Turbulence in the presence of internal waves in the bottom boundary layer of the California inner shelf

Turbulence measurements were collected in the bottom boundary layer of the California inner shelf near Point Sal, CA, for 2 months during summer 2015. The water column at Point Sal is stratified by temperature, and internal bores propagate through the region regularly. We collected velocity, temperature, and turbulence data on the inner shelf at a 30-m deep site. We estimated the turbulent shear production (P), turbulent dissipation rate (ε), and vertical diffusive transport (T), to investigate the near-bed local turbulent kinetic energy (TKE) budget. We observed that the local TKE budget showed an approximate balance (P?≈?ε) during the observational period, and that buoyancy generally did not affect the TKE balance. On a finer resolution timescale, we explored the balance between dissipation and models for production and observed that internal waves did not affect the balance in TKE at this depth.     

Effects of the bottom boundary condition in numerical investigations of dense water cascading on a slope

The flow of dense water along continental slopes is considered. There is a large literature on the topic based on observations and laboratory experiments. In addition, there are many analytical and numerical studies of dense water flows. In particular, there is a sequence of numerical investigations using the dynamics of overflow mixing and entrainment (DOME) setup. In these papers, the sensitivity of the solutions to numerical parameters such as grid size and numerical viscosity coefficients and to the choices of methods and models is investigated. In earlier DOME studies, three different bottom boundary conditions and a range of vertical grid sizes are applied. In other parts of the literature on numerical studies of oceanic gravity currents, there are statements that appear to contradict choices made on bottom boundary conditions in some of the DOME papers. In the present study, we therefore address the effects of the bottom boundary condition and vertical resolution in numerical investigations of dense water cascading on a slope. The main finding of the present paper is that it is feasible to capture the bottom Ekman layer dynamics adequately and cost efficiently by using a terrain-following model system using a quadratic drag law with a drag coefficient computed to give near-bottom velocity profiles in agreement with the logarithmic law of the wall. Many studies of dense water flows are performed with a quadratic bottom drag law and a constant drag coefficient. It is shown that when using this bottom boundary condition, Ekman drainage will not be adequately represented. In other studies of gravity flow, a no-slip bottom boundary condition is applied. With no-slip and a very fine resolution near the seabed, the solutions are essentially equal to the solutions obtained with a quadratic drag law and a drag coefficient computed to produce velocity profiles matching the logarithmic law of the wall. However, with coarser resolution near the seabed, there may be a substantial artificial blocking effect when using no-slip.     

A numerical model of the wave boundary layer

A numerical model of deep, uniform, oscillatory, rough-turbulent boundary-layer flow is described. The model is based upon the governing horizontal momentum equation and a closure scheme involving the turbulent-energy equation and various turbulence-scaling laws. Finite difference solutions of these equations are obtained for a range of values of the ‘relative roughness’ (A₀/k_s), whereA₀ is the excursion amplitude of the water particles in the free-stream flow andk_s is the ‘equivalent bed roughness’. Typical vertical profiles of horizontal velocity, turbulence energy and eddy viscosity, and time-series of the bed shear stress are presented. The model results are then used to determine the wave drag coefficient, boundary-layer thickness and phase lead of the bed shear stress over the free-stream velocity, each as a function ofA₀/k_s. These results are shown to be in generally good agreement with previous experimental and theoretical results. Finally, the model is used to test for the existence of a universal velocity distribution for uniform oscillatory (sinusoidal) rough-turbulent flow. The ‘law of the wall’ and the ‘defect law’ proposed by Jonsson (1980, Ocean Engineering, 7, 109–152) are well supported by the model, and the existence of a logarithmic ‘velocity overlap layer’ in which both of these laws are valid is demonstrated forA_o/k_s30.     

Barotropic instability of a boundary jet on a sloping bottom

Abstract

The stability of a shear flow on a sloping bottom in a homogeneous, rotating system was investigated by means of a laboratory experiment.

