CHARACTERISTICS OF CHAOS OF THE LORENZ SYSTEM WITH VELOCITY SHEAR

Chaotic motions may appear when the velocity shear damper is added into the Lorenz equation for the Prandtl number σ=0.7. The critical Rayleigh number with velocity shear is larger than that without velocity shear. The chaos is a aperiodic phenomenon. The trajectory of chaotic motions is irregular in phase space. There are many ways to reach turbulence. The behaviour is of general turbulence when shear is small. It is of intermittent turbulence when shear is larger and of transient laminar when moderate. The research on chaotic motion with velocity shear is of significance for understanding atmospheric turbulence.