Session X42: Turbulence: Wall-Bounded VI

Causality between streaks and bursts in wall-bounded turbulence

Structural models of wall-bounded turbulence are rooted in two distinctive but interacting entities: bursts and streaks. The prevailing understanding is that both structures are involved in a self-sustaining cycle at each scale in a relatively isolated manner. However, some recent evidence from numerical experiments and observations casts doubt on current models. The root problem is that the causal relation between streaks and bursts has yet to be elucidated. Traditional causal inference based on interventions, while powerful, might result in misleading causal relations by unintentionally altering key dynamics of the system. Here, we propose a non-intrusive method using information flux based on information theory to infer causality between streaks and bursts. By analyzing time-resolved signals representative of streaks and bursts obtained from direct numerical simulations, we investigate the causality between these structures at different proximity levels. Our results reveal that bursts are causal to streaks located closely downstream in the streamwise direction. Similarly, streaks are causal to bursts in the proximity of the streak located downstream. The analysis also shows that most of the causality on these localized structures cannot be explained merely by the dynamics of their single closest streak or burst.   

Adjoint macroscopic forcing method for computing the nonlocal eddy viscosity in a turbulent channel flow

The nonlocal eddy viscosity relates the Reynolds stress at a spatial point to the mean velocity gradient at all points. With this, one can inform models, e.g., RANS models, about the sensitivity to the mean velocity gradient and the suitability of local approximations. Previous brute force approaches (Mani and Park, Phys. Rev. Fluids, 2021; Hamba, Phys. Fluids, 2005) compute the nonlocal eddy viscosity by forcing the mean velocity gradient at each point in the averaged space and examining the Reynolds stress response. They require a separate simulation for each mean velocity gradient point. So, obtaining the nonlocal eddy viscosity requires as many simulations as degrees of freedom in the averaged space. For large problems, the number of simulations required becomes cost prohibitive. We present the adjoint macroscopic forcing method (MFM) as a strategy to obtain the nonlocal eddy viscosity at a given Reynolds stress location using a single simulation. This method recovers the Reynolds stress dependence at a point of interest, such as a separation point or near the wall, on the mean velocity gradient at all points. We demonstrate the adjoint MFM on a canonical turbulent channel flow.    

A reduced resolvent model of linear amplification mechanisms in channel flow

The linearized Navier-Stokes (LNS) equations are employed in channel flow to study linear amplification mechanisms. We examine wave-number regions corresponding to streamwise streaks, oblique waves and Tollmien-Schlichting waves, linking these mechanisms back to the linearized Navier-Stokes equations. In particular, we examine the Orr-Sommerfeld and Squire (OSS) equations from an input-output point of view, considering the full LNS system, and a reduced model in which the OSS equations are considered separately as subsystems. This approach enables individual analysis of the Orr-Sommerfeld and Squire systems, revealing the relationship between linear amplification and the linear mechanisms from which it arises. In order to accomplish this, we use a Reynolds number scaling argument to justify the simplification of pathways in the linear model. Results indicate that the Orr-Sommerfeld system contains amplified regions for all three flow features, while the Squire system only amplifies streamwise streaks and oblique waves. Analysis is performed for laminar Poiseuille flow, laminar Couette flow, and turbulent Poiseuille flow using an eddy-viscosity model. Additionally we compare modal structures between the full and reduced models using singular value decomposition.   

Modification of vortical structures in a drag-reduced flow created by transverse wall oscillations in a pipe

We present results of Direct Numerical Simulations of drag reduction in a turbulent pipe flow with transverse wall oscillations at Re_tau=720. Drag-reduced flow exhibits turbulence characteristics that are significantly modified with respected to a standard pipe flow without wall oscillations. In particular, this talk focuses on identification of the number and strength of the hairpin vortices in the buffer and log layers of the flow. We present the evidence of a suppression of the number of the vortical structures with wall oscillation, identified using instantaneous snapshots of the swirling-strength parameter. This reduction in the number of vortices is consequently associated with a weakened signature of the vortex packets and large-scale motions in this flow, albeit the very-large-scale motions still persist. A suppression of the near-wall turbulent eddies and their auto-generation mechanisms is believed to cause drag reduction in this flow.    

