SPECTRAL ANALYSIS ON REYNOLDS STRESS TRANSPORT EQUATION IN HIGH RE WALL-BOUNDED TURBULENCE

Abstract

Despite its importance in many applications, the nature of wall-bounded turbulent flow is not well-understood. The dynamics of near-wall turbulence has been well studied, with direct numerical simulation (DNS) making an important contribution. It has been difficult to study the interaction of near-wall and outer-layer turbulence via DNS because the Reynolds numbers available via DNS have not been sufficiently high to exhibit significant scale separation. In the work presented here, we correct that short-coming. We have performed direct numerical simulation(DNS) of turbulent channel flow using a Fourier-Galerkin method in the streamwise(x) and spanwise (z) directions and a BSplines collocation method in the wall-normal (y) direction. The highest Reynolds number based on shear velocity (uτ = √ τw/ρ), Reτ is approximately 5200. To study the scale dependence of the dynamics of the Reynolds stress components, we applied a spectral analysis to the terms in the Reynolds stress transport equation (RSTE). Result shows that the large (or very large) scale motion has an important role in turbulent transport terms. Also, it has been observed that a non-trivial portion of turbulent kinetic energy (TKE) is transported to the near-wall region and dissipated by large scale motion. Introduction Recently, much research has been directed at understanding wall-bounded turbulent flows at high Reynolds number (Re). Recent advances of experimental techniques (Nagib et al., 2004; Kunkel & Marusic, 2006; Westerweel et al., 2013; Bailey et al., 2014) and computing power (Lee et al., 2013; Borrell et al., 2013; El Khoury et al., 2013) provide information not previously available. One of the most important feature of high Re wall-bounded turbulence is the separation of scales between the near wall and outer layer turbulence. Two distinct peaks of the streamwise velocity energy spectral density are observed experimentally: a small-scale peak in the near-wall region and a large-scale peak in the outer region (Hutchins & Marusic, 2007; Monty et al., 2009; Marusic et al., 2010a,b). Two such spectral peaks were confirmed by direct numerical simulation(DNS) by Lee & Moser (2015). Lee & Moser (2015) have also found that there is peak distinction in the spectral density of Reynolds stress, −u′v′, but this has not yet been observed in experiments. Since the DNS can provides such richer data with high fidelity, it is possible to compute higher order terms in three dimensions. In this work, we have focused on the Reynolds stress transport equation (RSTE) which give us information about production, transport and dissipation of the Reynolds stress tenor. However, RSTE is an averaged equation, so it is difficult to study detailed roles of turbulent motions. Hence, we have performed a spectral analysis on each terms in RSTE to observe how the motions in different length scales contribute the transport of Reynolds stresses. To our knowledge, such a spectral analysis of terms in RSTE has not previously been performed. In this work we have focused on the turbulent kinetic energy (TKE) equation and the interaction between components of the velocity fluctuations. This paper is organized as follow. First, the simulation methods and the definition of terms in RSTE are described. Then, the following are discussed: Re dependencies of terms in RSTE, spectral analysis of production, transport and dissipation, enhanced analysis of turbulent transport and interaction of velocity fluctuations in different direction by pressure-strain terms. 1 June 30 July 3, 2015 Melbourne, Australia 9 4A-3