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

On the interaction of internal tides over two adjacent sills in a fjord

The problem of to what extent two topographic features, namely, adjacent sills in a fjord, interact to modify the internal waves between the sills is considered using a two-dimensional vertical slice nonhydrostatic model. Motion is generated by forcing with a barotropic tide at the M2 frequency. Calculations are performed with a range of sill depths hs and sill separations L. Initially, a single sill is considered and a progressive internal tide, lee waves, and a baroclinic jet are formed in the region of the sill. When a second sill is introduced, the intensity of the sill jet is reduced and a standing internal tide is generated between the sills, with an associated increase in mixing and change in tidal energy flux. However, as the sill separation increases, the energy flux increases toward its single sill value. For higher harmonics of the tide, which have a wavelength shorter than the intersill separation, their magnitude is increased for certain sill separations L due to focusing with an associated broadband resonance. In essence, nonlinear interaction of waves between the sills increases mixing, which explains the observed enhanced mixing found in observations made in such region

Application of an unstructured mesh model to the determination of the baroclinic circulation of the Irish Sea

A three‐dimensional finite volume model with horizontally varying, but fixed in time mesh, is used to compute the baroclinic circulation of the Irish Sea during 1995. Tidal forcing was applied along the model's open boundary with meteorological forcing taken from observations. Initial calculations were performed with a mesh that had high resolution in the well mixed near coastal region; a necessary requirement in order to reproduce tides in the region, although offshore in the stratified area the mesh was slightly coarser than that used in earlier finite difference models. Subsequent calculations were performed using an enhanced resolution which is significantly finer than earlier finite difference models in the offshore region which is thermally stratified in summer due to solar heating and low tidal mixing. This produces a cold water bottom dome separated from the well mixed shallow water regions by strong tidal fronts. Calculations show that both model meshes can reproduce the observed major features of the baroclinic circulation of the western Irish Sea, with the coarse mesh model giving comparable results to earlier finite difference models. In the case of the finer mesh model there are sharper horizontal density gradients in the region of the fronts, which show the presence of baroclinic instability and associated small scale variability as observed in satellite images but not found in the coarser mesh model due to lack of resolution. Results from the fine mesh model show significantly more spatial variability comparable to that found in the measurement

Influence of multiple sills upon internal wave generation and the implications for mixing

A cross sectional non-hydrostatic model of a fjord is used to examine to what extent the internal tide is modified by two closely spaced sills. The model is forced with an M2 barotropic tide and internal tides, unsteady lee waves and a jet are generated at the sills. In contrast to an isolated sill, calculations with two closely spaced sills show that the presence of the second sill leads to standing internal wave generation with associated changes in wave spectrum and Richardson number in the inter sill region. Associated with these there is a cascade of energy towards short waves leading to enhanced mixing between the sills. This increase in mixing is consistent with enhanced mixing between closely spaced sills found in observations. It is also relevant to enhanced oceanic and lake mixing, and suggest that future mixing measurements in both oceans and lakes should focus on these regions

Internal wave trapping and mixing in a cold water dome

A cross-sectional nonlinear numerical model of a shallow sea basin containing a cold water dome is used to examine the influence of wind frequency and dome characteristics upon internal waves and mixing. At superinertial forcing frequencies, nonlinear effects in the frontal regions of the dome give rise to propagating internal waves which are reflected by the dome's fronts. This reflection gives a standing internal wave trapped within the dome. The spatial variability of the wave is determined by forcing frequency, stratification and dome length. The magnitude of the internal wave and the length of the dome are related to the horizontal distribution of density in the frontal region. At the inertial frequency there is little internal wave propagation, while at subinertial forcing frequencies the internal wave is trapped in the frontal region, and energy cannot radiate away. Consequently, vertical mixing is enhanced in the frontal regions, while in the center of the dome the mixed layer increases due to the vertical diffusion of the wind's momentum to depth as in a single point model. In the case of wind forcing at a superinertial frequency, there is less mixing in the frontal region with internal wave propagation leading to mixing in the center of the dome. These calculations suggest that the breakdown of cold water domes in response to winter wind events may be due to a number of mixing processes depending upon wind frequency