The basic flow was driven near a vertical wall of a circular container by a ring-shaped plate that contacted with a free surface of the working fluid and rotated relative to the fluid container. The velocity profile was asymmetric in the radial direction and had only one inflection point. The velocity profile was well expressed by a linear theory for the vertical shear layer.

The effect of the circular geometry was checked by comparing experimental results obtained in two fluid systems in which only the sign of the curvature was opposite and it was confirmed that circular geometry was not essential for the shear flow on the sloping bottom in this experiment.

It was found that the sloping bottom stabilizes the basic flow only when the drift direction of the topographic Rossby wave is opposite to that of the basic flow. The viscous dissipation in both the Ekman layer and the interior region was also important in determining the critical Rossby number.

The eddy fields caused by the instability can be classified into two types: One is the stationary eddy field in which a row of eddies moves along the basic flow without changing form. The other is the flow pattern in which eddies have finite life times and their configuration is not well organized. When the sloping bottom does not stabilize the basic flow, the former flow pattern is realized, otherwise the latter flow pattern appears.

The wave numbers of the eddies in the regular flow pattern were observed as a function of the Rossby number. The relation did not fit to linear preferred modes predicted by an eigenvalue problem.     

A nonlinear numerical model for sloped‐bottom tuned liquid dampers

Shaking‐table data for a tuned liquid damper with a sloped bottom of 30° with the horizontal are investigated using a non‐linear numerical model previously developed by Yu, Jin‐kyu, Nonlinear characteristics of tuned liquid dampers. Ph.D. Thesis, Department of Civil Engineering, University of Washington, Seattle, WA, 98195 (1997). Stiffness and damping parameters for this model are obtained and compared with those previously derived for box‐shaped tanks. The values for these parameters reflect the softening spring behaviour of the sloped‐bottom system in contrast to the hardening system evident for the box‐shaped TLD. Consequently, the sloped‐bottom tank should be tuned slightly higher than the fundamental structural frequency in order to obtain the most effective damping. Copyright © 2001 John Wiley & Sons, Ltd.     

Large-scale impacts of bottom trawling on shelf primary productivity

Disturbance of the seabed resulting from bottom trawling affects ecosystem processes, such as the rate and magnitude of nutrient regeneration. The potential responses of the plankton community arising from such effects can be modelled, provided that reliable data on the effects on nutrient fluxes are available. In a north Cretan outer continental shelf and upper slope fishing ground (Heraklion Bay, Crete, Eastern Mediterranean) we applied a new field instrument which can simulate the passage of trawl groundropes across the sea floor and made direct seasonal measurements of the rate of dissolved and particulate nutrient releases resulting from seabed disturbance. These observational data were then integrated in a 3D ecosystem model. Results revealed that bottom trawling may trigger off considerable productivity pulses, in addition to pulses from the natural seasonal cycle.     

Numerical study of three-dimensional shelf circulation on the Scotian Shelf using a shelf circulation model

A numerical shelf circulation model was developed for the Scotian Shelf, using a nested-grid setup consisting of a three-dimensional baroclinic inner model embedded inside a two-dimensional barotropic outer model. The shelf circulation model is based on the Princeton Ocean Model and driven by three-hourly atmospheric forcing provided by a numerical weather forecast model and by tidal forcing specified at the inner model's open boundaries based on pre-calculated tidal harmonic constants. The outer model simulates the depth-mean circulation forced by wind and atmospheric pressure fields over the northwest Atlantic Ocean with a horizontal resolution of 1/12°. The inner model simulates the three-dimensional circulation over the Gulf of St. Lawrence, the Scotian Shelf, and the adjacent slope with a horizontal resolution of 1/16°. The performance of the shelf circulation model is assessed by comparing model results with oceanographic observations made along the Atlantic coast of Nova Scotia and in the vicinity of Sable Island (on the Scotian Shelf) during two periods: October 2000–March 2001 and April–June 2002. Analysis of model results on Sable Island Bank indicates that tidal currents account for as much as ∼80% of the total variance of near-bottom currents, and currents driven by local winds account for ∼30% of the variance of the non-tidal near-bottom currents. Shelf waves generated remotely by winds and propagating into the region also play an important role in the near-bottom circulation on the bank.     

