Turbulent energy scale budget equations in a fully developed channel flow

Abstract

Kolmogorov's equation, which relates second- and third-order moments of the velocity increment, provides a simple method for estimating the mean energy dissipation rate 〈ε〉 for homogeneous and isotropic turbulence. However, this equation is usually not verified in small to moderate Reynolds number flows. This is due partly to the lack of isotropy in either sheared or non-sheared flows, and, more importantly, to the influence, which is flow specific, of the inhomogeneous and anisotropic large scales. These shortcomings are examined in the context of the central region of a turbulent channel flow. In this case, we propose a generalized form of Kolmogorov's equation, which includes some additional terms reflecting the large-scale turbulent diffusion acting from the walls through to the centreline of the channel. For moderate Reynolds numbers, the mean turbulent energy transferred at a scale r also contains a large-scale contribution, reflecting the non-homogeneity of these scales. There is reasonable agreement between the new equation and hot-wire measurements in the central region of a fully developed channel flow.

Solar Wind Turbulence and the Role of Ion Instabilities

“…This law has been indeed observed in the neutral fluid turbulence, e.g. Danaila et al (2001). Note that Kolmogorov 4/5 law can be obtained from the more general Yaglom (1949) law in case of Navier-Stokes isotropic turbulence.…”

The inertial subrange in turbulent pipe flow: centreline

“…It should be pointed out however, that Lundgren's theory is developed for decaying isotropic turbulence. A greater challenge is presented by the effects of transport, even at the centre line - Danaila et al (2001) (see also Antonia & Burattini 2006) have investigated the need for corrections to (1.7) at low Reynolds numbers to account for the effects of the large scales. There is no clear plateau in the third-order moment even when corrected for the effects of boundary conditions as described by K62, or empirically.…”

“…Therefore, in the present measurements at much higher Reynolds numbers, we take the 4 5 ths law as a reasonably accurate estimate of centre-line disspation rate. Danaila et al (2001) have proposed a generalized form of Kolmogorov's equation to account for the effects of large scale transport in fully developed channel flow appearing through the left-hand side of (1.6). However, the additional term involves the longitudinal structure function for the wall normal fluctuations.…”

Cascades and wall-normal fluxes in turbulent channel flows

“…There are however complications arising from the fact that both forward and backward energy transfer are present. A generalized form of the Kolmogorov's equation is proposed by Danaila et al (2001) showing how the inhomogeneity of the large scales quantitatively acts along the direction normal to the wall. The energy transfer has been studied also from a phenomenological point of view in terms of size of turbulent structures.…”

“…88-94). Indeed, the Kolmogorov equation is an exact balance between second-and third-order 420 A. Cimarelli, E. De Angelis, J. Jiménez and C. M. Casciola moments (Monin & Yaglom 1975;Danaila et al 2001;Danaila, Anselmet & Zhou 2004;Germano 2007;Gomes-Fernandes, Ganapathisubramani & Vassilicos 2015) showing that the rate of energy dissipation is associated, at any scale, with fluxes which in turn are fed by local sources. Following the different ranges of scales and positions encountered by the fluxes, the second-and third-order moments eventually assume their physical interpretation of scale energy and scale-energy flux.…”