On the deviation of the average pressure at a fixed point in a moving fluid from its “hydrostatic” value

Summary

A homogeneous, non-viscid fluid with a free surface, moving under the influence of gravity, is considered. If the motion, between a fixed point P and the surface, can be considered as statistically steady and horizontally statistically homogeneous, the pressure at the point P, averaged over a sufficiently long time interval, is given by the corresponding average hydrostatic expression minus ρ$\rho \overline {w1^2 }$, where ρ = density and $\overline {w1^2 }$= corresponding average square of the vertical velocity at the point P. The approximate validity of this relation is shown for the example of waves approaching and breaking over a sloping beach.