  A numerical study of the Kelvin-Helmholtz instability in compressible
magnetohydrodynamics is presented. The three-dimensional simulations consider
shear flow in a cylindrical jet configuration, embedded in a uniform magnetic
field directed along the jet axis. The growth of linear perturbations at
specified poloidal and axial mode numbers demonstrate intricate non-linear
coupling effects. The physical mechanims leading to induced secondary
Kelvin-Helmholtz instabilities at higher mode numbers are identified. The
initially weak magnetic field becomes locally dominant in the non-linear
dynamics before and during saturation. Thereby, it controls the jet deformation
and eventual breakup. The results are obtained using the Versatile Advection
Code [G. Toth, Astrophys. Lett. Comm. 34, 245 (1996)], a software package
designed to solve general systems of conservation laws. An independent
calculation of the same Kelvin-Helmholtz unstable jet configuration using a
three-dimensional pseudo-spectral code gives important insights into the
coupling and excitation events of the various linear mode numbers.
