  The Whitham equation was proposed as an alternate model equation for the
simplified description of uni-directional wave motion at the surface of an
inviscid fluid. As the Whitham equation incorporates the full linear dispersion
relation of the water wave problem, it is thought to provide a more faithful
description of shorter waves of small amplitude than traditional long wave
models such as the KdV equation.
  In this work, we identify a scaling regime in which the Whitham equation can
be derived from the Hamiltonian theory of surface water waves. The Whitham
equation is integrated numerically, and it is shown that the equation gives a
close approximation of inviscid free surface dynamics as described by the Euler
equations. The performance of the Whitham equation as a model for free surface
dynamics is also compared to two standard free surface models: the KdV and the
BBM equation. It is found that in a wide parameter range of amplitudes and
wavelengths, the Whitham equation performs on par with or better than both the
KdV and BBM equations.
