ON OBTAINING THE STEADY-STATE SOLUTIONS OF THE LINEARIZED 3-DIMENSIONAL HYDRODYNAMIC EQUATIONS

Three techniques are presented for solving the depth-average hydrodynamic equations to yield steady-state solutions that are compatible with the full three-dimensional linearized equations. The first technique establishes criteria for ensuring that two-dimensional (in plan) models, using the convolution method for bottom friction, converge to a steady-state solution that is compatible with a full 3-D model. A simple form of convolution kernel (an exponential), which may be represented by a simple recurrence relationship, is described. The second technique uses an alternative form of the convolution method, expressing the depth-averaged velocity directly as an exponential convolution integral. A variant of this technique is very similar to the conventional linear friction method and therefore may be easily implemented in existing models. The third technique replaces the dynamic equation with the steady-state solution itself. The resultant set of equations may be solved by conventional time-stepping or by the numerical solution of a Poisson equation.