sw_scaling

1D shallow water without bathymetry:

\[ \begin{align} h_t + (hu)_x & = 0 \\ (hu)_t + (hu^2 + \frac{1}{2}gh^2)_x & = 0 \end{align} \]

Units: (m=mass, d=distance, t=time)

• \(h\): \(d\)
• \(u\): \(d/t\)
• \(hu^2\): \(d^3/t^2\)
• \(g\): \(d/t^2\)

\[g = 9.8 \ m/s^2 = 980 \ cm/s^2\]