A Progress Report on the Control of the Free Surface in a 3D Navier Stokes Solver for Coastal Applications

This paper reports work in progress on the development of a data assimilation capability for an existing 3D Navier Stokes solver with application as an ocean model. The project is a collaboration between University of Strathclyde and Imperial College, London with the assistance of Dr Neill from the University of Wales, Bangor. The paper reports work carried out at Strathclyde University. The 3D NS solver developed by the Imperial team uses finite element methods with adaptive meshing, is non-hydrostatic and includes the free surface. However, proper treatment of the free surface in the adjoint problem is not straightforward. This paper describes a method of controlling the forward solution using either surface elevation or current data by solving an appropriate adjoint problem. This is formulated in a new way using a co-ordinate transformation such that the control problem appears in a fixed domain even though the forward problem has a variable domain due to the presence of the free surface.