O. Cadot et al., ENERGY INJECTION IN CLOSED TURBULENT FLOWS - STIRRING THROUGH BOUNDARY-LAYERS VERSUS INERTIAL STIRRING, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(1), 1997, pp. 427-433
The mean rates of energy injection and energy dissipation in steady re
gimes of turbulence are measured in two types of flow confined in clos
ed cells. The first flow is generated by counterrotating stirrers and
the second is a Couette-Taylor flow. In these two experiments the soli
d surfaces that set the fluid into motion are at first smooth, so that
everywhere the velocity of the stirrers is locally parallel to its su
rface. In all such cases the mean rate of energy dissipation does not
satisfy the scaling expected from Kolmogorov theory. When blades perpe
ndicular to the motion are added to the stirring surfaces the Kolmogor
ov scaling is observed in all the large range of Reynolds numbers ( 10
(3) < Re<10(6)) investigated. However, with either smooth or rough sti
rring the measurements of the pressure fluctuations exhibit no Reynold
s number dependence. This demonstrates that, though the smooth stirrer
s are less efficient in setting the fluid into motion, their efficienc
y is independent of the Reynolds number so that the Kolmogorov scaling
characterizes, in all cases, the dissipation in the bulk of the fluid
. The difference in the global behaviors corresponds to a different ba
lance between the role of the different regions of the flow. With smoo
th stirrers the dissipation in the bulk is weaker than the Reynolds-nu
mber-dependent dissipation in the boundary layers. With rough (or iner
tial) stirrers the dissipation in the bulk dominates, hence the Kolmog
orovian global behavior.