Abstract
During reflection from a solid vertical wall, surface gravity waves produce a steady force on the wall, which was calculated earlier by the momentum method. Recently the linear momentum of these waves has been estimated to be twice as large as deduced from the classical Stokes drift formula. Therefore, the magnitude of the reflected wave force has been doubled here and the algebraic form of the equation is converted to be more understandable physically. Wave force equals fluid density times the square of the particle’s orbital speed and a numerical constant. Observations are welcomed to compare with the theory.
Highlights
There would seem to be a certain amount of urgency in better understanding the magnitude of the force on a wall caused by the reflection of surface gravity waves hitting the wall
A recent unexpected theoretical result [3] can be used to modify the earlier force formula derived from the momentum balance, because it has been found that the linear momentum of surface gravity waves is very likely twice the value obtained from the Stokes drift equation that was derived over 170 years ago
In a mathematical examination of propagating surface gravity waves he made a calculation that the orbits of the fluid particles are not completely closed circles, in such a way that at the end of a wave period there is a tiny advancement of fluid in the direction of wave travel, which since has been called the Stokes drift
Summary
There would seem to be a certain amount of urgency in better understanding the magnitude of the force on a wall caused by the reflection of surface gravity waves hitting the wall. One reason for urgency is the potential practical application of the force equation to various marine structures on beaches and in harbors within the field of ocean engineering. Another reason is to clear up the conceptual confusion springing from the existence of so many available theories of the wave force. A recent unexpected theoretical result [3] can be used to modify the earlier force formula derived from the momentum balance, because it has been found that the linear momentum of surface gravity waves is very likely twice the value obtained from the Stokes drift equation that was derived over 170 years ago
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