MASS-TRANSPORT OF INTERFACIAL WAVES IN A 2-LAYER FLUID SYSTEM

Effects of viscous damping on mass transport velocity in a two-layer f luid system are studied. A temporally decaying small-amplitude interfa cial wave is assumed to propagate in the fluids. The establishment and the decay of mean motions are considered as an initial-boundary-value problem. This transient problem is solved by using a Laplace transfor m with a numerical inversion. It is found that thin 'second boundary l ayers' are formed adjacent to the interfacial Stokes boundary layers. The thickness of these second boundary layers is of O(epsilon(1/2)) in the nondimensional form, where epsilon is the dimensionless Stokes bo undary layer thickness defined as epsilon = (k) over cap<(delta)over c ap> = (k) over cap (2 (v) over cap/<(sigma)over cap>)(1/2) far an inte rfacial wave with wave amplitude (a) over cap wavenumber (k) over cap and frequency <(sigma)over cap> in a fluid with viscosity (v) over cap . Inside the second boundary layers there exists a strong steady strea ming of O(alpha(2) epsilon(-1/2)), where alpha = (k) over cap (a) over cap is the surface wave slope. The mass transport velocity near the i nterface is much larger than that in a single-layer system, which is O (alpha(2)) (e.g. Longuet-Higgins 1953; Craik 1982). In the core region s outside the thin second boundary layers, the mass transport velocity is enhanced by the diffusion of the mean interfacial velocity and vor ticity. Because of vertical diffusion and viscous damping of the mean interfacial vorticity, the 'interfacial second boundary layers' dimini sh as time increases. The mean motions eventually die out owing to vis cous attenuation. The mass transport velocity profiles are very differ ent from those obtained by Dore (1970, 1973) which ignored viscous att enuation. When a temporally decaying small-amplitude surface progressi ve wave is propagating in the system, the mean motions are found to be much less significant, O(alpha(2)).