Session T42: Turbulence: Wall-Bounded V

Mechanisms Underlying the Generation of the Surface Layer with Linear Increase in Integral Scale

The surface layer (SL) concept originated with law-of-the-wall (LOTW) phenomenology whereby a canonical turbulent boundary layer (TBL) contains an inertia-dominated sublayer outside a very thin viscous or roughness layer adjacent to a wall where key horizontal integral scales increase linearly with wall-normal distance, z. Because mean shear-rate both reflects and contributes to wall-normal turbulent momentum flux, LOTW also requires that the TBL SL be characterized by a single dominant velocity scale set by the level of turbulent momentum flux through the SL. The existence of a single velocity scale and key integral scale ~z implies a 1/z dependence for mean velocity gradient in a layer typically conflated with the SL. In the current study we explore the hypothesis that the linear variation in key SL integral scales is driven directly by blockage of vertical turbulence fluctuations at the impermeable surface unrelated to the existence of mean shear. To test this hypothesis we measured with sPIV two classes of wall-bounded turbulent flow, a flat plate TBL with shear-dominated SL, and a class of shear-less wall-bounded turbulence created by advecting inertia-dominated grid turbulence over a flat plate. The grid turbulence structure, we find, changes in response to blockage such that the vertical fluctuations within wall-modified turbulence eddies develop correlation lengths in the horizontal that increase linearly with z over an inertial shear-free SL within a larger wall-modified layer. We analyze generalizable mechanisms underlying the turbulence correlations specific to the SL.   

Coherent structures in stably stratified wall-bounded turbulent flows

To date, a growing body of literature has documented the existence and impacts of coherent structures known as large- and very-large-scale motions within wall-bounded turbulent flows under neutral and unstable thermal stratification. Stable stratification limits vertical transport and turbulent mixing within flows, which makes it unclear the extent to which these previous findings on coherent structures are applicable to stably stratified flows. In this study, we investigate the existence and characteristics of coherent structures under stable stratification with a wide range of statistical and spectral analyses. Outer peaks in premultiplied spectrograms under weak stability indicate the presence of large-scale motions, but these peaks become weaker with increasing stability. A quadrant analysis of turbulent transport efficiencies (the ratio of net fluxes to their respective downgradient components) demonstrates dependencies on both stability and height above ground, which is evidence of morphological differences in the coherent structures under increasing stability. Amplitude modulation by large-scale streamwise velocity was found to decrease with increasing gradient Richardson number, whereas modulation by large-scale vertical velocity was approximately zero across all stability ranges. For sufficiently stable stratification, large eddies are suppressed enough to limit any inner-outer scale interactions.   

Hybrid Lagrangian/Eulerian for Probability Density Function Transport Models of Wall Bounded Turbulence

A large part of efforts to develop probability density function (PDF) approaches to turbulence modeling have focused on canonical applications and developing theory for Lagrangian viewpoints. Pure Lagrangian models require complex regression techniques in higher dimensions to find mean quantities. To simplify implementation in complex problems and mitigate some challengings due to sampling and regression, a hybrid Eulerian-Lagrangian RANS/PDF method is used for wall-bounded turbulent flows. The Eulerian transport equations in finite-volume form are used to time-advance mean quantities. Particle properties are used to close the Eulerian transport equations. Emphasis is placed on consistency between the finite-volume and particle representations. This method is applied to a turbulent channel flow, using an elliptic relaxation model. Additionally, inverse modeling based on direct numerical simulation data is used to guide the formulation of the elliptic relaxation model. The results are verified for against DNS data, and the impact of several modeling assumptions are discussed.   

Direct numerical simulation of wall-bounded magnetohydrodynamic turbulent flows at moderate Reynolds and Hartmann numbers.

Wall-bounded (WB) magnetohydrodynamic (MHD) turbulence is crucial in various technological fields, especially in fusion energy sciences. However, our understanding of WBMHD turbulence still lags behind its non-magnetic counterpart. In this study, we conduct direct numerical simulations (DNS) of WBMHD turbulence at moderate Reynolds (Re) and Hartmann (Ha) numbers to understand the nature of WBMHD turbulence. We use the pseudo-spectral method in streamwise and spanwise directions and the high-order basis spline method in the wall-normal direction. We impose a constant magnetic field in the wall-normal direction for simplicity with low magnetic Re assumptions. Ha ranges from 1 to 100, while Re reaches up to 40000, equivalent to a friction Re of 1000 without magnetic fields. Preliminary results show that the mean-velocity profile of Re = 40000 flows is significantly influenced when Ha is greater than 10, and this influence starts from the outer flows. Additionally, we analyze the impact of the magnetic field on the turbulent kinetic energy (TKE) through the terms in the TKE budget equations. Our presentation emphasizes the key differences between WBMHD turbulence and canonical WB turbulence as a function of Re and Ha.   

