Some aspects in Kelvin-Helmholtz instability with and without Boussinesq approximation

INCAS BULLETIN, vol. 13, pp. 25–33

Abstract

The topic of this paper is the Kelvin-Helmholtz instability, a phenomenon which occurs on the interface of a stratified fluid, in the presence of a parallel shear flow, when there is a velocity and density difference across the interface of two adjacent layers. This paper focuses on a numerical simulation modelled by the Taylor-Goldstein equation, which represents a more realistic case compared to the basic Kelvin-Helmholtz shear flow. The Euler system is solved with new modelled smooth velocity and density profiles at the interface. The flux at cell boundaries is reconstructed by implementing a third order WENO (Weighted Essentially Non-Oscillatory) method. Next, a Riemann solver builds the fluxes at cell interfaces. The use of both Rusanov and HLLC solvers is investigated. Temporal discretization is done by applying the second order TVD (total variation diminishing) Runge-Kutta method on a uniform grid. Numerical simulations are performed comparatively for both Kelvin-Helmholtz and Taylor-Goldstein instabilities, on the same simulation domains. We find that increasing the number of grid points leads to a better accuracy in shear layer vortices visualization. Thus, we can conclude that applying the Taylor-Goldstein equation improves the realism in the general fluid instability modelling.

Authors 2

1. Ilinca-Laura BURDULEA Aachen Faculty of Aerospace Engineering Department of Aerospace Sciences

   RWTH Aachen University · Universitatea Națională de Știință și Tehnologie Politehnica București

   Affiliation as printed

   POLITEHNICA University of Bucharest, Faculty of Aerospace Engineering, Department of Aerospace Sciences, Splaiul Independentei 313, 060042, Bucharest, Romania and Rheinisch-Westfälische Technische Hochschule Aachen, Deutchland, ilinca.burdulea@stud.aero.upb.ro, ilinca.burdulea@rwth-aachen.de

   POLITEHNICA University of Bucharest, Faculty of Aerospace Engineering,

2. Alina Bogoi

   Universitatea Națională de Știință și Tehnologie Politehnica București

   Affiliation as printed

   POLITEHNICA University of Bucharest, Faculty of Aerospace Engineering, Department of Aerospace Sciences, Splaiul Independentei 313, 060042, Bucharest, Romania, alina.bogoi@upb.ro

   POLITEHNICA University of Bucharest, Faculty of Aerospace Engineering,