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 -.001*tanh(2.0*2.6467/5*(x-50.0));

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

$$\frac{\rho}{\rho_0} = -\frac{1}{2}\frac{\Delta\rho}{\rho_0} ... ...anh}^{-1}(\alpha)}{\delta}\left(x-\frac{L}{2}\right)\right] ,$$

where

• $\Delta\rho/\rho_0=2\times 10^{-3}$: Density difference.
• $\alpha=0.99$: Parameter that defines interface extent.
• $\delta=5$ m: Interface thickness.
• $x$: Horizontal coordinate.
• $L=100$ m: Length

and is shown in Figure 9.

Figure 9: Initial density distribution in $x$-$z$ (a) and as a profile at $x=L/2$ (b) for the lock exchange test case.

0.8