| abstracts | This paper presents the theoretical development of stochastic properties for orbital velocities of random water waves in intermediate water depth. Both emergence effect and weak nonlinear effects are studied. An analytic formula for probability distribution for velocities modified by the emergence effect, as well as by non-linearities of the wave motion in intermediate water depth is developed. This probability function gives us the first statistical moment, the second statistical moment for modified velocities in an analytical form, and by numerical integration the third statistical moment for modified velocities.The theoretical formulae for the statistical moments for surface elevation and for velocities of up to the third order, with non-linearities of motion taken into account, in case the emergence effect can be neglected, i.e., below the surface layer, have been developed. This includes a generalised formula for free surface elevation setdown and calculation of the asymmetry of the horizontal velocity.From the first statistical moment of the modified horizontal velocity, the mean flux between any two levels is obtained. When the integration is carried out from the bottom up to +∞, the formula for total mean flux is obtained.In Part 2 of this paper (Cieślikiewicz, Gudmestad 1994b) the theoretical predictions are compared with measured kinematics. Moreover, in the vicinity of the mean water level, currents in two different directions are noted. 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.Theoretical prediction of the measured kinematics has allowed for a better estimation of the return flow in the wave flume. |