The influence of initial conditions and open boundary conditions on shelf circulation in a 3D ocean-shelf model of the North East Atlantic

Data from climatology (World Ocean Atlas) and two large scale operational ocean models (Forecasting Ocean Assimilation Model (FOAM), UK Met. Office and the Navy Coastal Ocean Model (NCOM), US Naval Research Laboratory) are used to give initial and open boundary conditions for a northeast Atlantic implementation of the Proudman Oceanographic Laboratory Coastal Ocean Model System (POLCOMS). We study the effects of using the different datasets on the temperature fields and the circulation. On the continental shelf, comparisons of POLCOMS output with Advanced Very High Resolution Radiometer sea surface temperature data suggest that the effect of using different ocean model initial and boundary conditions is small and that, after 15 months of model time, the impact of the different initial conditions is negligible. Stronger evidence of influence is seen in the deeper oceanic regions of the domain. Volume fluxes through sections governing flow into and out of the North Sea, through the Irish Sea and along the shelf edge show that the impact of the different boundary conditions is small on the shelf but significant elsewhere. These results are contrasted with the use of climatology to assess the value of these Global Ocean Data Assimilation Experiment ocean model products.     

Benthic oxygen fluxes and sediment properties on the northeastern New Zealand continental shelf

We examined spatial variations in benthic remineralisation (measured as sediment oxygen consumption (SOC)) and sediment properties on the northeastern New Zealand continental shelf and slope to assess the importance of benthic mineralisation in this ecosystem and to provide data for more complete global carbon budgets. SOC measured in dark incubations conducted in early summer ranged from 128 μmol m⁻² h⁻¹ at the deepest (360 m) to 1222 μmol m⁻² h⁻¹ at the shallowest (4.2 m) site and decreased significantly with water depth (p<0.001, r²=0.78, SOC=1222.8−456.3×log₁₀[water depth], n=14 sites). These rates were in the range found on continental shelves elsewhere (64–1750 μmol m⁻² h⁻¹, n=30 studies) and had a very similar distribution with water depth. SOC was also measured in light incubations at seven sites (4.2–35 m water depth) to examine the effects of microphytobenthos and accounted for 42–106% of rates measured in the dark. Measurements of near-bed light intensities suggested that microphytobenthos production was not solely regulated by light intensity but evidently influenced by other factors. A two-dimensional PCA ordination of surface sediment properties accounted for 83.3% of the total variance in the data and divided the study area into three clusters that corresponded well to its spatial division into the shallow (<30 m) Firth of Thames, the Hauraki Gulf (30–50 m) and the northern shelf-slope region. In the Firth of Thames sediments were very fine-grained with low CaCO₃ and high total organic matter and pigment content, and low C:N ratios. The northern shelf-slope sediments showed the opposite trends to the Firth of Thames and those in the Hauraki Gulf had mostly intermediate values. Dark SOC was significantly correlated with sediment organic matter, carbon, nitrogen, pigments and silt/clay content (p<0.05, r=0.55–0.85) but a multiple linear regression revealed that water depth was the only significant predictor. Calculations suggest that approximately 13%, 10% and 34% of primary production is remineralised in the sediments of the northern shelf-slope region, Hauraki Gulf and Firth of Thames, respectively, indicating a strong benthic–pelagic coupling on the northeastern New Zealand continental shelf that was particularly pronounced in the Firth of Thames due to its shallow depth and significant terrestrial and riverine inputs.     