The presence of inner layer streaks in large-defect APG TBLS

Turbulent boundary layers (TBLs) develop a defect in their mean velocity profile when they are exposed to an intense or prolonged adverse pressure gradient (APG). The changes in the mean velocity profile affect the turbulent activity significantly. In large-defect TBLs, the outer-layer turbulent activity dominates the flow and the inner peak of the 2>-spectra, which is also the signature of the inner-layer streaks, disappears. However, it is not clear if the streaks disappear or become hidden due to the imprints of energetic outer-layer structures in the near-wall region. In this study, our aim is to determine the presence of inner-layer streaks in large-defect TBLs. For this, we have generated a non-equilibrium APG TBL database using direct numerical simulation, based on a previous APG TBL, where the outer-layer turbulence is artificially eliminated to examine the inner layer without the effect of the outer layer. We investigate the two-point correlations and the spectral distributions in the inner layer and the preliminary results suggest that the inner-layer streaks are present in large-defect TBLs even when the mean shear is very low. Together with the variations of the streaks characteristics, we are currently determining the proportions of streaks generated locally and those convected from a position upstream where the shear is still not that small.   

Spectral data-driven analysis of high Reynolds-number turbulent pipe flows

Accurate computation of high-Reynolds-number wall turbulence, relevant to many technological applications, presents unresolved questions about modelling, prediction, and the underlying mechanisms of generation and interaction of coherent structures. Smooth circular pipe flow of radius R and length of 10πR is studied. The analysis is based on the comprehensive dataset comprising well-resolved DNS up to Re_τ = 5200 by Yao et al. (2023). Using Fourier-based Proper Orthogonal Decomposition (POD), we identify the spatially coherent structures and classify them according to their location, spatial extent, and lifetime as functions of the Reynolds number. At the high Reynolds numbers, we observe two distinct characteristics. Firstly, there are very large-scale motions (VLSM) which dominate the rankings of the most energetic POD modes. Our findings suggest that these structures exhibit spatial correlation over a length greater than that of the pipe itself. Secondly, the POD classification directly identifies attached eddies with their size scaling linearly from the wall, as well as detached eddies located at roughly 0.5R away from the wall. We can thus draw a comprehensive picture of the structures in pipes using POD, and track the influence of the Reynolds number.   

On the statistics of instantaneous wall-normal integrals

Wall-bounded turbulence is characterized by large (and very-large) scale motions with wall-normal extent comparable to the boundary layer thickness or channel half-height and with larger streamwise extent. These (V)LSMs are known to carry a substantial proportion of the turbulent kinetic energy and Reynolds stresses. Inspired by classical (RANS-based) integral methods for boundary layers, the statistics of instantaneous wall-normal integrals of velocity are analyzed. Spectral analysis is performed on turbulent channel flow data from Johns Hopkins Turbulence Database to assess the extent to which the use of instantaneous integrals could potentially enhance our ability to understand and model large scale motions. It is found that roughly 40-45% of the Reynolds shear stress is resolved by the instantaneously integrated velocity; a proportion that is made substantially larger when only long streamwise wavelengths are considered.   

Symbolic dynamics and nonlinear forecasting of a low-Reynolds-number turbulent channel flow

We numerically study the dynamic state and predictability of streamwise velocity in a low-Reynolds-number turbulent channel flow from the viewpoint of symbolic dynamics and nonlinear forecasting. We conduct direct numerical simulation (DNS) under the friction Reynolds number of 180. Applying two sophisticated analytical methods, i.e., orbital-instability-based forecasting method (OIFM) and ordinal partition transition network (OPTN), in combination with the surrogate data method to the time series data obtained by DNS, a low-dimensionally and high-dimensionally chaotic states of the streamwise velocity fluctuations emerge at a viscous sublayer and a logarithmic layer, respectively. The present method identifies the possible presence. The predictable time of the low-dimensional chaotic state in the streamwise velocity at the viscous sublayer is about 100 times as long as the time resolution of DNS. The OIFM has a high potential for predicting the chaotic streamwise velocity from the viscous sublayer to the logarithmic layer.