Optimal prediction of wall stress and pressure from outer velocity observations

Probing near-wall turbulence experimentally is challenging, which leads to difficulty in accurately evaluating the wall stresses and pressure fluctuations. When measurements satisfy the conditions for synchronization (Wang & Zaki, J. Fluid Mech 943, 2022), the near-wall flow can be reconstructed with machine accuracy. When synchronization is not possible, we determine the most accurate estimation of the near-wall region using adjoint-variational data assimilation. The estimated flow field satisfies the Navier-Stokes equations, optimally reproduces the available data, and provides full access to the unknown near-wall turbulence and wall shear stresses and pressure. When the thickness of the unobserved layer is up to fifty viscous units, the reconstructed velocity and pressure fields are almost identical to the true state. As the observations are further separated from the wall, only the inner-layer large-scale structures are accurately estimated. These trends are explained using the coherence spectrum between inner and outer flow quantities: longer wavelength structures have larger coherence depth towards the wall. Lastly, the robustness of the estimation accuracy is demonstrated using filtered and sub-sampled outer observations.   

Turbulent-wall pressure fluctuations in permeable-rough surfaces

Permeable and rough walls are known to affect the turbulent boundary layers (TBLs) developing over them differently. Permeability relaxes wall blockage, while roughness increases surface drag. A realistic representation of a permeable wall might consist of both permeability and roughness, to a varying degree. In the presence of rough walls, the near-wall turbulent structures in smooth wall TBLs are replaced by coherent roughness element-sized structures, while the flow penetration into a permeable wall has been observed to alter the dynamics of coherent structure formation above the wall. Independently, the effects of these wall conditions on their flow characteristics and wall-pressure statistics are relatively well-established. Their combined effects, however, are still largely unknown.

    

In this study, we aim to explore and decouple the effects of permeability and roughness in the flow and wall-pressure statistics. Simultaneous hot-wire anemometry and microphone measurements are conducted inside a boundary layer wind tunnel over a wide range of Reynolds numbers, where TBLs develop over various porous and rough walls (with a systematic variation of the roughness effects). Present results suggest that the footprints of permeability and roughness are apparent in the energy spectra of turbulent fluctuation for isolated permeable and rough walls. Explorations of this phenomenon in porous-rough combinations, the coherence between turbulence and wall-pressure statistics, as well as decoupling of roughness and permeability effects, will follow.   

A wall function for turbulent compressible boundary layer flow

Here we propose a method to develop a wall function for a turbulent compressible boundary layer flow. We reduce the governing equations of motion to a lower-order form through application of shock-layer and boundary layer analysis of the compressible RANS equations. The equations are closed using the Spalart-Allmaras one equation model. We derive the governing equations for an idealized high Mach number flow over an insulated plate with Pr = Pr_T = 1. The equations yield a wall function for turbulent compressible boundary layer flows that have potential to improve upon the more commonly used wall function presented by Van Driest.   

Mesoscale study of turbulent boundary layer over an in-situ grown soft fouling

Biofouling of ship hulls is a ubiquitous phenomenon and causes substantial maintenance costs each year. While real-world flow near a ship hull is highly turbulent, past laboratory studies focus largely on understanding of biofilm formation mechanisms and identifications of phenotypical responses by microbes to a wall under low and laminar flow shear. Recent findings on formation of biofilms in turbulent flows capable of resisting shear have reignited interests in interactions of turbulent flow and biofilm. To provide new insights on flow and soft-fouling interactions at scales relevant to real-world applications, we developed a mesoscale flow facility enabling the study of in-situ biofilm formation at high turbulent flow shear conditions.  The flow facility is instrumented for simultaneous biofilm measurements and the near-film flow field via coupled particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) systems. Results on hydrodynamic interactions of turbulent boundary layer (TBL) and in-situ grown biofilms from natural seawater are presented.  The temporal evolution of TBL at different growth stages is investigated.   

Water-lubricated channel flow

We use direct numerical simulation (DNS) to study the problem of drag reduction in a lubricated channel, a flow instance in which two thin layers of a lubricating fluid (density ρ1, viscosity η1, thickness h1) are injected in the near-wall region of a plane channel, so to favor the transportation of a primary fluid (density ρ2, viscosity η2, thickness h2). All DNS are run within the constant power input (CPI) approach, which prescribes that the flow rate is adjusted according to the actual pressure gradient so to keep constant the power injected into the flow. The CPI approach has been purposely extended here for the first time to the case of multiphase flows. A phase-field method (PFM) is used to describe the dynamics of the liquid-liquid interface. We unambiguously show that a significant drag reduction (DR) can be achieved for all four configurations considered. Upon a detailed analysis of the turbulence activity in the two lubricating layers and of the interfacial wave dynamics, we are able to characterize the effects of surface tension forces, surfactant concentration, and viscosity contrast on the drag reduction performance.