Interplay of Kelvin–Helmholtz instability with acoustics in a viscous potential flow

2020 ◽  
Vol 32 (8) ◽  
pp. 084108
Author(s):  
Serdar Bilgili ◽  
Orlando Ugarte ◽  
V’yacheslav Akkerman
Keyword(s):  
Potential Flow ◽  
Helmholtz Instability ◽  
Viscous Potential Flow

Pressure Corrections for the Potential Flow Analysis of Kelvin-Helmholtz Instability

2011 ◽  
Vol 110-116 ◽  
pp. 4628-4635 ◽  
Author(s):  
Mukesh Kumar Awasthi ◽  
Rishi Asthana ◽  
G.S. Agrawal
Keyword(s):  
Normal Stress ◽  
Potential Flow ◽  
Energy Equation ◽  
Mechanical Energy ◽  
Flow Analysis ◽  
Helmholtz Instability ◽  
Viscous Potential Flow ◽  
Two Fluids ◽  
Tangential Stresses ◽  
Viscous Pressure

The present paper deals with the study of viscous contribution to the pressure for the viscous potential flow analysis of Kelvin-Helmholtz instability of two viscous fluids. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses for two fluids are not continuous at the interface. Here we have considered viscous pressure in the normal stress balance along with the irrotational pressure and it is assumed that the addition of this viscous pressure will resolve the discontinuity between the tangential stresses and the tangential velocities at the interface. The viscous pressure is derived by mechanical energy equation and this pressure correction applied to compute the growth rate of Kelvin-Helmholtz instability. A dispersion relation is obtained and a stability criterion is given in the terms of critical value of relative velocity. It has been observed that the inclusion of irrotational shearing stresses stabilizes the system.

VISCOUS CONTRIBUTIONS TO THE PRESSURE FOR THE POTENTIAL FLOW ANALYSIS OF MAGNETOHYDRODYNAMIC KELVIN–HELMHOLTZ INSTABILITY

2012 ◽  
Vol 04 (01) ◽  
pp. 1250001 ◽  
Author(s):  
MUKESH KUMAR AWASTHI ◽  
G. S. AGRAWAL
Keyword(s):  
Normal Stress ◽  
Potential Flow ◽  
Mechanical Energy ◽  
Flow Analysis ◽  
Shear Stresses ◽  
Helmholtz Instability ◽  
Viscous Potential Flow ◽  
Two Fluids ◽  
Tangential Stresses ◽  
Viscous Pressure

The present paper deals with the study of viscous contributions to the pressure for the viscous potential flow analysis of Kelvin–Helmholtz instability with tangential magnetic field at the interface of two viscous fluids. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses for two fluids are not continuous at the interface. Here, we have considered viscous pressure in the normal stress balance along with the irrotational pressure and it is assumed that the addition of this viscous pressure will resolve the discontinuity between the tangential stresses and the tangential velocities at the interface. The viscous pressure is derived by mechanical energy equation and this pressure correction applied to compute the growth rate of magnetohydrodynamic Kelvin–Helmholtz instability. A dispersion relation is obtained and stability criterion is given in the terms of critical value of relative velocity. It has been observed that the inclusion of irrotational shear stresses have stabilizing effect on the stability of the system.

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