The three dimensional linear hydrodynamic equations which describe wind induced flow in a sea are solved using the Galerkin method. A basis set of eigenfunctions is used in the calculation. These eigenfunctions are determined numerically using an expansion of B-splines.



Using the Galerkin method the problem of wind induced flow in a rectangular basin is examined in detail. A no-slip bottom boundary condition with a vertically varying eddy viscosity distribution is employed in the calculation. With a low (of order 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s near the sea bed together with high current shear in this region are physically realistic and have been observed in the sea.



In order to accurately compute the eigenfunctions associated with large (of order 2000 cm2/s at the sea surface to 1 cm2/s at the sea bed) vertical variation of viscosity, an expansion of the order of thirty-five B-splines has to be used. The spline functions are distributed through the vertical so as to give the maximum resolution in the high shear region near the sea bed.



Calculations show that in the case of a no-slip bottom boundary condition, with an associated region of high current shear near the sea bed, the Galerkin method with a basis set of the order of ten eigenfunctions (a Galerkin-eigenfunction method) yields an accurate solution of the hydrodynamic equations. However, solving the same problem using the Galerkin method with a basis set of B-splines, requires an expansion of the order of thirty-five spline functions in order to obtain the same accuracy.



Comparisons of current profiles and time series of sea surface elevation computed using a model with a slip bottom boundary condition and a model with a no-slip boundary condition have been made. These comparisions show that consistent solutions are obtained from the two models when a physically relistic coefficient of bottom friction is used in the slip model, and a physically realistic bottom roughness length and thickness of the bottom boundary layer are employed in the no-slip model.

Formulation of a linear three-dimensional hydrodynamic sea model using a Galerkin-eigenfunction method

Three dimensional modal model of wind induced flow in a sea region

Spectral Models in Continental Shelf Sea Oceanography

A three-dimensional numerical hydrodynamic model was used to study the tides and certain aspects of the wind-forced flow in Narragansett Bay. The governing equations are solved using the Galerkin-spectral method in the vertical and explicit finite differences in the horizontal and time. A split-mode formulation is used to minimize computational time. Simulations of the M 2 tide gave average errors of less than 2% in amplitude and 2° in phase when compared with observations at 12 tidal-height stations within the Bay. An investigation of the Bay's response to steady, spatially uniform wind forcing indicated that the non-linear interaction between the tidal and wind induced motions strongly affected the predicted steady state current pattern. Calculation of the steady-state wind-induced transports showed that a significant exchange exists between the West Passage, East Passage and Sakonnet River. The dependence of the exchange on the wind magnitude and direction and on the choice of vertical eddy viscosity was investigated. A comparison between modeled results and measurements of current at three locations in the Bay indicated that the model is capable of reproducing some of the features of the wind-induced flow.

Numerical simulations of the tidal- and wind-driven circulation in Narragansett Bay

A three-dimensional numerical model system was developed to predict circulation and water quality induced by surface discharges in estuarine and coastal waters. The model system consists of hydrodynamic, pollutant-transport, and turbulence models. The model employs a new vertical γ-coordinate system, using an algebraic transformation within the well-known σ-coordinate transformation. Grids can be concentrated near the surface and bottom boundaries with a concentration factor proportional to the local water depth. Conservation equations are solved by finite-difference techniques. A semiimplicit algorithm is used for the vertically averaged exterior flow, and a vertically implicit procedure for the interior flow as well as salinity, pollutant constituents, and turbulent kinetic energy and dissipation. The hydrodynamic model was tested against analytical solutions for tidal forcing and density-induced flow in an open channel, and wind-forced flow in a closed basin. The vertical γ-grid system was tested for w...

A.M. Davies

Papers

On formulating a three-dimensional hydrodynamic sea model with an arbitrary variation of vertical eddy viscosity