Saturation of vorticity growth in fully-developed fluid turbulence

Abstract

Turbulence can be defined as that state of matter characterized by a loss of coherence in space and time, as a result of the non-linear interaction of a large number of degrees of freedom, in excess of billions even for most familiar phenomena, such as flow past an automobile (Frisch 1995; Chen et al. 2003; Davidson 2004). This raises a formidable computational barrier even for the most powerful computational methods in the foreseeable future, let alone analytical methods. It is therefore not surprising that fluid turbulence has continued to attract attention by scientists from many disciplines. The research and literature on the topic is so vast that even the problem definition is not the same for different communities of researchers (Sreenivasan 1999; Frisch 1995; Liepmann 1979; Pope 2000; Lumley & Yaglom 2001). Among others, primary goals of turbulence research can be summarized as follows: i) unveil statistical universalities (Frisch 1995; Sreenivasan & Antonia 1997; Toschi & Bodenschatz 2009; Dhar et al. 1997), underlying the irreducible dynamical complexity of different turbulent flows, ii) develop robust and accurate methods to compute the (statistical) dynamics of turbulent flows (Moin & Mahesh 1998; Germano 1992; Lesieur & Metais 1996; Ansumali et al. 2004; Moin & Mahesh 1998) in realistic geometries, where universal and non-universal behavior must necessarily coexist, and iii) understanding the basic mechanisms controlling the transition from laminar to turbulent behavior (Sreenivasan 1999; Moxey & Barkley 2010).