AssumptionsAssumptions

Inviscid: no term in Navier-Stokes Non-rotating, uniform density atmospheric pressure constant and uniform.

Shallow Water Equations Equation of Continuity:

Depth Integration:

Equation of Continuity

m = density( ) * h* dx Dx = u*dt m = *h*u*dt

Hydrostatic Balance

Pressure increases with depth according to

overhead mass per unit area.

Pressure at depth h-z:

Integrating

Depth Integration

But,=>

Therefore Net Force =>F = F

s + F1 – F2

Thus we get,

Shallow Water Equation => (h)

tx= - (uh)

xx

=> (u)

tt = - g(h)

tx

Eliminating (h)tx on both sides,

(uh) xx

- 1/g*u tt = 0.

(u)xx

– (1/gh)*utt=0 (Hyperbolic PDE)

Wave Equation -> c2(u)

xx – u

tt = 0

Thus, c=root(gh);

- Tushar Athawale.