On the nature of multitude scalings in decaying isotropic turbulence

• Published in: International journal of non-linear mechanics Vol. 95; pp. 143 - 150
• Main Authors: Layek, G.C., Sunita
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.10.2017; Elsevier BV
• Subjects: Decay; Experiments; Fluid flow; Group dynamics; Integrals; Isotropic turbulence; Mathematical models; Mechanics; Modelling; Multitude scaling laws; Power law; Reynolds number; Scaling laws; Symmetry transformation; Turbulence; Turbulence intensity; Multitude scaling laws; Isotropic turbulence; Symmetry transformation
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2017.06.007

We report multitude scaling laws for isotropic fully developed decaying turbulence through group theoretic method employing on the spectral equations both for modelling and without any modelling of nonlinear energy transfer. For modelling, besides the existence of classical power law scalings, an exponential decay of turbulent energy in time is obtained subject to exponentially decaying integral length scale at infinite Reynolds number limit. For the transfer without modelling, at finite Reynolds number, in addition to general power law decay of turbulence intensity with integral length scale growing as a square root of time, an exponential decay of energy in time is explored when integral length scale remains constant. Both the power and exponential decaying laws of energy agree to the theoretical results of George (1992), George and Wang (2009) and experimental results of fractal grid generated turbulence by Hurst and Vassilicos (2007). At infinite Reynolds number limit, a general power law scaling is obtained from which all classical scaling laws are recovered. Further, in this limit, turbulence exhibits a general exponential decaying law of energy with exponential decaying integral length scale depending on two scaling group parameters. The role of symmetry group parameters on turbulence dynamics is discussed in this study. •Classical and recently found scaling laws of isotropic decaying turbulence are established through Lie point symmetry method.•The analysis is carried out both for modelling of nonlinear energy transfer as well as without its modelling in decaying turbulence.•Connection between initial conditions of turbulence production and symmetry group parameters are established for some cases.