APS -70th Annual Meeting of the APS Division of Fluid Dynamics- Event - Emergence of multi-scaling in fluid turbulence

摘要

We present new theoretical and numerical results onthe transition to strong turbulence in an infinite fluid stirred by aGaussian random force.The transition is defined as a first appearance of anomalous scaling ofnormalized moments of velocity derivatives (or dissipation rates)emerging from the low-Reynolds-number Gaussian background. Itis shown that due to multi-scaling, strongly intermittent rare events can bequantitatively describedin terms of an infinite number of different ``Reynolds numbers'' reflecting amultitude of anomalousscaling exponents. We founs shown that due to multi-scaling, strongly intermittent rare events can bequantitatively describedin terms of an infinite number of different ``Reynolds numbers'' reflecting amultitude of anomalousscaling exponents. We found that anomalous scaling forhigh order moments emerges at very low Reynolds numbers implying thatintense dissipative-range fluctuations are established at even lowerReynolds number than that required for an inertial range.Thus, our results suggest that information about inertial range dynamicscan be obtained from dissipative scales even when the former does not exit.We discuss our further prediction that transition to fully anomalous turbulence disappears at $R_lambda < 3$.