Internal waves,baroclinic energy fluxes and mixing at the European shelf edge

The energy flux in internal waves generated at the Celtic Sea shelf break was estimated by (i) applying perturbation theory to a week-long dataset from a mooring at 200 m depth, and (ii) using a 2D non-hydrostatic circulation model over the shelf break. The dataset consisted of high resolution time-series of currents and vertical stratification together with two 25-h sets of vertical profiles of the dissipation of turbulent kinetic energy. The observations indicated an average energy flux of 139 W m⁻¹, travelling along the shelf break towards the northwest. The average energy flux across the shelf break at the mooring was only 8 W m⁻¹. However, the waves propagating onshelf transported up to 200 W m⁻¹, but they were only present 51% of the time. A comparison between the divergence of the baroclinic energy flux and observed dissipation within the seasonal thermocline at the mooring showed that the dissipation was at least one order of magnitude larger. Results from a 2D model along a transect perpendicular to the shelf break showed a time-averaged onshelf energy flux of 153–425 W m⁻¹, depending on the magnitude of the barotropic forcing. A divergence zone of the energy flux was found a few kilometre offshore of the location of the observations in the model results, and fluxes on the order of several kW m⁻¹ were present in the deep waters further offshelf from the divergence zone. The modelled fluxes exhibited qualitative agreements with the phase and hourly onshelf magnitudes of the observed energy fluxes. Both the observations and the model results show an intermittent onshelf energy flux of 100–200 W m⁻¹, but these waves could only propagate ∼20–30 km onshore before dissipating. This conclusion was supported by a 25-h dataset sampled some 180 km onto the shelf, where a weak wave energy flux was found going towards the shelf break. We therefore conclude that shelf break generated internal waves are unlikely to be the main source of energy for mixing on the inner part of the shelf.     

Effect of stratification on tidal circulation over the Scotian Shelf and Gulf of St. Lawrence: a numerical study using a three-dimensional shelf circulation model

A three-dimensional shelf circulation model is used to examine the effect of seasonal changes in water-column stratification on the tidal circulation over the Scotian Shelf and Gulf of St. Lawrence. The model is driven by tidal forcing specified at the model’s lateral open boundaries in terms of tidal sea surface elevations and depth-averaged currents for five major tidal constituents (M₂, N₂, S₂, K₁, and O₁). Three numerical experiments are conducted to determine the influence of baroclinic pressure gradients and changes in vertical mixing, both associated with stratification, on the seasonal variation of tidal circulation over the study region. The model is initialized with climatological hydrographic fields and integrated for 16 months in each experiment. Model results from the last 12 months are analyzed to determine the dominant semidiurnal and diurnal tidal components, M₂ and K₁. Model results suggest that the seasonal variation in the water-column stratification affects the M₂ tidal circulation most strongly over the shelf break and over the deep waters off the Scotian Shelf (through the development of baroclinic pressure gradients) and along Northumberland Strait in the Gulf of St. Lawrence (through changes in vertical mixing and bottom stress). For the K₁ constituent, the baroclinic pressure gradient and vertical mixing have opposing effects on the tidal circulation over several areas of the study region, while near the bottom, vertical mixing appears to play only a small role in the tidal circulation.     

Assimilation of ERS-1 altimeter data in a tidal model of the continental shelf

Summary In this paper ERS-1 altimeter data are used for the calibration of a tidal model of the European Continental Shelf. The data assimilation procedure to estimate the uncertain parameters in the model is based on the adjoint method. Here the estimation problem is formulated as a large scale optimization problem, that is solved with a gradient based optimization method. The gradient is determined efficiently by using the solution of the adjoint problem. The data assimilation procedure is applied by using the ERS-1 data with and without other measurement information from water level stations.

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Assimilation von ERS-1 Altimeter Daten in einem Gezeitenmodell des Kontinentalschelfs

Zusammenfassung In dieser Arbeit werden ERS-1 Altimeter Daten zum Kalibrieren eines Gezeitenmodells des Europäischen Kontinentalschelfs benutzt. Das Verfahren der Datenassimilation zur Bestimmung der unbekannten Modellparameter beruht auf der adjungierten Methode. Die Aufgabe ist ein großskaliges Optimierungsproblem, das mit einem Gradientenverfahren gelöst wird. Zur Gradientenbestimmung benutzt man die Lösung des adjungierten Problems. Neben den Daten von ERS-1 werden wahlweise noch Beobachtungen von Küstenpegeln assimiliert.

