A three-dimensional hydrodynamic numerical model of the Hauraki Gulf, New Zealand

Abstract

A three dimensional finite difference hydrodynamic numerical model was developed and used to study the tidal and wind driven currents in the Hauraki Gulf. The model flow and energy output was verified through comparison of analytical and experimental data with numerical results. The tidal currents in the Hauraki Gulf were calibrated against acoustic Doppler field measurements recorded in Jellicoe Channel and the America's Cup race area, as well as data from previous numerical studies. Results from simulations performed using the calibrated model showed that wind driven currents in the Gulf are extremely three dimensional due to their interaction with the coastline, the bathymetry and background tidal currents. The advection terms of the momentum equations were solved using an explicit Eulerian-Lagrangian scheme that was shown to be stable under a mild stability condition. The interpolation function used in this scheme generated numerical diffusion that, for the grid sizes and time steps used in the Hauraki Gulf model, damped the solution more than it would have in reality. Despite this the fluid velocities in the Gulf were not affected significantly because few sharp velocity gradients were present Turbulence closure up to the level of a k-e model was used. Due in part to the artificial diffusion present in the model but also to the scale of circulation investigated, all the turbulence models implemented produced similar velocity profiles. For computational expense reasons the mixing length turbulence closure model was chosen to represent tidal currents while a parabolic distribution of eddy viscosity was chosen to represent wind driven currents. The acoustic Doppler measurements recorded showed fluid density effects that were not taken into account in the present study A graphical user interface was also developed for use in conjunction with the numerical model to assist with the input of data and the display of model output. This program was created using Visual C++ and· thus used the 'Windows' functionality of dialog boxes and menu items to allow easy user interfacing.