For waves much longer than the water depth h, the one-dimensional shallow-water equations apply: ∂η/∂t + ∂(h u)/∂x = 0 and ∂u/∂t + u ∂u/∂x = -g ∂η/∂x - friction, with surface height η and total depth h = η - bed. Small waves travel at c = √(g h), so they slow down over the sloping beach. Energy flux conservation then gives Green's law, amplitude ∝ h-1/4: the wave grows taller and steeper as it shoals, which is why a tsunami that is a few tens of centimetres in the deep sea becomes dangerous at the coast.
The bed here is the same profile as the 3D tank: h = 2 m in the flat part, then a ramp rising 3.4 m x^1.25 toward the beach. The solver is a staggered finite-difference scheme (forward-backward in time) with a simple quadratic bottom friction and a dry-cell cut-off. Simplifications: no breaking, no dispersion (real tsunami physics is also long-wave), no Coriolis, a tank 20 m long instead of an ocean. Checks: arrival time of a small pulse against the integral of dx/√(g h), and conservation of water volume in the closed tank.