flux ρ' w' where u', w', and ρ' are horizontal and vertical velocity fluctuations and density fluctuations, respectively. By relating u' w' and ρ' w' to mean gradients, we obtain Prandtl mixing lengths ℓv ≈ ℓρ ≈ 0.6 cm ≈ ℓs = ε1/2/S . The apparent equivalence of the mixing lengths suggests an extrapolation to ocean overflow conditions, e.g., the Mediterranean overflow , for which we predict turbulent eddy viscosity and diffusivity coefficients of about 600 cm2/s . 1. P. Odier, J. Chen, M.K. Rivera, and R.E. Ecke, Mixing in stratified gravity currents: Prandtl mixing length, arXiv:0901.4836 2. J. Price et al, Mediterranean outflow mixing dynamics , Science 259, 1277 (1993).
Velocity Profile Normalization of Field-Measured Turbidity Currents
Multiple occurrences of turbidity currents were observed in moored-ADCP measurements in Monterey (2002/03) and Hueneme (2007/08) submarine canyons, California. These turbidity currents, almost all of which were supercritical (densimetric Froude number greater than unity), lasted for hours and obtained a maximum speed of greater than 200 cm/s. The layer-averaged velocity of the turbidity currents varied from 100+ cm/s at the onset of the turbidity currents to 20+ cm/s toward the end of the events. The thickness of the turbidity currents tended to increase from 10 to 40 m over an event. Empirical functions, obtained from laboratory experiments whose spatial and time scales are two to three orders of magnitude smaller than the field measurements [e.g. Altinakar, Graf, and Hopfinger, 1996, Flow structure in turbidity currents, Journal of Hydraulic Research, 34(5):713-718], were found to represent the field data fairly well. However, the best similarity collapse of the turbidity current velocity profiles was obtained when the streamwise velocity was normalized by the layer-averaged velocity and the elevation was normalized by the turbidity current thickness. This normalization scheme can be generalized to the same empirical function y = exp (-α xm) for the jet region above the velocity maximum.
Turbulent Flow Characteristics near in the Bottom Boundary Layer of Experimental Density and Turbidity Currents
A series of experimental saline gravity currents and turbidity currents were analyzed to quantify the distribution of shear stress and turbulent kinetic energy in the bottom boundary layer. Profiles of Reynolds stress and turbulent kinetic energy were obtained from measurements of turbulent fluctuations of velocity components, made using a high-resolution acoustic Doppler velocimeter. We focused on the bottom 5 cm of the 20 cm deep gravity currents in order to characterize the bottom boundary layer. For flows that had similar velocity profiles, the sediment-laden flows had Reynolds stresses in the bottom boundary layer that were approximately 35% higher than the equivalent saline flows. The shear stress can also be expressed as a drag coefficients, so that CD = 1.3 × 10-3 for saline gravity currents and CD = 1.8 × 10-3 for the turbidity currents, in general agreement with some previous experimental studies. The Reynolds stress distribution mirrors the velocity gradient evolution as highest stresses occur where the gradient is largest and lowest stresses are found at the velocity maximum where the gradient is almost zero. At the base of the bottom boundary layer, we found that the Reynolds shear stress can be related to the gravity current's turbulent kinetic energy (TKE), by τ = 0.2 ×TKE. This result had previously been found in non-stratified boundary layers of channel flows. This relationship could allow bottom stresses to be estimated from single-component velocity measurements in the bottom boundary layer of a turbidity current.