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The utility of composite error-function velocity  profiles for the modeling of gas–liquid shear layers is examined by comparing  temporal stability results from such approximate error-function profiles with  results from the exact velocity profiles based on the two-fluid boundary layer  equations. The stability analysis is restricted to two-dimensional  perturbations. The two-fluid boundary layer equations are solved numerically  using a shooting method in each fluid layer. The composite error-function  profile is constructed by matching displacement thicknesses with the exact  solution. With given fluid properties, the displacement thicknesses depend on  the asymptotic velocity ratio of the liquid and gas stream in the laboratory  frame. For different sets of fluid properties, the maximum growth rates of the  Kelvin–Helmholtz instability show good numerical agreement between the exact and  the approximate velocity profiles, especially when the asymptotic velocities of  the gas and liquid phase are close.

Instability of two-phase mixing layers: analysis of exact and approximate base flows from boundary layer theory