The effects of large and small-scale topography upon internal waves and implications for tidally induced mixing in sill regions

A free surface non-hydrostatic model in cross-sectional form namely two dimensional in the vertical is used to examine the role of larger scale topography, namely sill width and smaller scale topography namely ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work, and the wider literature in order to emphasis the problems of simulating mixing in hydrographic models. Highlights from previous calculations, and references to the literature for detail together with new results presented here with smooth and “ripple” topography are used to show that an idealised cross sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales the presence of small scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small scale sill topography is varied, show for the first time that it is the small scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short term and longer term calculations with a reduced sill width, and associated time series, show that as the sill width is reduced the non-linear response of the system increases. In addition Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence a Froude number based on sill depth and local N is the critical parameter, rather than one based on total depth and mean N

A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms

We present a numerical kinetic scheme for an unsteady mixed pressurised and free surface model. This model has a source term depending on both the space variable and the unknown, U, of the system. The source term is composed by a topography, a section variation, a curvature (also called corrective) and a friction term. Using the Finite Volume and Kinetic (FVK) framework, we propose an approximation of the source terms following the principle of interfacial upwind with a kinetic interpretation: the source term is not treated as a volumic term, but included in the numerical fluxes. Then, several numerical tests are presented

Links between topography, wind, deflation, lakes and dust: The case of the Bodélé Depression, Chad

The Bodélé Depression, Chad is the planet's largest single source of dust. Deflation from the Bodélé could be seen as a simple coincidence of two key prerequisites: strong surface winds and a large source of suitable sediment. But here we hypothesise that long term links between topography, winds, deflation and dust ensure the maintenance of the dust source such that these two apparently coincidental key ingredients are connected by land-atmosphere processes with topography acting as the overall controlling agent. We use a variety of observational and numerical techniques, including a regional climate model, to show that: 1) contemporary deflation from the Bodélé is delineated by topography and a surface wind stress maximum; 2) the Tibesti and Ennedi mountains play a key role in the generation of the erosive winds in the form of the Bodélé Low Level Jet (LLJ); 3) enhanced deflation from a stronger Bodélé LLJ during drier phases, for example, the Last Glacial Maximum, was probably sufficient to create the shallow lake in which diatoms lived during wetter phases, such as the Holocene pluvial. Winds may therefore have helped to create the depression in which erodible diatom material accumulated. Instead of a simple coincidence of nature, dust from the world's largest source may result from the operation of long term processes on paleo timescales which have led to ideal conditions for dust generation in the world's largest dust source. Similar processes plausibly operate in other dust hotspots in topographic depressions

Topographical scattering of waves: a spectral approach

The topographical scattering of gravity waves is investigated using a spectral energy balance equation that accounts for first order wave-bottom Bragg scattering. This model represents the bottom topography and surface waves with spectra, and evaluates a Bragg scattering source term that is theoretically valid for small bottom and surface slopes and slowly varying spectral properties. The robustness of the model is tested for a variety of topographies uniform along one horizontal dimension including nearly sinusoidal, linear ramp and step profiles. Results are compared with reflections computed using an accurate method that applies integral matching along vertical boundaries of a series of steps. For small bottom amplitudes, the source term representation yields accurate reflection estimates even for a localized scatterer. This result is proved for small bottom amplitudes $h$ relative to the mean water depth $H$. Wave reflection by small amplitude bottom topography thus depends primarily on the bottom elevation variance at the Bragg resonance scales, and is insensitive to the detailed shape of the bottom profile. Relative errors in the energy reflection coefficient are found to be typically $2h/H$.Comment: Second revision for Journal of Waterways Ports and Coastal Engineerin

