OS53B-01
Modelling non-hydrostatic processes in sill regions
We use a non-hydrostatic model to compute tidally induced flow and mixing in the region of bottom topography representing the sill at the entrance to Loch Etive (Scotland). This site is chosen since detailed measurements were recently made there. With non-hydrostatic dynamics in the model our results showed that the model could reproduce the observed flow characteristics, e.g., hydraulic transition, flow separation and internal waves. However, when calculations were performed using the model in the hydrostatic form, significant artificial convective mixing occurred. This influenced the computed temperature and flow field. We will discuss in detail the effects of non-hydrostatic dynamics on flow over the sill, especially investigate non-linear and non-hydrostatic contributions to modelled internal waves and internal wave energy fluxes.
OS53B-02
Internal Tide Generation at the Sur Platform Region of Monterey Bay
Understanding the evolution of the internal tide field within the complex coastal ocean environment is essential to describing the interplay between bathymetry, internal tides, and areas of elevated dissipation. In an effort to gain insight into internal tide generation within the Monterey Bay area, we used high-resolution numerical simulation results from the nonhydrostatic, nonlinear, unstructured grid code SUNTANS. Our depth-integrated, M2-period averaged energy fluxes and energy flux divergences show the bulk of internal tide energy propagating from the south and into the Monterey Submarine Canyon from a location north of Sur Platform. From our previous simulations, a region of elevated internal tide activity occurs north of Sur Platform. Here we analyze and shed light on its structure and generation mechanism. Instantaneous plots of baroclinic velocity and horizontal kinetic energy are used to show the horizontal and vertical structure of the internal tide. When model results are plotted along with theoretical tidal characteristics, it may be concluded that the internal tide generated at the Sur Platform region is three-dimensional and linear. Furthermore, our simulation suggests the hotspot of internal tide activity north of Sur Platform results from the interaction between tidal beams generated from Sur Platform (north-south direction) and the shelf break (east- west direction). Acknowledgment: This work is supported by ONR grant N00014-05-1-0294. Simulations are carried out on the JVN cluster at the ARL Major Shared Resource Center. http://suntans.stanford.edu
OS53B-03
Non-hydrostatic Flow Observed in an Inlet Leading to Lake Pontchartrain
A fundamental assumption in estuarine dynamics is that the flow is hydrostatic, except for surface gravity waves. With increased refinement of high resolution numerical models, the need for non-hydrostatic models is again argued and such models are being developed widely. The observational aspect of this question is however rarely visited. Here, we present such observations in a tidal inlet leading to Lake Pontchartrain and show that the flow in the lake's inlet is non-hydrostatic. Strong upwelling and downwelling, on the order of 0.35 m/s and separated by 100 m, were repeatedly measured during flood tide using an acoustic Doppler current profiler within two 25-m bathymetric depressions 330 m apart. The flow was un-stratified due to tidal straining. The observed vertical acceleration can reach as high as 1.7x10-2 m/s2. The non-hydrostatic parameter was larger than 1, verifying that the flow was indeed non-hydrostatic. The significant implication of this study is that, since estuaries and tidal passes are numerous in coastal water, and they are places where the mixing of terrestrial water and coastal water occurs, it is necessary to include the non-hydrostatic dynamics for relevant environmental transport processes wherever it proves to have non-hydrostatic flows.
OS53B-04
Mathematical Classification and Laboratory Observations of Stratified Flow Components
New mathematical classification of a stratified fluid flow components based on analytical theory of partial differential equations with small coefficients and theory of continuous (Lie) groups is given. The conventional set of governing equations including equations of continuity, Navier-Stokes, Fourier, Fick and the state equation, was selected for further analysis as a result of comparison of general properties and infinitesimal symmetries of different sets of governing equations, which are mostly used in theoretical oceanography. Boundary and initial conditions are no-slip and no-flux on contact surfaces, decay of all disturbances at infinity and trivial for negative time. Firstly the diffusion induced flows on finite topography were studied analytically and numerically as an undisturbed state of stratified liquids. Then infinitesimal periodic flows were treated for different frequency ranges. In addition to waves of different types (inertial, internal, acoustical or hybrid) described by regular disturbed functions of complete solutions, a rich set of singular disturbed solutions is identified. The singular disturbed functions describe boundary layers on contact surfaces and their analogues in the fluid interior forming thin elongated structures. Viscosity effects cause two different boundary layers. They are linear predecessors of vortices and vortex systems. In frame of a homogeneous fluid approximation two different viscous boundary layers lost their features, turn to be identical and unified. So an insolubility of 3D Navier-Stokes equations both for compressible and incompressible fluids is explained by degeneration of the solvable equation set and incompleteness of problem posing. Exact solutions of linearized periodic internal waves generation problems induced by forced and free oscillating obstacles (strips, discs and spheres) are constructed and visualized numerically. Developed theory is compared with results of more than 4000 schlieren and probes experimental studies of flows generated in continuously stratified tanks by forced and free oscillating obstacles. Experiments with bodies of different shapes (strips, discs, spheres, cylinders) were performed in a wide range of buoyancy frequency, size, amplitude and direction of oscillations. On results of experiments we have identified a number of well-reproduced flow singular components besides the internal waves. They include boundary layers on the obstacle surface and high gradient interfaces inside continuously stratified fluid far from the source. Presented solutions of linear and weakly non-linear problems of 2D and 3D periodic internal wave generation match laboratory data rather well. Conditions of fine streaky structures existence are found and processes of their transformation into vortices directly inside the fluid are visualised. Following from the studies demands of completeness of a fluid dynamics experiment and direct control of accuracy are discussed. Extrapolation of received data on environmental systems is speculated.
