In these equations, f is the Coriolis parameter, p is density of water, p0 is reference density of water, p is the pressure, g is acceleration of gravity, and AM and KM are the eddy viscosity in horizontal and vertical motions.
Integrating (4) in z from the bottom(z = H) to the sea surface(z = η), the pressure is obtained by:
p=pa+pg(η-z) (7)
where pa is the atmospheric pressure.
The surface elevation is calculated by the following equation which is obtained by integrating (1) from the bottom to the sea surface:
A different treatment is needed to determine the fluid motion below the Mega-Float, because there is no surface elevation. Integrating the momentum equations vertically under the Mega-Float, we get the 2D Poisson equation with respect to the pressure underneath the Mega-Float3).
The density current is driven by the density difference, which is largely determined by the water temperature(T( and the salinity(S(%。)). We used the following formula by Mamayev4):
T and S are calculated by the following diffusion equations:
where γb2 is friction coefficient at the sea bottom; γf2 is friction coefficient below the mega-float; Cd is friction coefficient at the sea surface; (ub, vb) is velocity vector at the sea bottom; (uf,vf) is velocity vector at bottom of the mega-float; (uw,vw) is wind velocity; and Pa is atmospheric density.
The boundary conditions for T are derived from the thermal exchanges at each boundary. Usually, the adiabatic condition is applied at the coastline and the sea bottom. Thermal exchanges are used at the sea surface and the open boundaries.
At the sea surface, the following four components are taken into account: sun's radiative energy(Qs), long wave radiation(Qb), the latent heat transport by evaporation(Qe) and the sensible heat transport(Qc), Total thermal exchang at the sea surface is given as:
