Free-stream velocity descriptions under waves with skewness and asymmetry

In shallow water, when waves shoal their orbital velocities exhibit skewness (velocity skewness) and asymmetry (acceleration skewness) in response to corresponding changes in the free surface. Near the bed, changes in the skewness and asymmetry of the time-varying velocities have important consequences for the residual velocities ‘spun up’ by the bottom friction and for sediment transport. In the wave boundary layer, where the largest sediment transport often occurs, there is a need to represent the free-stream velocity (the orbital velocity at the edge of the wave boundary layer) in a systematic way such that it can be mimicked in wave tunnel experiments and wave boundary layer models which usually do not represent the free surface. Since there is no readily accessible dynamical theory for shoaling waves that includes both skewness and asymmetry, it is necessary to synthesize the shoaling effect in a free-stream velocity description that is general enough to fit observed velocity time series. This paper reviews previous free-stream velocity descriptions, including the description of Abreu et al. (2010), and introduces a new description based on generalising a sawtooth wave shape. The paper quantifies all the relevant measures of skewness and asymmetry for each description. It then demonstrates that Abreu et al.'s (2010) description represents the most general one and improves upon their fitting techniques to observed free-stream velocities to further simplify it. When this description is used in conjunction with a characterisation of the velocity for irregular waves, such as that of Elfrink et al. (2006), it is possible to relate velocity skewness and asymmetry directly to the non-dimensional wave and beach parameters (wave height, surface wavelength and surf similarity parameter as a proxy for beach slope). MATLAB scripts are provided for the improved description of Abreu et al. (2010) and Elfrink et al.'s (2006) characterisation.

► Reviews free-stream velocity descriptions for waves with skewness and asymmetry.
► Improves upon Abreu's description and introduces generalised sawtooth description.
► Includes fitting to observed velocities and Elfrink's characterisation.
► Quantifies all measures of skewness and asymmetry and provides MATLAB scripts.