Real turbulent flows are difficult to classify as either spatially homogeneous or isotropic. Nonetheless these idealizations allow the identification of certain universal features associated with the small-scale motions almost invariably observed in a variety of different conditions. The single most significant aspect is a flux of energy through the spectrum of inertial scales related to the phenomenology commonly referred to as the Richardson cascade. Inhomogeneity, inherently present in near-wall turbulence, generates additional energy fluxes of a different nature, corresponding to the spatial redistribution of turbulent kinetic energy. Traditionally the spatial flux is associated with a single-point observable, namely the turbulent kinetic energy density. The flux through the scales is instead classically related to two-point statistics, given in terms of an energy spectrum or, equivalently, in terms of the second-order moment of the velocity increments. In the present paper, starting from a suitably generalized form of the classical Kolmogorov equation, a scale-by-scale balance for the turbulent fluctuations is evaluated by examining in detail how the energy associated with a specific scale of motion - hereafter called the scale energy - is transferred through the spectrum of scales and, simultaneously, how the same scale of motion exchanges energy with a properly defined spatial flux. The analysis is applied to a data set taken from a direct numerical simulation (DNS) of a low-Reynolds-number turbulent channel flow. The detailed scale-by-scale balance is applied to the different regions of the flow in the various ranges of scales, to understand how - i.e. through which mechanisms, at which scales and in which regions of the flow domain - turbulent fluctuations are generated and sustained. A complete and formally precise description of the dynamics of turbulence in the different regions of the channel flow is presented, providing rigorous support for previously proposed conceptual models

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

No abstract

No abstract