Session BS: Buoyancy-Driven Flows II

Intrusive gravity currents in adjacent stratified fluids

In two adjacent fluids, differing vertical density stratifications necessarily entail horizontal density gradients. The resulting baroclinic torques may drive Intrusive Gravity Currents (IGCs), the primarily horizontal flow of one fluid into another at an intermediate depth. The literature has traditionally addressed intrusions into a stratified ambient by a fluid of uniform density. However, many oceanic and atmospheric flows involve two or more adjacent fluids of non-uniform density profiles. We present an experimental and numerical study of IGCs between fluids of non-uniform densities, considering only the `equilibrium' case in which adjacent fluids have equivalent depths and mean densities but differing, constant, non-zero buoyancy frequencies. Working from the available potential energy of the system and an assumed IGC thickness we develop an energy model to describe the speed of a mid-depth Boussinesq intrusion during its initial constant-velocity phase. We verify the theory over a range of buoyancy frequency ratios, using both laboratory measurements in a lock-exchange channel and corresponding two-dimensional direct numerical simulations. We also examine the role of internal waves in the interleaving process.   

Intrusions with variable inflow into a linearly stratified ambient

The propagation of an intrusion of volume $q t ^\alpha$ into a linearly stratified ambient along the plane of neutral buoyancy is considered ($t$ is the time and $q, \alpha$ are positive constants). Theoretical results are presented for rectangular and cylindrical axisymmetric (or wedge) geometries, for both inertial-buoyancy and viscous-buoyancy balances. However, a sharp practical criterion for the boundary between the regimes is not available. The flow may undergo change of regime inertial/viscous (or the inverse) after some time of propagation, depending on the value of $\alpha$. The differences with the non-stratified counterpart are discussed.   

Interaction and Stability of Two Buoyant Currents

Considerable work is needed to improve our understanding of how buoyant waters transport pollution and sediments along coastlines, in particular, when multiple buoyant sources are present. A combination of analytical calculations and laboratory experiments has been used to investigate the interaction and stability of two surface-trapped buoyant coastal currents having different densities. The possible horizontal and vertical alignment scenarios are obtained by varying the densities and volume transports of the two currents. These scenarios will be presented as a function of dynamically relevant non-dimensional numbers. Laboratory rotating experiments confirmed the analytical prediction of the location of the two currents. Furthermore, the two fronts were observed to go unstable. This coupled frontal instability presents interesting differences from the previously studied instability of a single current.   

A simplified approach for the direct numerical simulations of continuous turbidity currents

This work presents Direct Numerical Simulations of sediment-laden channel flows driven by the excess density of the suspended sediment, which provides a simplified model of a turbidity current. The main findings are: 1)The presence of sediment breaks the symmetry of the flow about the center plane due to self-stratification, which results in an average sediment concentration that declines in the upward-normal direction, and an average velocity profile that is skewed towards the bottom. 2)Self-stratification damps turbulence, particularly near the bottom wall. Two regimes are observed, one in which the flow remains turbulent but the level of turbulence is reduced, and another in which the flow relaminarizes near the bed. 3)The analysis allows the determination of a criterion for the break between these two regimes, in terms of an appropriately defined dimensionless settling velocity. Although the analysis reported here is not performed at the scale of large oceanic turbidity currents, the implication of flow relaminarization is of considerable importance even for swift oceanic turbidity currents.   

Experimental Analysis of Entrainment Rate in Wall-bounded Gravity Current at Different Richardson Numbers

Determining the entrainment rate of wall-bounded gravity current is of important implication in geophysical flows. A series of laboratory experiments are designed to investigate the small-scale flow structures and dynamics of mixing by simultaneous measuring the density and velocity in a gravity current introduced into a stratified environment along a inclined plate. The experiments are conducted at different Richardson number by varying the density stratification and mean flow velocity. The results are used to evaluate the Richardson number dependence of entrainment rate and compared with the prediction of different parameterizations.   

The role of turbulence in the equilibration of a symmetrically unstable front

The evolution of a lateral density front in the surface mixed layer of the ocean is examined using numerical simulations. When the horizontal density gradient is sufficiently large so that the mixed layer potential vorticity becomes negative, symmetric instability develops. Once the symmetric instability becomes finite amplitude, a secondary shear instability forms and rapidly breaks down into turbulence. The vertical turbulent fluxes efficiently transport heat and momentum across the mixed layer and stabilize the primary symmetric instability. The length and time scales associated with the onset of the secondary shear instability are accurately predicted by a linear stability analysis.   

Viscous grounding lines

We have used simple laboratory experiments with viscous fluids to explore the dynamics of grounding lines between Antarctic marine ice sheets and the freely floating ice shelves into which they develop. Ice sheets are shear-dominated gravity currents, while ice shelves are extensional gravity currents with zero shear to leading order. Though ice sheets have non-Newtonian rheology, fundamental aspects of their flow can be explored using Newtonian fluid mechanics. We have derived a mathematical model of this flow that incorporates a new dynamic boundary condition for the position of the grounding line, where the gravity current loses contact with the solid base. Good agreement between our theoretical predictions and our experimental measurements, made using gravity currents of syrup flowing down a rigid slope into a deep, dense salt solution, gives confidence in the fundamental assumptions of our model, which can be incorporated into shallow-ice models to make important predictions regarding the dynamical stability of marine ice sheets.   

Immersed Boundary Simulations of Shear and Buoyancy Driven Flows in Complex Enclosures

Driven cavity flows are rich in complexity, consisting of a hierarchical organization of corner eddies called Moffat eddies with a nearly precise ratio of vortex strengths and distances between vortex centers. The driven square cavity flow has been extensively studied as a canonical problem. Likewise, natural convection flows in enclosures with differential heating of two side-walls and adiabatic conditions at the other boundaries have been extensively studied. While the square enclosure has enjoyed the most attention, natural convection in other complex-shaped enclosures have attracted relatively less attention. In the present study, we have used the Immersed Boundary Method in conjunction with a staggered Cartesian grid fractional step procedure to simulate two-dimensional shear-driven and buoyancy-induced flows in several complex cavities. The selected cavity shapes are chosen to illustrate the rich complexity of shear and buoyancy induced flows in general and the ability to predict such complex flows with the Immersed Boundary Method. In the present study, we have limited the Reynolds numbers and Rayleigh numbers to keep the flow from becoming time-periodic or chaotic. In all cases, a time-invariant state has been achieved, and results are displayed for such a steady state.   

Experimental simulation of the fragmentation/breakup of a positively buoyant subaqueous volcanic eruption

The breakup of a positively buoyant subaqueous volcanic eruption was experimentally investigated using Particle Image Velocimetry. The surrogate for the volcanic discharge was silicone oil and the surrogate for the surrounding seawater was a mixture of glycerin and water, mixed in proportion to match the refractive index of the silicone oil and dyed with Rhodamine. The fragmentation/breakup of the jet/plume was only weakly affected by the discharge Richardson number and Reynolds number. To simulate the effect of volcanic volatiles, small amounts of the seawater surrogate were injected into the volcanic surrogate prior to discharge. The effect of the volatiles, even in very small concentrations, was to enhance fragmentation of the discharged fluid.