Two-fluid jets and wakes

Similarity solutions for laminar two-fluid jets and wakes are derived in the boundary-layer approximation. Planar and axisymmetric fan jets as well as classical and momentumless planar wakes are considered. The interface between the immiscible fluids is stabilized by the action of gravity, with the heavier fluid, taken to be a liquid, placed beneath the lighter fluid. Velocity profiles for the jets and the classical wake depend intimately, but differently, on the parameter χ = ρ₁μ₁/ρ₂μ₂, where ρ_i and μ_i are, respectively, the density and absolute viscosity of the fluid in the upper (i = 1 ) and lower (i = 2) fluid domains, while the momentumless wake profile depends on the parameter Ω = planar jet and the momentumless wake become flat in the particular case μ₁ = μ₂. Velocity profiles illustrating the strongly asymmetrical jet and wake profiles that arise in air-over-water, oil-over-water, and air-over-oil flows are presented.