Shear instability in fluids with a density-dependent viscosity

Phys Rev Lett. 2008 Jun 27;100(25):254502. doi: 10.1103/PhysRevLett.100.254502. Epub 2008 Jun 26.


We present a shear instability, which can be triggered in compressible fluids with density-dependent viscosity at shear rates above critical. The instability mechanism is generic: It is based on density-dependent viscosity, compressibility, as well as flow two-(three-)dimensionality that provides coupling between streamwise and transversal velocity components and density variations. The only factor stabilizing the instability is fluid elasticity. The corresponding eigenvalue problem for a plane Couette flow is solved analytically in the limiting cases of large and small wave numbers.