Stratification, forcing and Coriolis effects

For the base stratification the following we have used the following profile

$$\overline\rho=\left\{ \begin{array}{ll} a(b-e^{z/c+0.3125}... ...^{3.6})) & \mbox{if $-1\le z/c\leq 0$,} \end{array} \right.$$ (5)

where $a=3.5561\times 10^{-3},\,\,b=7.1724,\,\, c=16\,\mbox{m and}\, d=0.367.$ This profile fits reasonably well the stratification measured in the middle of the basin during the CTD cruises. We must bear in mind, however, that these measurements are aliased by the presence of the ISW field. No attempt was made to correct for this.

The magnitude of the barotropic forcing was chosen to match the vertically-averaged and low-pass filtered currents observed in the middle of the basin. Values ranged from 10 to 15 cm/s, as expected based on the diurnal variation in the elevation signal. We choose an averaged value of 12.5 cm/s. That is, we set the transport on the eastern boundary $Q_{\rm max}=23.12 {\rm m}^2/{\rm s}$, which gave a maximum speed of 45 cm/s and 12.8 cm/s on top of the Bank and in the middle of the Basin respectively, in agreement with the measurements of Chereskin and ours. The Rossby radius of deformation $c/f$, based on the observed stratification, is minimum at the crest of the Bank, being of the order of 2 Km and maximum in the middle of the basin, about 4 Km. Thus rotation will affect the dispersion of waves with wavelength of the order, or larger, than the Rossby radius of deformation. To investigate the effect of rotation on the long wave we consider the case with and without rotation. In both cases we start at the beginning of the ebb phase. In the former, the initial condition is simply that the fluid is at rest, that is $\omega=0$ and $\rho'=0$. In the latter, we still set $\omega=0$ and $\rho'=0$, but in addition we need to prescribe an initial condition for the component of the velocity normal to the domain. Following Lamb (JGR, 99, C1 843-864) we set

$$v(x,z)=-{f T\over 2\pi}{Q_t(T/2)\over D(x)} {x\over L},$$ (6)

where T is the period.