Session HG: Geophysical Fluid Dynamics V

Numerical modeling of tsunami wave run-up on beaches using a Lattice Boltzmann solver

In this contribution, the suitability of a LBGK modeling approach is tested to examine the behavior of free surface water waves in shallow water. The present 1-D LBGK model discretizes the tidal wave equations and approximate the collision between particles using a single time relaxation. The non-linear free-surface dynamics are accounted for through the non-equilibrium particle distribution function. It is notable that no additional algorithm or surface boundary conditions are required. We should stress that the present model can only expect to work well for a continuous surface in shallow water. The case study of concern involves testing the solvers ability to handle wave run-up on beaches. The predictions of the shoreline trajectory represent a classical bench mark test of numerical models, especially because of the challenge of accurately predicting the wave motion when the depths are vanishing into dry-states. The present test case represents a tsunami generated wave run-up/run-down study on a beach. No special treatment of the shoreline motion has been prescribed herein, as the LB solver handles the moving interface between water and land automatically. The LB solution compares fairly well with results of other investigators including an analytical solution, the non-linear shallow water equations and Boussinesq solutions.   

A Simplified Model for Levee Formation by Turbidity Currents

Turbidity currents are known to form channels, and in some cases to generate levees by deposition of sediments from channel overflows. The levees may follow a power law or exponential decay in thickness perpendicular to the channel. In the present study we provide a simple analytical model to describe the levee shape as function of the governing flow parameters. Entrainment of ambient fluid is found to have an important influence on the shape of the levee. Two-dimensional numerical simulations are conducted to provide supporting evidence to the theoretical model.   

Experimental Investigation of the Effect of Reynolds Number and H / $\delta$ Value on Flow Fields in Street Canyons with Cubical Buildings

Previous research on flows within idealized street canyons has documented that the aspect ratio determines the flow regime in the canyon. Although various works have recommended critical Reynolds Numbers to achieve Reynolds Number independent flows within street canyons, numerous papers have cited different flow regimes for different aspect ratios. The purpose of this study is to investigate the discrepancies in the relationships between flow regimes and aspect ratios. 2D PIV measurements were taken and the various flow regimes were investigated at different Reynolds Numbers, H/delta ratios and aspect ratios. Based on 200 cases considered over Reynolds Numbers between 4363 and 82,424, it is proposed that the flow regimes are not solely dependent on the aspect ratio but also on other parameters such as the ratio of the height of the building (H) to the depth of the incoming boundary layer (\textbf{delta}) for wind tunnel experiments. Other observations made during the course of this study that add insight into the urban flow physics are also presented.   

Reversals of the Large-scale Circulation in Turbulent Thermal Convection in Small Aspect-ratio Geometry

We present experimental studies of flow reversals and cessations in turbulent thermal convection in cells of aspect ratio ($\Gamma )$ less than one. It is found that cessations of the large-scale circulation (LSC) occur not only in $\Gamma $ =1 cells but also in $\Gamma $ = 1/2 and 1/3 cells, and they occur in these small aspect ratio cells an order of magnitude more frequently than in $\Gamma $ =1 cells. The experiment reveals that in these small aspect ratio cells 180$^{o}$ is the most probable orientational angular change of the LSC's circulation plane after a cessation. The time interval of successive cessations is found to distribute exponentially. It is further found that a cessation correspond to decoherence of the LSC.   

The effect of rotation on nonlinear stratified flow over topography

Steady, two-dimensional, rotating, stratified flow of large depth over topography is considered for the case of uniform flow speed and buoyancy frequency far upstream. Under these flow conditions, if rotation is not present, the nonlinear response due to finite-amplitude topography can be found analytically via Long's model. It turns out that rotation behaves as singular perturbation as it always becomes important in the far field, and we examine its effect on Long's nonlinear flow state by a matched-asymptotics procedure in the weak-rotation limit (large Rossby number). It is found that nonlinear interactions over the topography induce propagating gravity-inertial waves that alter the nature of the response far downstream. Representative streamline patterns are shown, and the implications for unsteady flow computations are discussed.   

Baroclinic turbulence on a polar beta-plane by Altimetric Imaging Velocimetry: laboratory experiments

A new method of optical altimetry with color coding was designed for measuring the slopes of the free surface elevation field and calculation of geostrophic velocity field. The examples of baroclinic flows on a rapidly rotating turntable will be demonstrated and discussed. The flows are created by releasing lighter fluid on the surface of the rotating layer or at the interface between the two layers. The surface of the rapidly rotating layer is of the form of a paraboloid which creates a dynamical effect of a polar beta-plane. The evolving turbulent flows include vortices, beta gyres, multiple zonal jets and Rossby waves. The geostrophic velocity, vorticity and surface elevation are measured by AIV with very high resolution of typically several million vectors. Two-dimensional spectra are documented and the features of these flows are discussed.