Michael D Patterson

Mixing efficiency in high-aspect-ratio Rayleigh-Taylor experiments

High-Reynolds-number turbulence generated by Rayleigh–Taylor instability is known to be much more efficient at mixing density-stratified fluids than mixing driven by most other mechanisms. We demonstrate here that the final state of the instability in a high-aspect-ratio environment is uniform, corresponding to the maximum mixing efficiency possible. The efficiency of the mixing appears to be constant throughout the evolution of the flow, despite the flow changing from being inertially dominated with a high-Reynolds-number initial growth of the mixing zone, to a viscously dominated late-time decay. The initial growth, in which vertical transport takes the form of a turbulent diffusion, is characterized by a t2/5 power law, indicating that the diffusivity is not constant but rather decreases as the strength of the unstable density gradient driving the flow decreases. As the unstable stratification is reduced, inertia begins to play a lesser role with molecular viscosity taking over the controlling dynamics, but with vertical transport still dominated by parcels of fluid needing to pass around many vortexlike structures during the exponential decay toward the well-mixed final state.

Vortical motion in the head of an axisymmetric gravity current

A series of experiments that examine the initial development of an axisymmetric gravity current have been carried out. The experiments highlight the growth of a ring vortex that dominates the dynamics of the gravity current’s early time propagation. In particular, the experiments show three distinct stages of early time development that have previously been described as the “initial phase” of a gravity current. The first phase of the early time development is dependent on the fractional depth of the lock release, followed by a secondary phase wherein the frontal speed is approximately constant and a third phase of reducing speed. The second phase of the gravity current’s propagation comes to an abrupt end with the breakdown of the ring vortex at a clearly defined position. All of the experimental results show the development of a complex flow field where the generation and collapse of a ring vortex dominate the gravity current’s early time propagation. The complexity of the flow field and the dependence of the propagation speed on the presence of the ring vortex in the head of the gravity current highlights the unsuitability of shallow-water modeling for axisymmetric lock releases at early times.

Note: Scanned multi-light-emitting-diode illumination for volumetric particle image velocimetry

We describe the development of both multilevel two-dimensional and grid-based three-dimensional illumination systems for volumetric particle image velocimetry (PIV) that uses a single camera and an arbitrary number of low powered lasers. This flexible system is robust and capable of capturing results over a range of spatiotemporal scales determined by the choice of camera, the depth of field of the lens, and the laser power. The system is demonstrated on a rotating spin-up experiment where we extract high fidelity velocity fields at up to 62 frames/s at a spatial resolution of 2352×1728 pixels. The flexibility and economy offered by this system--approximately one-tenth that of a comparable commercial package--may make it attractive to many laboratory users.

Streaks to rings to vortex grids: generic patterns in transient convective spin up of an evaporating fluid.

We observe the transient formation of a ringed pattern state during spin up of an evaporating fluid on a time scale of order a few Ekman spin up times. The ringed state is probed using infrared thermometry and particle image velocimetry and it is demonstrated to be a consequence of the transient balance between Coriolis and viscous forces which dominate inertia, each of which are extracted from the measured velocity field. The breakdown of the ringed state is quantified in terms of the antiphasing of these force components which drives a Kelvin-Helmholtz instability and we show that the resulting vortex grid spacing scales with the ring wavelength. This is the fundamental route to quasi-two-dimensional turbulent vortex flow and thus may have implications in astrophysics and geophysics wherein rotating convection is ubiquitous.

Spin-up and spin-down in a half cone: A pathological situation or not?

The spin-up and spin-down of a fluid in a rapidly rotating, fluid-filled, and closed half cone are studied both numerically and experimentally. This unusual set up is of interest because it represents a pathological case for the classical linear theory of Greenspan and Howard [J. Fluid Mech. 17, 385–404 (1963)10.1017/S0022112063001415] since there are no closed geostrophic contours nor a denumerable set of inertial waves (even a modified theory incorporating Rossby waves by Pedlosky and Greenspan [J. Fluid Mech. 27, 291–304 (1967)10.1017/S0022112067000321]—relies on geostrophy to leading order). The linearised spin-up/spin-down dynamics in a half cone is found to be dominated by topographical effects which force an ageostrophic leading balance and cause the large-scale starting vorticity to coherently move into the “westward” corner of the half cone for both spin-up and spin-down. Once there, viscous boundary layer effects take over as the dominant process ensuring that the spin-up/spin-down time scales c...