  Turbulent flows frequently accompany physical, chemical and biological
processes, such as mixing, two-phase flow, combustion and even foraging by
bacteria and plankton larvae, all of which are in principle subject to thermal
fluctuations already on scales of several microns. Nevertheless the large
separation between the millimeter scale at which turbulent fluctuations begin
to be strongly damped and the mean free path of the fluid has been generally
assumed to imply that thermal fluctuations are irrelevant to the turbulent
dissipation range. Here we use statistical mechanical estimates to show that
thermal fluctuations are not negligible compared to turbulent eddies in the
dissipation range. Simulation of the Sabra shell model shows that intermittent
bursts of turbulence lead to a fluctuating length scale below which thermal
fluctuations are important: over three decades of length, from sub-millimeter
scales down to the mean free path, thermal fluctuations coexist with
hydrodynamics. Our results imply that thermal fluctuations cannot be neglected
when modeling turbulent phenomena in the far dissipation range.
