Synchronization of Low Reynolds Number Plane Couette Turbulence

We demonstrate that a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition identifies subspaces with stable Lyapunov exponents and allows the dynamics to exhibit properties of an inertial manifold, such as the synchronization of the small scales in simulations sharing the same large scales or equivalently the decay of all small scale flow states to the state uniquely determined from the large scale flow. This behaviour occurs for deviations with streamwise wavelength smaller than 130 wall units which was shown in earlier studies to correspond to the streamwise spectral peak of the cross-flow velocity components of the top Lyapunov vector of the turbulent flow

Fluctuation covariance-based study of roll-streak dynamics in Poiseuille flow turbulence

The roll-streak (R-S) is fundamentally involved in the dynamics of wall-turbulence and, despite its central role, the physical mechanism responsible for its formation and maintenance remains controversial. In this work we investigate the dynamics maintaining the R-S in turbulent Poiseuille flow at $Re=1650$. Spanwise collocation is used to remove spanwise displacement of the streaks and associated flow components, which isolates the streamwise-mean flow R-S component and the second-order statistics of the streamwise-varying fluctuations that are collocated with the R-S. This streamwise-mean/fluctuation partition of the dynamics facilitates exploiting insights gained from the analytic characterization of turbulence in restricted nonlinear dynamics and its closely associated second-order statistical state dynamics (SSD) analogue, referred to as S3T. Symmetry of the statistics about the streak centerline permits separation of the fluctuations to sinuous and varicose components. The Reynolds stress forcing induced by the sinuous and varicose components to the R-S is shown to reinforce low- and high-speed streaks respectively. This targeted reinforcement of streaks by the Reynolds stresses occurs continuously as the fluctuation field is strained by the streamwise-mean streak and not intermittently as would be associated with streak-breakdown events. The Reynolds stresses maintaining the streamwise-mean roll can be attributed primarily to the dominant POD modes of the fluctuations, which were identified as the time average structure of optimal perturbations on the streak. These results are consistent with a universal process of streak instability in turbulent shear flow arising from torques generated by straining turbulent fluctuations, which was identified using the S3T SSD.Comment: 23 pages, 17 figures, submitted for publication to the Journal of Fluid Mechanic

POD-based study of structure and dynamics in turbulent plane Poiseuille flow: comparing quasi-linear simulations to DNS

Turbulence supported in the quasi-linear restricted nonlinear (RNL) dynamics is analyzed and compared with DNS of Poiseuille turbulence at Reynolds number $R=1650$. The turbulence structure is obtained by POD analysis of the two components of the flow partition used in formulating the RNL dynamics: the streamwise-mean flow and the associated fluctuations. POD analysis of the streamwise-mean flow indicates that the dominant structure in both RNL and DNS is a coherent roll-streak in which the roll is collocated with the streak in a manner configured to reinforce the streak by the lift-up process. POD analysis of fluctuations from the streamwise-mean streak reveals that similar complex structures, consisting in part of oblique waves collocated with the streak, characterize these fluctuations in both the RNL simulations and DNS. The origin of these structures is identified by their correspondence to POD modes obtained by stochastically forcing the DNS and RNL streaks white in energy and solving for the POD structure predicted by the associated stochastic turbulence model (STM), which elicits a response determined primarily by optimally growing structures on the streak. The mechanism sustaining turbulence in RNL comprises rolls forced by Reynolds stress torques arising from fluctuations in the form of Lyapunov vectors that maintain the streak by lift-up. This close correspondence between the roll-streak structure and the fluctuations in RNL, DNS and the STM implies that the self-sustaining mechanism in DNS is the same as that in RNL, which has the advantage that its mechanism and components have been analytically characterized.Comment: 31 pages, submitted to the Journal of Fluid Mechanic

Synchronization of low Reynolds number plane Couette turbulence

We demonstrate that in plane Couette turbulence a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition allows us to identify an active subspace comprising a small number of the gravest streamwise components of the flow that can synchronize all the remaining streamwise flow components. The critical streamwise wavelength, l(xc), that separates the active from the synchronized passive subspace is identified as the streamwise wavelength at which perturbations to the time-dependent turbulent flow with streamwise wavelengths l(x) < l(xc) have negative characteristic Lyapunov exponents. The critical wavelength is found to be approximately 130 wall units and obeys viscous scaling at these Reynolds numbers

Economic evaluation of energy saving measures in a common type of Greek building

This paper deals with the economic analysis and evaluation of various energy saving measures in the building sector, focusing on a domestic detached house in Greece, i.e. in a typical Mediterranean climate. In order to detect the energy saving measures that, in addition to energy benefits, can also provide economic profits, the study examines the following measures: all kinds of insulation; upgrading of the heating system; use of thermal solar systems; upgrading of lighting; upgrading of electric appliances; upgrading of the cooling system. The economic evaluation methods used for ranking the energy saving measures are the Net Present Value, the Internal Rate of Return, the Savings to Investment Ratio and the Depreciated Payback Period. It has been found that amongst the most effective energy saving methods are the upgrading of lighting, the insulation of the roof of the building and the installation of an automatic temperature control system.Detached house Energy saving measures Economic evaluation Ranking of measures Greece