### TURBULENT CURRENTS IN THE PRESENCE OF WAVES

#### Abstract

This paper presents an approximate theory for the reduction of the velocity of a current due to the presence of sinusoidal waves. For a given slope, S, in water of constant depth, d, the current velocity profile is U(z) = U^ (2.5'ln — - A) (1) t zo as a function of the height, z, above the bed. Eq. 1 is valid only above the thin wave boundary layer near the bed, the roughness of which is k = 30 z . Uf is the current friction velocity defined by p Ul = y d S = T (2) f ' cw CW Values of A can be found from: Fig. 2 where Aj applies when the direction of wave propagation is parallel to the current direction, and Fig. 3 where A2 applies when the direction of wave propagation is perpendicular to the current direction, cf. Notation in Sec. 2. The theory is based upon a number of assumptions (see Sec. 4).

#### Keywords

turbulence; current; turbulent current

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