     

Biological enhancement of solute exchange between sediments and bottom water on the Washington continental shelf

Solute exchange between the interstitial waters and overlying waters on the Washington continental shelf was investigated based on measurements of the pore-water sulfate distribution and sulfate reduction rates as well as through models describing the distribution of sulfate in anaerobic pore waters. The depth-integrated sulfate reduction rate greatly exceeded the influx of sulfate attributable to molecular diffusion and sediment accumulation acting on the measured vertical sulfate gradients, and indicated that additional transport mechanisms must have been operating. Sediment mixing was probably not the primary mechanism since high eddy diffusivities would be required to depths of 30 cm to maintain the observed sulfate distribution, whereas previously measured²¹⁰Pb distributions indicated sediment mixing is primarily restricted to depths <7 cm. Irrigation of bottom water through animal burrows was the most likely mechanism. To describe this process, a general diffusive irrigation coefficient, B, was formulated. Vertical profiles of B showed the main irrigation zone occurred between 2 and 10 cm with reduced irrigation rates occurring below this. These coefficients calculated from the sulfate distribution were similar to ones calculated from previously published radon measurements at the same stations, indicating that this formulation of irrigation exchange may be useful in modelling the exchange of dissolved solutes between the pore water and the bottom water.     

Changes in material fluxes from the Changjiang River and their implications on the adjoining continental shelf ecosystem

This study aims to examine the changing patterns of Changjiang material fluxes, which are influenced by anthropogenic activities, and the resultant modifications to the coastal and shelf oceanographic conditions, and to propose future research about the effect of these changes on the estuarine and shelf ecosystem. Within the catchment basin of the Changjiang River, the construction of more than 48,000 dams has caused significant sediment discharge reduction, together with modifications to the timing of seasonal freshwater discharge. In the future, the mean freshwater discharge will decrease following the completion of the water-diverting project for water supply to northern China. At the same time, the riverine nutrient loadings (N and P) have increased due to the extensive use of chemical fertilizers and the large discharge of industrial wastewater and domestic sewage. These changes are modifying the oceanographic conditions of the estuarine and shelf waters. The flushing time for the river water becomes longer in wet seasons but shorter in dry seasons. An increase in salinity can be expected after the completion of the water-diverting project. Nutrient concentrations will be enhanced in the shelf waters. In contrast to the decrease in the suspended sediment concentration of the river water, field measurements have not shown well-defined patterns of changes within the estuary; nevertheless, net sediment accumulation and carbon burial rates would be reduced in the deltaic areas because of the reduced sediment discharge. Finally, increase in the nutrient input appears to enhance the primary production in the East China Sea region, which, in turn, may enhance the fishery catch.     

Experiments using a long-time-scale shelf circulation model of relevance to the Labrador Current

Experiments are described using a three-dimensional, shelf circulation model. The model geometry consists of a rectangle in latitude-longitude space with a shelf-slope region bordering the northern and western boundaries and a deep ocean region in the southeast. Relatively light water is flushed in through the northern boundary and allowed to exit through the southern boundary, a situation of relevance to the southward flowing Labrador Current. In an earlier paper, we showed the downstream development of a shelf break current. In that paper, bottom friction was parallel to bottom geostrophic velocity. In this paper, bottom friction is parallel to bottom velocity. This leads to a more diffuse downstream jet. We show that changing the density contrast across the front does not change its width. On the other hand, a sharper front is obtained when a small trough is introduced into the bottom topography. We also describe an experiment in which the density of the inflowing water is varied seasonally. This leads to a seasonal redistribution of the southward transport across the shelf, similar to a suggestion made by Myers et al. [(1989) Seasonal and interannual variability of the Labrador Current and West Greenland Current. Department of Fisheries and Oceans, Canada] for the Newfoundland Shelf. This redistribution results from the seasonal pulsing of fresh water down the shelf, which, in turn, influences transport through the Joint Effect of Baroclinicity And Relief (JEBAR), and is similar to the mechanism proposed by Lazier and Wright [(1993) Journal of Physical Oceanography, 23, 659–678].Other results concern the splitting of the shelf break jet. We show that in the previous paper, the splitting of the jet was influenced by the numerical formulation of the outflow condition at the southern boundary. We also show that the splitting can be suppressed by specifying the density of water flowing into the model domain through the southern boundary, rather than allowing this to be determined by the previous history of mixing and outflow on the boundary.     

