Modelling Coastal Sea Processes

The following sections are included:

• Preface

• Acknowledgements

• Contents

The dynamics which control the spread of tracers in the N.W. European Shelf Seas are reviewed. The perspective of this review is to allow a comparison with the vastly different regimes found in Australian waters. Whilst these N.W. European Shelf Seas are dominated by the influence of the M₂ semi-diurnal tide, the Gulfs off South Australia have significant diurnal constitutents and a peculiar near equality of M₂ and S₂—producing ‘dodge’ tides. Nevertheless, generalised expressions for both the annual mean and the seasonal amplitude of sea surface temperature (derived from North Atlantic data) are generally applicable.

The greater sensitivity of diurnal tidal constituents to bed friction coupled with the proximity to the related inertial latitude suggests that tidal propagation models may require more tuning of the bed stress coefficient. However the greatest contrast is for ‘estuaries’ where the excess of evaporation over precipitation and river flow produces ‘inverse estuaries’ unknown in Europe. Whilst flushing time concepts can be used in similar fashions, the extraction of tracers from such estuaries occurs close to the bed via ‘inverse’ salt wedges. This contrast with mean surface extraction in European estuaries will have significant influences on the related ecology.

A ‘Future Work’ section describes recent developments and plans to extend marine forecasting via Operational Oceanography. Whilst Australian requirements will differ considerably, the need to maintain awareness and adopt common practices is important to fulfill the wider goals of GOOS—the Global Ocean Observing System.

A system is described, based on finite-difference discretisations of the governing hydrodynamic equations, which determines the three-dimensional motions in well mixed coastal seas, produced by tidal and meteorological influences. It has been thoroughly tested and has been found to be very robust and accurate.

Closure of the system of equations is achieved using forms of the Boussinesq approximation to determine the coefficients in the turbulent eddy viscosity terms. A method of calibrating the model is also described.

A model that predicts tidal elevations and flow velocities is developed and applied to the Persian Gulf. The model uses finite difference techniques applied to two-dimensional spherical-coordinate equations that govern tidal movement in coastal regions. Because of the importance of the Gulf to the shipping and fishing industries, it is necessary to be able to predict tidal elevations and flows at many near-shore locations. However, it would be impractical to use a very fine finite difference grid over the whole Gulf, because of its size. A technique is developed for nesting a fine grid within a coarse grid, so that important areas can be modelled more accurately.

Analysis and prediction of fine resolution tidal model output for northern Spencer Gulf has previously proved troublesome due to its complex bathymetry. In this article techniques are described that allow for a complete and accurate analysis of tidal data, with three main issues being investigated:

• analysis and prediction of tidal velocities in transient tidal eddies,

• analysis and prediction of tidal elevations and velocities at intertidal flat locations, and

• analysis of short length tidal records using related tidal constituents.

A three-dimensional spherical co-ordinate tide and storm surge model has been forced on the open boundary with the five major tidal constituents (O₁, K₁, M₂, S₂ and M₃) of the Great Australian Bight to investigate the tides and currents therein. The model has also been used to compute the surge produced by the passage of a 11–13 April 1996 storm with the aim of determining whether the surge observed at Thevenard was due to the amplitude of surge which passed Esperance or due to meteorological forcing.

Sea level data were available at Esperance, Thevenard and Port Lincoln, with meteorological data available in the form of diagrams of isobars. These were used to derive variable pressure and wind fields, and combined with the surge which occurred on the western model boundary at Esperance and the south-eastern model boundary near Port Lincoln. Excellent agreement between modelled and recorded surge at Thevenard was found.

In this article we review and draw together recent work on the dynamical structure of storm surges. We demonstrate that, particularly in the region outside the main forcing zone, storm surges are primarily low-mode shelf waves. Some issues concerning the parameterization of the wind stress and frictional processes are also discussed briefly; for the latter case in particular, we discuss the effect of wind-generated waves in enhancing the bottom friction in the near-shore zone.

This article discusses the processes that contribute to storm surges and coastal flooding and describes numerical techniques used for modelling such processes, particularly with regard to overland coastal flooding. A storm surge model, which features a nesting capability and inundation algorithm, is described. The flooding and draining is dependent on the modelled current in adjacent ‘wet’ grid cells which ensures realistic and smoothly varying results. Several examples of the application of this system are presented. Through these examples, it is demonstrated that the inundation model is robust in a variety of geographical locations and under a range of grid resolutions. Surge heights at the coast are also compared with simulations where overland inundation is switched off and it is found that elevations are greater by up to 17% when the coastal boundary is approximated by a fixed wall. The applications of this system to hazard management and impact studies are also discussed.

