Abstract
The mean velocities within both deterministic and random waves are examined in the Eulerian frame. The total mean flux on the basis of linear wave theory, with emergence effect taken into account, is derived. It is shown that the approximation of the total mean flux for random waves leads to the result obtained by Phillips (1960) and is equal to the joint statistical moment of second order for surface elevation and horizontal velocity taken at the mean water level. The same approach adapted to regular small-amplitude waves gives in approximation the well-known formula usually derived in the Lagrangian frame. Referring the theoretical predictions to the measured kinematics allows the estimation of the return flow in the wave flume. In the vicinity of the mean water level the currents in opposite directions to each other have been noticed. Firstly, the emergence effect gives rise to a current at the mean water level in the direction of the wave advance. Secondly, a flow in the opposite direction, interpreted as a return current in the wave flume, is noticed just below that level.
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