John M. Huthnance

Circulation, exchange and water masses at the ocean margin: the role of physical processes at the shelf edge

Abstract The coastal ocean meets the deep sea at the continental shelf edge. Questions of global change entail elucidation of the processes that determine the quantities, transformation and fate of materials transported between the shelf and ocean, the measurement and definition of exchange processes, and the development of prognostic models of exchanges. Physical processes control the large-scale movement and irreversible small-scale mixing of water and its constituents. At the shelf edge, steep bathymetry may inhibit ocean-shelf exchange, but in combination with stratification gives rise to special processes and modelling challenges. A preliminary assessment is made of coastal-trapped waves; along-slope currents, instability and meanders; eddies; upwelling, fronts and filaments; downwelling, cascading; tides, surges; internal tides and waves as potentially influential processes in ocean-shelf exchange, water-mass structure and general circulation, according to their scales and context. For this purpose, theory and previous measurements are interpreted. Future studies needed to improve this assessment are discussed.

On one mechanism forming linear sand banks

Asymmetric tidal currents ( Huthnance, 1973 ) provide a fluid-dynamical basis for Castons (1972) description of linear sand-bank maintenance by converging sand transport. We suppose (i) depth-uniform tidal currents, slightly inclined to the bank crest, (ii) bottom-drag, which retards the current more over the bank and (iii) a faster-than-linear increase of sand transport with current. Then over a sloping bank side the total tidal current having an upslope component and the associated onto-bank sand transport are stronger than the retarded reverse tidal current and transport coming off the bank. Supposing that (iv) sand is more easily transported ‘downhill’ shortwavelength perturbations on a level sea floor are suppressed. There is a maximum bed-form growth rate at a particular wavelength (typically 250 times the water depth) and orientation (relative to the tidal currents) which probably evolve and persist during subsequent sand-bank growth. The orientation is sensitive to the (uncertain) formulation of supposition (iv), and is probably also susceptible to (for example) the trend of an adjacent coastline. In the representative context of friction-dominated tidal currents, the banks evolve to an equilibrium profile which is flatter on top than a sinusoid owing to wind-wave erosion and the inclination to the tidal current. For a limited sand supply the banks narrow to about one-fifth of their separation; further restriction mainly reduces their height. A net sand-transport overall due to a stronger ebb tide (say) than flood, as occurs over the Norfolk Sandbanks, yields the observed steeper slope on the obliquely downstream side of the bank (as viewed by the stronger ebb current).

On Coastal Trapped Waves: Analysis and Numerical Calculation by Inverse Iteration

Abstract Waves of sub-inertial frequency in a continuously stratified ocean and trapped over a continental shelf and slope are considered. They form one infinite discrete sequence of modes with frequencies decreasing to zero. The mode frequencies increase with stratification. All modes progress with the coast on their right in the Northern Hemisphere. In three formal asymptotic limits the waves adopt special forms: (1) large longshore wavenumber [Rhines (1970) bottom–trapped waves]; (2) small stratification [barotropic continental shelf waves]; and (3) large stratification [baroclinic (internal) Kelvin-like waves]. These results are illustrated by numerical calculations using the method of inverse iteration, which avoids time integration. Further calculations demonstrate the strong influence of the depth and density profiles on the wave forms. In particular, a realistic context (i.e., a gently sloping shelf bounded by a steeper continental slope, together with greater stratification near to the surface) a...

Slope Currents and “JEBAR”

Abstract For currants along continental slopes, the joint effect of baroclinicity and bottom relief (JEBAR) provides important local forcing, comparable with the wind stress. The poleward density increase (or corresponding sea level decline) typically drives O(0.1 m s−1) poleward currents confined over the continental slope and independent of the wind. This transport is significant at eastern oceanic margins.

