A complete spherical harmonic approach to luni-solar tides

In this work a spherical harmonic theory of ocean tides is presented. The theory is based on Laplace tide equations modified to include turbulence with constant eddy viscosity, linearized bottom friction, and oceanic loading and self-gravitation. Variable bathymetry is also treated in harmonic terms, and no-flow boundary conditions are applied at continental coastlines. The tide and boundary constraint equations are reduced to matrix form and solved by a weighted least-squares procedure. Five zonal luni-solar tides, ranging in period from 14 days to 18.6 yr, are investigated using the theory; such tides have typically been difficult to compute using traditional numerical approaches. The polar motion and changes in the length of day induced by these long-period tides are calculated. Tidal solutions are compared extensively with results from other tidal theories and from recent satellite and sea-level observations. The greatest limitation to accurate prediction of zonal tides - for any theory - appears to be the marginal failure of all tide theories to conserve mass globally; the use of additional mass constraints may be warranted.