Mixing in the surf zone

Two important mixing mechanisms are operative within the surf zone, each having distinctive length and time scales determined by the intensity of the waves and the dimensions of the surf zone. The first is associated with the breaking wave and its bore, which produce rapid mixing in an on-offshore direction. This mixing, when normalized and averaged over the surf zone width Xb, gives coefficients of eddy diffusivity of the order of HbXb/T where Hb and T are the breaker height and the period of the waves. The second process is advective and is associated with the longshore and rip current systems in the nearshore circulation cell. For constant longshore discharge of water between cells Qi, this process gives a concentration Nn in the nth cell down-current from a continuously injected source of dye of Nn=N0(Qi/Qm)n where N0 is the concentration leaving the injection cell, and Qm is the maximum longshore discharge within a cell. As an approximation, the concentration decreases exponentially with distance y from the injection point when n is replaced by y/Y, where Y is the spacing between rip currents. This relation gives an apparent longshore eddy mixing coefficient of the order of Y〈υi〉 where 〈υi〉 is the longshore current velocity. Along ocean beaches HbXb/T and Y〈υi〉 are about 10 m2 sec−1 and 100 m2 sec−1 respectively.