Initial conditions

The initial velocity field is quiescent, the initial free surface height is 0, and the initial density distribution is defined in the function ReturnSalinity in initialization.c as

  return -.03*tanh(2.0*2.6467/20*(z+50-cos(PI*x/100)));

Because $\beta=1$ in suntans.dat (the parameter beta), this is also the initial density distribution, since $(\rho-\rho_0)/\rho_0 = \beta(s-s_0)$ More generally, then, this density distribution is given by

$$\frac{\rho}{\rho_0} = -\frac{1}{2}\frac{\Delta\rho}{\rho_0} ... ...-1}(\alpha)}{\delta}\left(z+\frac{D}{2}-\zeta\right)\right] ,$$

where

• $\Delta\rho/\rho_0=0.06$: Density difference between layers.
• $\alpha=0.99$: Parameter that defines interface extent.
• $\delta=20$ m: Interface thickness.
• $z$: Vertical coordinate
• $D=100$ m: Depth
• $\zeta = \cos(\pi x/L)$: Interface profile, where $L=100$ m is the domain length.

and is shown in Figure 7.

Figure 7: Initial density distribution in $x$-$z$ (a) and as a profile at $x=L/2$ (b) for the time accuracy test case.

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