Problem #3:
More Geostrophic Adjustment

Again consider geostrophic adjustment in shallow water theory, this time with η(x,0)=(1/L)exp(-(Sqrt[(x^2)]) /L).

Your tasks:
 ☺ Find an expression for (Subscript[η, g])(x,0).
 ☺ Make a plot of (Subscript[η, g])(x,0) for the case for ((Subscript[L, R])/L)=0, .25, 1 and 4.