Session R1: Geophysical Flows: General II

Evolution of shallow, horizontal shear layers with a horizontal density contrast

Shallow coastal ocean flows frequently involve strong horizontal shear layers in combination with a horizontal density gradient. In the absence of the density contrast, the flow undergoes the classic Rayleigh instability leading to the roll-up of the shear layer into vertical vortices. The density contrast results in a transverse gravity-driven tilting of the interface resembling a lock-exchange. The evolution of this rapid buoyancy-induced tilting of horizontal shear is explored with laboratory experiments performed in a new open-channel flume with a flapping, splitter-plate entrance. Measurements of the downstream evolution are made with co-incident PIV and LIF in horizontal planes at several vertical locations spanning the water column. The measurements show vortex roll-up and tilting and the subsequent emergence of horizontal Kelvin-Helmholtz billows that form on the interface and interact with the primary vortices. The characteristics of flow are discussed, including phase averaged and mean velocity, vorticity and density fields as a function of a scaling parameter that quantifies the relative effects of lateral shear and buoyancy adjustment. The experiments compare favorably with three-dimensional, implicit-LES, numerical model solutions for the experimental configuration and parameters.   

Self-similar structure of a corner wave at short times

We study theoretically the flow near the corner of a vertical flat plate partially submerged across an uniform stream. When the Froude number is large enough, a three dimensional wave forms at the corner of the plate which evolves downstream in a similar way as a time-evolving two dimensional plunging wave. We have performed pressure-impulse asymptotic analysis of the flow near the origin of the corner wave to describe the initial evolution of the wave and to clarify the physical mechanism that leads to its formation. The analysis shows that the wave crest exhibits a self similar behavior at short times. After this self-similar stage, the wave crest detaches plunges following a nearly ballistic trajectory. The results improve our computational modeling of the flow near the stern of a high-speed surface ship, providing the initial condition needed for CFD simulations to properly capture the behavior of these stern waves.   

Breaking Wave Impact on a Partially Submerged Rigid Cube in Deep Water

The impact of a plunging breaking wave on a partially submerged cube is studied experimentally. The experiments are performed in a wave tank that is 14.8~m long, 1.15~m wide and 2.2~m high with a water depth of 0.91~m. A single repeatable plunging breaker is generated from a dispersively focused wave packet (average frequency of 1.4~Hz) that is created with a programmable wave maker. The rigid ($L = 30.5$~cm) cube is centered in the width of the tank and mounted from above with one face oriented normal to the oncoming wave. The position of the center of the front face of the cube is varied from the breaker location ($x_b \approx 6.35$~m) to $x_b +0.05$~m in the streamwise direction and from $-0.25L$ to $0.25L$ vertically relative to the mean water level. A high-speed digital camera is used to record both white-light and laser-induced fluorescence (LIF) movies of the free surface shape in front of the cube before and after the wave impact. When the wave hits the cube just as the plunging jet is formed, a high-velocity vertical jet is created and the trajectory and maximum height of the jet are strongly influenced by the vertical position of the cube.   

Simulation-based study of wind load on surface-piercing body and its dependency on waves

The wind load acting on surface ships and offshore structures are important for their operation and safety. In this study, we simulate the flow fields of wind and wave past a surface-piercing structure using a multi-scale modeling strategy. At large scales, the turbulent wind is simulated using large-eddy simulation on boundary-fitted grid coupled with nonlinear wavefield simulation using a high-order spectral method. The large-scale simulation provides environmental inputs for the local-scale simulation around the body. At local scales, the air and water flows are simulated by a coupled level-set and volume-of-fluid method. An immersed boundary method is used to represent the body. From the simulation, the statistics and structure of the wind and wave fields around the body are elucidated, and the loads on the body are quantified. A variety of developing and fully developed wave spectra at different sea states are considered. Swells and their interactions with the local wind-waves are included in the simulation. It is found that the mean wind loads are highly dependent on the wave conditions, and the instantaneous wind forcing varies with the wave phase.   

Simulation of flow past a sphere in a stratified fluid

Direct numerical simulation is used to simulate spatially-evolving flow past a sphere in a stratified fluid. The immersed boundary method is used to treat the sphere inside the domain. The main objective of this study is to characterize the near wake region. Statistics of interest include the drag coefficient, separation angle, Strouhal number, and the spatial evolution of the velocity fluctuations and the defect velocity. In addition to quantitative statistics, visualizations of the vortex structures in the wake will also be provided and discussed. Results are compared and contrasted with previous experimental and numerical data for unstratified and stratified flow past a sphere.   

Falling bodies through sharply stratified fluids: theory and experiments

The motion of bodies and fluids moving through a stratified background fluid arises naturally in the context of carbon (marine snow) settling in the ocean, as well as less naturally in the context of the DWH Gulf oil spill. The details of the settling rates may affect the ocean contribution to the earth's carbon cycle. We look at phenomena associated with many falling spheres in stratified fluids, as well as behavior of multiphase buoyant plumes penetrating strong stratification. We present careful measurements critical heights for fully miscible jets and companion analytical prediction. In turn, we examine cases involving clouds of sinking particulate and rising buoyant oil emulsions and associated plume trapping behaviors.   

Vortex rings passing through sharp density transitions

In this presentation the various behaviors of a dense miscible vortex ring descending through a sharp stratification are explored. By varying experimental parameters it is found the ring dynamics can transition from those which pass through the interface to those which can become totally entrapped within the density transition, even though in all cases the ring is the most dense fluid in the system. Experimental results will outline these various behaviors and quantify this transition with an experimental phase diagram. A scaling law will be derived from dimensional considerations to predict this transition in behavior. Numerical simulations will also be presented and compared to the previous experimental results.   

A comparison between laboratory and numerical simulations of gravity-driven coastal currents with a geostrophic theory

Laboratory and numerical simulations of buoyant, gravity-driven coastal currents are summarized and compared to the inviscid geostrophic theory of Thomas \& Linden 2007.\footnote{Thomas, P. J. and Linden, P.F. 2007. Rotating gravity currents: small-scale and large-scale laboratory experiments and a geostrophic model. \textit{J. Fluid Mech.} \textbf{578}, 35-65.} The lengths, widths and velocities of the buoyant currents are studied. Agreement between the laboratory and numerical experiments and the geostrophic theory is found to depend on two non-dimensional parameters which characterize, respectively, the steepness of the plumes isopycnal interface and the strength of horizontal viscous forces (quantified by the horizontal Ekman number). The best agreement between experiments (both laboratory and numerical) and the geostrophic theory are found for the least viscous flows. At elevated values of the horizontal Ekman number, laboratory and numerical experiments depart more significantly from theory.