OS53B-05
Stability and nonlinear evolution of coupled density fronts
We study the linear stability of coupled density fronts with the help of the collocation method, which enables us to treat flows with arbitrary potential vorticity (PV). In their classical work, Griffiths, Killworth and Stern (1982) have shown that coupled density fronts are unstable to perturbations with small wavenumbers and that flows with zero PV are, more precisely, unstable over an interval of finite width of small wavenumbers. Paldor and Ghil (1990) have shown that coupled density fronts with zero PV are unstable to perturbations with finite wavenumbers on finite intervals separated by intervals of stability, and when the wavenumber increases the maximum growth rate in each interval of unstability decreases. We have reproduced the results of Griffiths, Killworth and Stern (1982) and of Paldor and Ghil (1990), and we found, for zero PV flows, a new instability interval. For flows with non-zero PV the picture is qualitatively the same: we find several instability intervals, separated by stability zones in the wavenumber space. Each unstable interval has a maximum growth rate inferior to those of unstable intervals with smaller wavenumbers. We then study the nonlinear stage of evolution of the instability with the help of the high-resolution finite-volume numerical scheme by Bouchut (2007). The simulations are initialized with the most unstable eigenmode recovered from the linear analysis. We observe that as the instability develops the flow is reorganized into a series of rotating anticyclonic elliptic vortices connected by thin filaments of fluid. The parameters of vortices are close to those of rodons (Cushman-Roisin, Heil and Nof 1985), the exact lens-like solutions of the nonlinear shallow water equations. References: B. Cushman-Roisin, W.H. Heil and D. Nof, Journal of Geophysical Research, 1985. F. Bouchut in: V. Zeitlin et al, Edited Series on Advances in Nonlinear Science and Complexity, 2007. R.W. Griffiths, P. D. Killworth and M.E. Stern, Journal of Fluid Mechanics, 1982. N. Paldor and M. Ghil, Journal of Physical Oceanography, 1990.
OS53B-06
On a spectrum of nonlinear internal waves near the ocean coast
This work studies the internal wave band of temperature fluctuation spectra in the coastal zone of Pacific ocean. It is observed that on the central Mexican Pacific Shelf in the high-frequency band of temperature spectra the spectral exponent tends to ~ω-1 at the time of spring tide and ~ω-2 at the time of neap tide. On the western shelf of the Japan/East Sea, in the Ømega\llω\ll N* range, where N* is the representative buoyancy frequency and Ømega is the inertial frequency, the rate tends to ~ω-3. These features of spectra are simulated by the model spectrum of nonlinear internal waves in the shallow water. Interaction of high-frequency internal waves with an internal wave of semidiurnal frequency is considered. It is shown that as a result of the interaction the spectrum of high-frequency internal waves take the universal form and the spectral exponent tends to ~ω-1.
OS53B-07
Understanding Mixing and Entrainment of Oceanic Overflows Using Laboratory Experiments
Oceanic overflows are important elements of the Earth's global thermohaline circulation but the mixing and entrainment that occur for such overflows is poorly understood. In particular, as overflow water moves down an inclined slope its stability is governed by the competition between stratification, which stabilizes the flow, and vertical shear, which tends to destabilize the flow. The properties of our laboratory experiment are designed to mimic oceanic overflows to the extent achievable on laboratory-accessible length scales. The flow exits a nozzle and flows along an inclined plane such that there is gravitational forcing of the flowing gravity current. We inject turbulent velocity fluctuations into the fluid using an active rotating grid prior to its exit from the nozzle, thereby generating a turbulent boundary layer condition at the plane boundary. The Taylor Reynolds number of the flow coming out of the nozzle is about 150. Velocity and density fields are measured simultaneous using particle image velocimetry and planar laser induced fluorescence. The flow structure and dynamics of mixing at different downstream locations are investigated for a standard stratified case and a non-stratified case where there is no density difference between the injected current and the ambient fluid. The role of turbulence is examined by comparing cases of turbulent and the laminar gravity currents. The implication of these results for ocean simulations will be presented.