Global distribution of energetic proton precipitations equatorward of the boundary of isotropic fluxes

Based on data of the NOAA POES satellite, the global distribution of the occurrence rate of precipitations of energetic protons (E > 30 keV) equatorward of the boundary of isotropic fluxes has been constructed for the first time. It has been shown that the occurrence rate of proton precipitations inside the zone of anisotropic fluxes is maximum in daytime hours (1100–1600 MLT) at latitudes L = 6–9 and decreases in evening and morning hours. Comparison of the obtained results about proton precipitations with the spatial distribution of the occurrence rate of electromagnetic ion–cyclotron (EMIC) waves in the equatorial magnetosphere according to results of satellite observations demonstrates a close relationship between them. This corroborates that precipitations of energetic protons equatorward of the boundary of isotropic fluxes are a consequence of the development of the ion–cyclotron instability in the equatorial magnetosphere.     

A model of secondary upwelling over the shelf break

Motivated by our puzzling high-resolution radar observations of surface vortices in the nearly rectangular Gulf of Eilat/Aqaba, northern Red Sea, we propose and explore the driven cavity approach to this geophysical phenomenon. While the lid-driven cavity has long been considered a benchmark problem in computational fluid dynamics, its oceanographic context has not been considered. Despite the additional effects of rotation and stratification, our modeling demonstrates that when the fluid within a cavity geometrically similar to the Gulf of Eilat is driven by the external current, an interior vortex can develop as in our observations. Furthermore, the Eilat vortices appear only under relatively calm conditions, adding evidence to the intriguing possibility of their simple shear-driven origin.     

Flow modelling in gravel‐bed rivers: rethinking the bottom boundary condition

A key problem in computational fluid dynamics (CFD) modelling of gravel‐bed rivers is the representation of multi‐scale roughness, which spans the range from grain size, through bedforms, to channel topography. These different elements of roughness do not clearly map onto a model mesh and use of simple grain‐scale roughness parameters may create numerical problems. This paper presents CFD simulations for three cases: a plane bed of fine gravel, a plane bed of fine gravel including large, widely‐spaced pebble clusters, and a plane gravel bed with smaller, more frequent, protruding elements. The plane bed of fine gravel is modelled using the conventional wall function approach. The plane bed of fine gravel including large, widely‐spaced pebble clusters is modelled using the wall function coupled with an explicit high‐resolution topographic representation of the pebble clusters. In these cases, the three‐dimensional Reynolds‐averaged continuity and Navier–Stokes equations are solved using the standard k ? ε turbulence model, and model performance is assessed by comparing predicted results with experimental data. For gravel‐bed rivers in the field, it is generally impractical to map the bed topography in sufficient detail to enable the use of an explicit high‐resolution topography. Accordingly, an alternative model based on double‐averaging is developed. Here, the flow calculations are performed by solving the three‐dimensional double‐averaged continuity and Navier‐Stokes equations with the spatially‐averaged 〈k ? ε〉 turbulence model. For the plane bed of fine gravel including large, widely‐spaced pebble clusters, the model performance is assessed by comparing the spatially‐averaged velocity with the experimental data. The case of a plane gravel bed with smaller, more frequent, protruding elements is represented by a series of idealized hypothetical cases. Here, the spatially‐averaged velocity and eddy viscosity are used to investigate the applicability of the model, compared with using the explicit high‐resolution topography. The results show the ability of the model to capture the spatially‐averaged flow field and, thus, illustrate its potential for representing flow processes in natural gravel‐bed rivers. Finally, practical data requirements for implementing such a model for a field example are given. Copyright © 2011 John Wiley & Sons, Ltd.