Kelvin-Helmholtz Instability
Mines Nancy - Department Energy & Fluid Mechanics - 2A

Kelvin-Helmholtz Instability in Fluid Mechanics

     In an extension of the problem 3.2 of the Lecture Notes, one may study the stability of a monophasic shear flow, without interface. The basic flow has the following profile:

With a numerical linear stability analysis, one observes a Kelvin-Helmholtz Instability. It is displayed below by the temporal evolution of streamlines and fluid particles (black disks) that sit, initially, on the line of maximum shear y=0, which is somehow the `interface' between the fluid flowing to the right (particles in magenta) and the fluid flowing to the left (particles in brown):

The state obtained, when the instability has well developed, is a `vortex street':

The `interface' between the fluid flowing to the right and the fluid flowing to the left has `rolled up' in the vortices. This `interface' may be, sometimes, visualized thanks to a cloud. That is, at least, what suggests the analogy between this computation and this photography by Brooks Martner, of the NOAA Environmental Technology Laboratory:

The computations have been performed with a spectral method. Some precisions and literature references can be found in the section 2.5 of this article published in 2008 in the Journal of Fluid Mechanics.
Please cite as follows:

PLAUT, E. Mécanique des Fluides. Mines Nancy Lecture 2014.

Animations realized with

Emmanuel Plaut
 Last modified: Tue Dec 22 10:40:18 CET 2015