Current effects on scattering of surface gravity waves by bottom topography

Scattering of random surface gravity waves by small amplitude topography in the presence of a uniform current is investigated theoretically. This problem is relevant to ocean waves propagation on shallow continental shelves where tidal currents are often significant. A perturbation expansion of the wave action to second order in powers of the bottom amplitude yields an evolution equation for the wave action spectrum. A scattering source term gives the rate of exchange of the wave action spectrum between wave components, with conservation of the total action at each absolute frequency. With and without current, the scattering term yields reflection coefficients for the amplitudes of waves that converge, to the results of previous theories for monochromatic waves propagating in one dimension over sinusoidal bars. Over sandy continental shelves, tidal currents are known to generate sandwaves with scales comparable to those of surface waves. Application of the theory to such a real topography suggests that scattering mainly results in a broadening of the directional wave spectrum, due to forward scattering, while the back-scattering is generally weaker. The current may strongly influence surface gravity wave scattering by selecting different bottom scales with widely different spectral densities due the sharp bottom spectrum roll-off.Comment: submitted to Journal of Fluid Mechanics 7 Oct 200

Dynamic sea surface topography, gravity and improved orbit accuracies from the direct evaluation of SEASAT altimeter data

A method for the simultaneous solution of dynamic ocean topography, gravity and orbits using satellite altimeter data is described. A GEM-T1 based gravitational model called PGS-3337 that incorporates Seasat altimetry, surface gravimetry and satellite tracking data has been determined complete to degree and order 50. The altimeter data is utilized as a dynamic observation of the satellite's height above the sea surface with a degree 10 model of dynamic topography being recovered simultaneously with the orbit parameters, gravity and tidal terms in this model. PGS-3337 has a geoid uncertainty of 60 cm root-mean-square (RMS) globally, with the uncertainty over the altimeter tracked ocean being in the 25 cm range. Doppler determined orbits for Seasat, show large improvements, with the sub-30 cm radial accuracies being achieved. When altimeter data is used in orbit determination, radial orbital accuracies of 20 cm are achieved. The RMS of fit to the altimeter data directly gives 30 cm fits for Seasat when using PGS-3337 and its geoid and dynamic topography model. This performance level is two to three times better than that achieved with earlier Goddard earth models (GEM) using the dynamic topography from long-term oceanographic averages. The recovered dynamic topography reveals the global long wavelength circulation of the oceans with a resolution of 1500 km. The power in the dynamic topography recovery is now found to be closer to that of oceanographic studies than for previous satellite solutions. This is attributed primarily to the improved modeling of the geoid which has occurred. Study of the altimeter residuals reveals regions where tidal models are poor and sea state effects are major limitations

Noise-Sustained currents in quasigeostrophic turbulence over topography

We study the development of mean structures in a nonlinear model of large scale ocean dynamics with bottom topography and dissipation, and forced with a noise term. We show that the presence of noise in this nonlinear model leads to persistent average currents directed along isobaths. At variance with previous works we use a scale unselective dissipation, so that the phenomenon can not be explained in terms of minimum enstrophy states. The effect requires the presence of both the nonlinear and the random terms, and can be though of as an ordering of the stochastic energy input by the combined effect of nonlinearity and topography. The statistically steady state is well described by a generalized canonical equilibrium with mean energy and enstrophy determined by a balance between random forcing and dissipation. This result allows predicting the strengh of the noise-sustained currents. Finally we discuss the relevance that these noise-induced currents could have on real ocean circulation.Comment: 11 pages REVTeX. Includes 4 figures using epsf. Related material in http://www.imedea.uib.es/Nonlinear and http://www.imedea.uib.es/Oceanograph

Electric fields as a means of controlling thin film flow over topography

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.Gravity-driven, steady-state flow of a thin liquid film over a substrate containing topography in the presence of a normal electric field is investigated. The liquid is assumed to be a perfect conductor and the air above it an ideal dielectric. The Navier-Stokes equations are solved using a new depth-averaged approximation that is capable of analysing film flows with inertia, with the flow coupled to the electric field via a Maxwell normal stress term that results from the solution of Laplace’s equation for the electric potential above the film. The latter is solved analytically using separation of variables and Fourier series. The coupled solver is used to analyse the interplay between inertia and electric field effects for flow over onedimensional step and trench topographies and to predict the effect of an electric field on three-dimensional Stokes flow over a two-dimensional trench topography. Sample results are given which investigate the magnitude of the electric fields needed to suppress free surface disturbances induced by topography in each of the cases considered.This study is funded by the European Union via Marie Curie Action Contract MEST-CT-2005-020599