On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows

The ability of linear stochastic response analysis to estimate coherent motions is investigated in turbulent channel flow at friction Reynolds number Re$_\tau$ = 1007. The analysis is performed for spatial scales characteristic of buffer-layer and large-scale motions by separating the contributions of different temporal frequencies. Good agreement between the measured spatio-temporal power spectral densities and those estimated by means of the resolvent is found when the effect of turbulent Reynolds stresses, modelled with an eddy-viscosity associated to the turbulent mean flow, is included in the resolvent operator. The agreement is further improved when the flat forcing power spectrum (white noise) is replaced with a power spectrum matching the measures. Such a good agreement is not observed when the eddy-viscosity terms are not included in the resolvent operator. In this case, the estimation based on the resolvent is unable to select the right peak frequency and wall-normal location of buffer-layer motions. Similar results are found when comparing truncated expansions of measured streamwise velocity power spectral densities based on a spectral proper orthogonal decomposition to those obtained with optimal resolvent modes

Steady streamwise transpiration control in turbulent pipe flow

A study of the the main features of low- and high amplitude steady streamwise wall transpiration applied to pipe flow is presented. The effect of the two transpiration parameters, amplitude and wavenumber, on the flow have been investigated by means of direct numerical simulation at a moderate turbulent Reynolds number. The behaviour of the three identified mechanisms that act in the flow: modification of Reynolds shear stress, steady streaming and generation of non-zero mean streamwise gradients, have been linked to the transpiration parameters. The observed trends have permitted the identification of wall transpiration configurations able to reduce or increase the overall flow rate in -36.1% and 19.3% respectively. A resolvent analysis has been carried out to obtain a description of the reorganization of the flow structures induced by the transpiration

Shear-Improved Smagorinsky Model for Large-Eddy Simulation of Wall-Bounded Turbulent Flows

A shear-improved Smagorinsky model is introduced based on recent results concerning shear effects in wall-bounded turbulence by Toschi et al. (2000). The Smagorinsky eddy-viscosity is modified subtracting the magnitude of the mean shear from the magnitude of the instantaneous resolved strain-rate tensor. This subgrid-scale model is tested in large-eddy simulations of plane-channel flows at two different Reynolds numbers. First comparisons with the dynamic Smagorinsky model and direct numerical simulations, including mean velocity, turbulent kinetic energy and Reynolds stress profiles, are shown to be extremely satisfactory. The proposed model, in addition of being physically sound, has a low computational cost and possesses a high potentiality of generalization to more complex non-homogeneous turbulent flows.Comment: 10 pages, 6 figures, added some reference

Coherent dynamics of large scale turbulent motions

My thesis work focused on ‘dynamical systems’ understanding of the large-scale dynamics in fully developed turbulent shear flow. In plane Couette flow, large-eddy simulation (L.E.S) is used to model small scale motions and to only resolve large-scale motions in order to compute nonlinear traveling waves (NTW) and relative periodic orbits (RPO). Artificial over-damping has been used to quench an increasing range of small-scale motions and prove that the motions in large-scale are self-sustained. The lower-branch traveling wave solutions that lie on laminar-turbulent basin boundary are obtained for these over-damped simulation and further continued in parameter space to upper branch solutions. This approach would not have been possible if, as conjectured in some previous investigations, large-scale motions in wall bounded shear flows are forced by mechanism based on the existence of active structures at smaller scales. In Poseuille flow, relative periodic orbits with shift-reflection symmetry on the laminar-turbulent basin boundary are computed using DNS. We show that the found RPO are connected to the pair of traveling wave (TW) solution via global bifurcation (saddle-node-infinite period bifurcation). The lower branch of this TW solution evolve into a spanwise localized state when the spanwise domain is increased. The upper branch solution develops multiple streaks with spanwise spacing consistent with large-scale motions in turbulent regime