Kelvin-Helmholtz instability is an instability to be formed on the discontinuity of fluid velocity. Let's consider the differense of its growth when magnetic field exists with the case of without magnetic field.

[Initial Condition]

A discontinuity in both density and velocity between upper and lower fluids. Upper sky blue region is low density and moving to right with 0.5 times its sound speed. Lower orange region is high density and in the rest. The density ratio of two regions is 4.0. Magnetic field is parallel to the discontinuity surface and its strength is about 0.01 of the plasma beta. We add 10% perturbation of growing mode of the instability.

In the figure, color shows density, arrows show velocity, and lines show magnetic field lines.

[Nonlinear Growth Stage]

The boundary of discontinuity starts surging as a sinusoidal wave but the tension of the magnetic field suppress its growth. Under this high magnetic field strength, the non-linear crests of waves are not seen.