Homogeneity and the inertial range in driven two-dimensional turbulence

Abstract

To be compared with current theory, turbulent velocity fluctuations should be homogeneous throughout the measurement volume as well as have a significant inertial range. For two-dimensional (2D) systems, these requirements are difficult to achieve. The difficulty with homogeneity stems from the fact that the outer scale, rout, grows with increasing Reynolds number or with decreasing external friction. If the outer scale begins to exceed the system size, rsys, homogeneity is sacrificed throughout the system. Current 2D systems have rsys about a decade removed from the injection scale, rinj. Thus to maintain homogeneity, rout must be kept small. A consequence of small rout is that there is little to no inertial range in such systems. This is because the inertial range extends between rinj and the integral scale rint∝ (rinjrout) 1/2, which is smaller than rout. To have a significant inertial range as well as maintain homogeneity throughout that range, 2D systems must be made larger in size than current systems. This paper demonstrates these facts in a particular experimental setup, an electromagnetically driven soap film. However, the results are expected to be applicable to other 2D turbulence systems. © 2002 American Institute of Physics.