Pseudo‐spectral computation of interfacial waves dynamics in an air/water turbulent sheared flow via a conformal mapping technique

Abstract

AbstractThe dynamics of a deformable interface in a counter‐current air/water turbulent flow is analyzed here using the Direct Numerical Simulation (DNS) of the Navier Stokes equations. An algebraic mapping technique is employed to transform the deformed physical domain into a rectangular domain, where the governing equations are solved by a pseudo‐spectral Fourier‐Chebyshev method. The problem is described by the Reynolds number (Reτ), the Weber number (We), and the Froude number (Fr). Keeping Reτ constant and varying We and Fr, we show that the interfacial waves growth is a two‐stage process. At the beginning, capillary forces always dominate and waves grow as t2/5. Later, when gravity becomes important, waves grow exponentially as et/5 (in the present configuration), until they reach a steady‐state condition. The importance of the form drag during the stage of exponential growth of waves is clearly addressed.