Effects of thermal noise in Taylor-Couette flow with corotation and axial through-flow

The intensity of the thermal noise force acting on the amplitude equation for corotating Taylor-Couette cylinders near the threshold to Taylor vortices is calculated starting from the Navier-Stokes equation with Landau-Lifshitz noise sources. The noise is predicted to increase with increasing rotation frequency of the outer cylinder. In the limit of a small gap and equal rotation frequencies of inner and outer cylinders, the result is also shown to agree with the value obtained earlier for Rayleigh-Bénard convection, with unit Prandtl number, where the two systems are identical. In the presence of axial through-flow the noise provides a mechanism for excitation of a permanent pattern of traveling Taylor vortices in the convectively unstable regime. Comparison with the noise intensity derived from experiments shows that the calculated value is smaller than the measured one by a factor of 270. An alternative calculation due to Lücke and Recktenwald leads to a smaller value of the noise. Both calculations are sensitive to the details of the flow at the inlet, where the model is highly idealized. A more realistic calculation is expected to give an even smaller value, but it has not been attempted here. The predicted rise in noise strength with outer cylinder rotation frequency could be tested by experiments or by numerical simulations.