Using parabolized stability equations to model boundary-layer transition in direct and large-eddy simulations

We examine the potential of the nonlinear parabolized stability equations (PSE) to provide an accurate yet computationally efficient treatment of the growth of disturbances in H-type transition to turbulence. The PSE capture the nonlinear interactions that eventually induce breakdown to turbulence, and can as such identify the onset of transition without relying on empirical correlations. Since the local PSE solution at the onset of transition is a close approximation of the Navier-Stokes equations, it provides a natural inflow condition for direct numerical simulations (DNS) and large-eddy simulations (LES) by avoiding nonphysical transients. We show that a combined PSE/DNS approach, where the pre-transitional region is modeled by the PSE, can reproduce the skin-friction distribution and downstream turbulent statistics from a DNS of the full domain.

Modeling boundary-layer transition in direct and large-eddy simulations using parabolized stability equations

We examine the potential of the nonlinear parabolized stability equations (PSE) to provide an accurate yet computationally efficient treatment of the growth of disturbances in H-type transition to turbulence. The PSE capture the nonlinear interactions that eventually induce breakdown to turbulence and can as such identify the onset of transition without relying on empirical correlations. Since the local PSE solution at the onset of transition is a close approximation of the Navier-Stokes equations, it provides a natural inflow condition for direct numerical simulations (DNS) and large-eddy simulations (LES) by avoiding nonphysical transients. We show that a combined PSE-DNS approach, where the pretransitional region is modeled by the PSE, can reproduce the skin-friction distribution and downstream turbulent statistics from a DNS of the full domain. When the PSE are used in conjunction with wall-resolved and wall-modeled LES, the computational cost in both the laminar and turbulent regions is reduced by several orders of magnitude compared to DNS.

Turbulence intensities in large-eddy simulation of wall-bounded flows

A persistent problem in wall-bounded large-eddy simulations (LES) with Dirichlet no-slip boundary conditions is that the near-wall streamwise velocity fluctuations are overpredicted, while those in the wall-normal and spanwise directions are underpredicted. The problem may become particularly pronounced when the near-wall region is underresolved. The prediction of the fluctuations is known to improve for wall-modeled LES, where the no-slip boundary condition at the wall is typically replaced by Neumann and no-transpiration conditions for the wall-parallel and wall-normal velocities, respectively. However, the turbulence intensity peaks are sensitive to the grid resolution and the prediction may degrade when the grid is refined. In the present study, a physical explanation of this phenomena is offered in terms of the behavior of the near-wall streaks. We also show that further improvements are achieved by introducing a Robin (slip) boundary condition with transpiration instead of the Neumann condition. By using a slip condition, the inner energy production peak is damped, and the blocking effect of the wall is relaxed such that the splatting of eddies at the wall is mitigated. As a consequence, the slip boundary condition provides an accurate and consistent prediction of the turbulence intensities regardless of the near-wall resolution.

Causal analysis of self-sustaining processes in the logarithmic layer of wall-bounded turbulence

Despite the large amount of information provided by direct numerical simulations of turbulent flows, their underlying dynamics remain elusive even in the most simple and canonical configurations. Most common approaches to investigate the turbulence phenomena do not provide a clear causal inference between events, which is essential to determine the dynamics of self-sustaining processes. In the present work, we examine the causal interactions between streaks, rolls and mean shear in the logarithmic layer of a minimal turbulent channel flow. Causality between structures is assessed in a non-intrusive manner by transfer entropy, i.e., how much the uncertainty of one structure is reduced by knowing the past states of the others. We choose to represent streaks by the first Fourier modes of the streamwise velocity, while rolls are defined by the wall-normal and spanwise velocity modes. The results show that the process is mainly unidirectional rather than cyclic, and that the log-layer motions are sustained by extracting energy from the mean shear which controls the dynamics and time-scales. The well-known lift-up effect is also identified, but shown to be of secondary importance in the causal network between shear, streaks and rolls.

A multifractal model for the momentum transfer process in wall-bounded flows

The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation τ l ' , where l is the filtering length scale. According to the multifractal formalism, 〈 τ ' 2 〉 ~ log ( R e τ ) and 〈 exp ( p τ l ' ) 〉 ~ ( L / l ) ζ p in the log-region, where Re _τ is the friction Reynolds number, p is a real number, L is an outer length scale and ζ _p is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Re _τ = 4200.