  We investigate numerically the dynamics of a single polymer in a linear shear
flow. The effects of thermal fluctuations and randomly fluctuating velocity
gradients are both analyzed. Angular, elongation and tumbling time statistics
are measured numerically. We perform analytical calculations and numerical
simulations for a linear single-dumbbell polymer model comparing the results
with previous theoretical and experimental studies. For thermally driven
polymers the balance between relaxation and thermal fluctuations plays a
fundamental role, whereas for random velocity gradients the ratio between the
intensity of the random part and the mean shear is the most relevant quantity.
In the low-noise limit, many universal aspects of the motion of a polymer in a
shear flow can be understood in this simplified framework.