On the influence of stratification and tidal forcing upon mixing in sill regions

A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill. Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood stage. Their magnitude and hence the mixing increased with increasing Froude number (F (r)). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F (r) number, with its value below influencing internal waves magnitude at depth. At high F (r) values particularly with strong currents, short waves and overturning occurred

Processes influencing wind-induced current profiles in near coastal stratified regions

Cross sectional and single point models of wind-induced currents in a stratified sea coastal region are used to determine the role of internal waves due to various wind periods upon mixing and current profiles. The limitations of a point model in reproducing current profiles are also examined. Calculations are performed with both fixed vertical diffusion coefficients and those derived from a turbulence closure model. Wind forcing at sub-inertial, inertial and super-inertial frequencies together with a wind impulse are considered. Results show that the offshore extent of the coastal boundary layer where mixing occurs depends upon the frequency of the wind forcing. The extent of this region and offshore propagation of internal waves influences the offshore variability of current profiles and the extent to which they can be reproduced by a single point model. Calculations with periodic wind forcing show that within the coastal boundary layer a point model cannot reproduce the current profile due to the internal pressure gradients associated with the internal wave field. However outside this region, current profiles from a point model are in good agreement with those computed with the cross section model when a barotropic pressure gradient forcing proportional to the local wind forcing is included. In the case of transient wind forcing, the inertial period dominates and determines the offshore extent of the coastal boundary layer. The transient nature of the response is such that although the single point model, outside the coastal region can reproduce the surface current due to direct wind forcing, the current at depth is not reproduced. The offshore extent of the coastal boundary layer computed with the turbulence energy model is comparable to that found with fixed diffusion coefficients although in some cases there are important differences which influence current profiles

Influence of stratification and topography upon internal wave spectra in the region of sills

A non-hydrostatic model in vertical cross section form is used to examine the role of sill width and buoyancy upon the energy cascade into the internal tidal band and higher frequencies in sill regions. Power spectra analysis of computed time series show that as sill width is reduced the energy transfer from the baroclinic tide to its higher harmonics is reduced. However, there is an increase in energy at higher frequencies corresponding to lee wave periods. In addition internal mixing on the lee side of the sill increases. The addition of small scale topography on the sill slope produces a similar spectral change in the internal wave distribution and mixing. For a narrow sill the addition of a surface buoyant layer with a higher buoyancy frequency, significantly reduces the energy cascade to higher frequencies with a corresponding reduction in mixing. The associated spectra have characteristics resembling wide sill topography

Assessment of non-hydrostatic ocean models using laboratory scale problems

Numerical ocean models have become important in scientific studies of oceans, for the management of marine systems, and for industrial off-shore activities. It is therefore essential that the increasing amounts of model outputs are to be trusted. However, the development of quantitative methods for skill assessment of ocean models has proved to be very difficult. Exercises on comparisons of model results from different models and on comparisons of model results with observations often reveal significant differences. Most numerical studies of the oceanic flow are today performed with hydrostatic ocean models. With increasing spatial resolution the hydrostatic assumption becomes more questionable, and the interest in non-hydrostatic models for the ocean is increasing. In computational fluid dynamics there is a tradition for assessment of the models through comparisons with laboratory experiments. Non-hydrostatic ocean models may also be assessed using this approach. In the present paper a non-hydrostatic z-coordinate model and a non-hydrostatic σ-coordinate model are applied to study lock release gravity currents in a flat bottom tank, and the propagation and breaking of an internal solitary wave in a tank with a sloping bottom. The focus of the latter case is especially on model outputs showing the propagation and breaking of the solitary wave up an incline. The agreement between the results from the two models is generally very good, and front speeds and wave speeds are in good agreement with corresponding values from experimental data

Free surface, current profile and buoyancy effects upon internal wave energy flux profiles in sill regions

A non-hydrostatic ocean circulation model is used to determine the distribution of the horizontal energy flux terms due to internal waves in sill regions. Calculations show that although the linear energy flux term is significant, the contribution from the non-linear terms is appreciable. In addition, unlike as is often assumed in deep ocean situations, the free surface contribution to the energy flux distribution often dominates. The magnitude and relative importance of the energy flux terms are influenced by how the fluctuating velocity due to internal waves is computed. In addition changes in vertical stratification affects the relative contribution of the energy flux terms although the free surface term still dominates. Crown Copyright (C) 2009 Published by Elsevier B.V. on behalf of IMACS. All rights reserved