Forces at the Sea Bed using a Finite Element Solution of the Mild Slope Wave Equation

Abstract

An algorithm to compute forces at the sea bed from a finite element solution to the mild slope wave equation is devised in this work. The algorithm is best considered as consisting of two logical parts: The first is concerned with the computation of the derivatives to a finite element solution, given the associated mesh; the second is a bi-quadratic least squares fit which serves to model the sea bed locally in the vicinity of a node. The force at the sea bed can be quantified in terms of either lift and drag, the likes of Stokes' formula or traction. While the latter quantity is the most desireable, the direct computation of tractions at the sea bed is controversial in the context of the mild slope wave equation as a result of the irrotationality implied by the use of potentials. This work ultimately envisages a ``Monte Carlo'' approach using wave induced forces to elucidate presently known heavy mineral placer deposits and, consequently, to predict the existance of other deposits which remain as yet undiscovered.