The Rockall slope current and shelf-edge processes

Recent knowledge of physical-oceanographic processes is reviewed for the eastern shelf-edge boundary of the Rockall Channel. A year-round northward current flows along the steep continental slope. Mean currents vary from 3 to 30cm/s, generally increasing northwards, but estimates of transport inshore of the 2000 m depth contour are much more consistent, averaging about 1·5 × 106m3/s. The current is thought to be forced largely by a long-shelf pressure gradient, associated with large-scale N-S density variations in the upper ocean. Although cross-slope changes of temperature and salinity are much less than occur, for example, east of the U.S.A., cross-slope exchange velocities appear to be only around 2cm/s (1/5 of long-slope fluctuations). There is a sharp change between winter-cooled water on the shelf and adjacent slope water. Upwelling against the upper continental slope may occur following northerly long-slope winds. Tidal currents and surges depend strongly on continental shelf wave properties. At near-diurnal frequencies, and in response to winds of short scale (< 100 km), clockwise-rotating currents near the shelf break are expected, especially where the shelf is broadest. Tidal currents show this character. Internal tides are significant; any non-linearity is most likely when stratification is present but weak. Bottom stirring has been observed, and may be important at some depth (where the bottom slope becomes as steep as the semi-diurnal internal characteristics) almost everywhere around the Rockall Channel. The energetic internal waves should contribute significant internal mixing as they approach the shelf break, intensify and dissipate.

On the formation of sand banks of finite extent

We consider a model where the fluid depth depends on both horizontal coordinates, quasi-steady depth-uniform non-divergent fluid flow is governed by inertial, pressure and bottom-frictional forces, sand transport is proportional to the cube of the instantaneous current but augmented by a down-slope component and by wind-wave action, and sand is conserved. It is found that low parallel banks grow fastest, so that in an extensive spatially uniform sea previous calculations for linear banks are appropriate. The inclination of banks to the tidal currents can be interpreted in terms of similarly inclined deposition bands resulting from vorticity generation and advection in flow over a small isolated hump. A small bump can evolve to an equilibrium bank (typically after an initial rapid extension across the tidal currents) provided that sand is sufficiently restricted and particularly if some wind-wave action prevents growth up to the sea surface. Sand banks are likely to be in a late stage of evolution, when the main change is a slow lengthening as the net current and transport along the bank side slows and turns around the bank end with net deposition. The equilibrium is apparently stable except when there is an overall bed slope in the direction of the tidal currents, or when sand is abundant.

Waves and currents near the continental shelf edge

The abrupt depth increase which characterises the edge of many continental shelves determines a reduced horizontal length scale and a localised transition from shelf seas to the deep ocean. Particular forms of motion which may arise from the steep slopes include topographically guided currents along the slope, shelf-break upwelling, topographic Rossby waves and internal lee waves in the tidal current. The ocean/shelf mismatch may lead to a clear separation of water types, substantial reflection (from the shelf-edge neighbourhood) of all oceanic and shelf motions with periods greater than a few hours, and interaction between barotropic and baroclinic motions. Unstable longshelf currents, interleaving water masses, strong internal tides and internal waves, and narrow canyons enhance mixing across the shelf edge.

On trapped waves over a continental shelf

Any straight continental shelf of monotonic depth profile is shown to have as its entire complement of barotropic trapped modes (i) an infinite discrete set of ‘continental-shelf waves’, (ii) a single ‘Kelvin wave’, and (iii) an infinite discrete set of ‘edge waves’. The decomposition of energy density and fluxes into modal constituents is discussed.

On mass transports generated by tides and long waves

For small-amplitude barotropic wave motion in a shallow fluid, Moore (1970) found that the associated mean mass transport is geostrophic, but otherwise arbitrary in the absence of friction. We show how weak friction, or starting the motion from rest, determines the mass transport by restricting circulation around closed geostrophic (f/h) contours. The resulting transport is quadratic in oscillatory quantities and depends on the friction type, but not on its (weak) magnitude. Comparison is made with earlier results in particular geometries. A tendency for anticyclonic circulation around shallow regions is found, and extends to large-amplitude oscillations where particle excursions exceed the topographic length scale. We suggest that numerical schemes for calculating tidal residuals should conserve mass and vorticity.

Physical oceanography of the North Sea

The oceanography of the North Sea is described, with emphasis on physical aspects; bathymetry, the dominant tides, surges and waves which form the dynamical background for, for example, dispersive process and stratification; the seasonal cycle; water types, frontal boundaries and circulation; sea level trends and statistics. Some constituent distributions are described, including mobile sediments, with some discussion of their relation to differing inputs and dispersive influences. The status of data, process understanding and modelling is discussed.