This article discusses dispersion modelling in coastal seas, with particular application to western king prawn (Penaeus latisulcatus) larvae in Spencer Gulf, South Australia.

A three-dimensional (3D) numerical hydrodynamical modell (Noye et al., 1999) approximates tidal currents, at more than one depth, in the region of interest. An advection-diffusion dispersion model—derived by Nixon (1996) using an underlying two-dimensional ( 2D) numerical transport scheme chosen from many alternative finite-difference schemes—approximates larval concentrations up to a specified time after initial P. latisulcatus spawning.

Previous prawn larvae dispersion studies determined a depth-averaged model unsuitable (Noye et al., 1992), a first-order method inaccurate (Nixon and Noye, 1995), and a zero wind-stress approach unsatisfactory (Nixon and Noye, 1996a). Nixon and Noye (1996b) determined wind-stress effects on Spencer Gulf currents near the sea-surface and sea-bed and related these to larval dispersion therein. In this article, these effects for two dispersion periods corresponding to observed P. latisulcatus spawning peaks are compared. Simulations are found to adequately approximate dispersion processes observed in the field.

A Lagrangian-Stochastic particle tracking procedure has been developed for use in conjunction with tide and storm surge models for modelling dispersion in coastal seas. The behaviour of the scheme applied to two grid structures has been investigated and tested at the coastal and open sea boundaries, as well as in the interior of a hypothetical model. The particle tracking routine has been applied to the Gulf St. Vincent region in South Australia to model the dispersion of western king prawn (Penaeus latisulcatus) from spawning grounds to coastal nurseries in the Gulf.

A three-dimensional hydrodynamic-numeric computer program to compute sea levels and currents caused by tides, winds and surges at the open boundary was applied to Boston Bay, South Australia to calculate near-surface and near-bottom currents during the tuna mortalities of April 1996. A particle tracking computer program, based on a Lagrangian–Stochastic procedure, using these currents as input was then applied to the lower part of the water column to compute the movement of suspended sediment near the sea floor. When compared with cumulative tuna deaths, a significant connection between suspended sediment concentrations and mortality percentages at tuna farm locations is evident if a three to five day time lag is assumed.

Shallow estuarine basins have small ocean exchange rates during periods of drought (when they are vertically mixed). This exchange is primarily due to gravitational processes. These are forced by a density difference between the basin and ocean produced by the surface buoyancy flux. This flux is dependent on the estuarine temperature, which is itself affected by the ocean exchange of heat. This creates a strong interaction between the buoyancy flux, and the density difference, and may be represented by a Stommel(1961) non-linear estuarine model. It involves a meteorological constant Γ, and a parameter ε, which measures the strength of the (buoyancy forced) gravitational exchange processes. The model has two stable states, or attractors, one of which corresponds to a classical, and the other to an inverse, estuary. The analysis considers the range of (ε, Γ²) under which both of these steady states exist and investigates their comparative attractions. On seasonal time scales, the estuary may be in a transitory state (described here by manifold theory) in which the estuary may be ‘positive’ or ‘negative’ according to the sign of the buoyancy flux. For typical meteorological conditions, four categories of transitory estuary emerge which are dependent on the magnitude of ε.

The tidal flushing of an estuary or inlet is often used to assist with the dispersal of waste water on a falling tide. During inflow, water is generally drawn radially towards the estuary mouth. The nature of the inflow and outflow depends on the topography of the sea floor, particularly if the floor is shelving into deeper water or if there is an off-shore bar.

The analytic model of Wolanski and Imberger (1987) is examined in detail and a full set of similarity solutions are derived for the inflow regime. These are applicable to a range of bottom profiles which may be used to model a limited set of practical examples or to provide verification for a numerical scheme.

A numerical solution is also developed for more general depth profiles. It uses a five point finite-difference stencil to derive an algebraic system representing the elliptic equation satisfied by the stream function. MATLAB programming is used to implement and display the solution on an 80486 AT machine (IBM PC).

A variety of bottom profiles were investigated to assess the effects of the slope of the sea floor, and of a sand bar along the beach and across the inlet mouth. Implications of the bar on the inflowing movement of water were also investigated, with special reference to the Tweed River mouth and neighbouring coastline.

The maturity of a scientific field can be measured by its capacity to formulate models. On this basis coastal modelling is in a mature stage with a range of models that have been developed and tested, both analytically and more importantly, in the field.

This article gives details of numerical packages that can hindcast the seastate, solve the wave and current fields around structures in the nearshore zone, make predictions about medium to long-term morphological developments, and predict the effects of storm attack on sandy beaches and dune systems. The models have an accepted mathematical basis and have been tested over a widerange of analytical and field situations.

The following sections are included:

• Index