Nonequilibrium effect of the turbulent-energy-production process on the inertial-range energy spectrum

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Abstract
The importance of the nonequilibrium effect of the turbulent-energy-production process is discussed in the context of the inertial-range energy spectrum. A dynamical property of the process related to the Lagrange derivative of the turbulent-energy transfer rate gives rise to an important deviation of the inertial-range spectrum from Kolmogorov’s -5/3 power law at the energy-containing side. Through this deviation, the turbulent-viscosity concept possesses a nonequilibrium character that is indispensable for describing statistically highly time- and space-dependent properties of turbulence. It is concluded that the inertial-range energy spectrum cannot be specified using only the energy transfer rate.