Session A42: Turbulence: Wall-Bounded I

Modeling Two-Point Spatial Statistics in Turbulent Channel Flow

Two-point spatial statistics in turbulent channel flow are studied by numerical simulations combined with spectral analyses of the Orr Sommerfeld/Squire (OS/SQ) system of equations. The simulations vary in Re_τ from 180 to 5200. The OS/SQ equations are assumed to have to have stochastically-forced  source terms representing the nonlinear terms in the full dynamical equations for ▽²v  and ω_y. Using eigenfunction expansions we derive the two-point correlations for v , ω_y , and their cross-correlation  explicitly in terms of their corresponding nonlinear source correlations. These expressions contain the known eigenfunctions, the corresponding eigenvalues, and the statistics of the forcing term for each mode with possible cross correlations between modes. The modeling proceeds by attempting to represent the known simulation results by an optimal choice of the covariance matrix of the eigenmode forcing amplitudes. The modes chosen for the expansion are ranked in importance by the real part of the eigenvalues so that those with  a smaller magnitude of the real part (slower decaying modes) are ranked higher. Once the nonlinear source statistics  are determined the remaining two-point statistics involving u, w,  and uv may be computed.      

Revisiting ‘bursts’ in wall-bounded turbulence

Since the advancements in technologies to measure turbulence, it has been widely observed that a turbulent signal exhibits high-intensity activities that last for a certain duration followed by quiet periods. In our day-to-day lives, we experience the presence of such high-intensity turbulent bursts when suddenly strong gusts appear in the winds or those unpleasant bumpy flights with vigorous shaking. Apart from its pragmatic appeal, on a fundamental level, the presence of bursts renders the efforts toward developing a universal approach to turbulence modeling difficult. Therefore, understanding these bursts is of both theoretical and practical interest to the turbulence community. Motivated by this need, we demonstrate that the problem of turbulent bursts can be tackled through a complex systems approach, an emerging research area that has its roots at the heart of statistical physics. Specifically, by considering both the duration and intensity of the bursting events, one can incorporate the effect of bursts on the turbulence statistics at any specified scale of the flow, allowing the authors to connect the origin of bursts to the presence of organized eddy motions in turbulent flows called ‘coherent structures’, thereby revealing a hidden aspect of universality associated with turbulent bursts. Accordingly, this study paves the way toward the development of next-generation models of turbulent flows, by creating a union between complex systems science and fluid mechanics.    

Uniform momentum zones and internal shear layers in turbulent pipe flow

This study explores uniform momentum zones (UMZs) and their interfaces using direct numerical simulation data of fully-developed turbulent pipe flow at Reynolds number ranging from Re_τ = 550–6000. We identify UMZs and their corresponding interfaces by applying a histogram-based identification method, as proposed by Adrian et al. (J. Fluid Mech., vol. 422, 2000, pp. 209–331) and de Silva et al. (J. Fluid Mech., vol 786, 2016, pp. 209–331). We find that the number of UMZs exhibits a log-linear increase with the Reynolds number in a manner analogous to that reported in turbulent boundary layers. The topmost UMZs are demarcated by a streamwise velocity at 0.95U_CL (where U_CL is the centerline mean velocity) across a wide range of the Reynolds number, indicating the presence of a quiescent core region. We further investigate the turbulent statistics across the interfaces (or internal shear layers) of multiple UMZs. We will discuss the scaling of these interfaces and their relationship with the logarithmic mean velocity profile.   

Formation of wide backflow events via large-scale streak interactions in turbulent channel flow

This study investigates the formation mechanism of wide backflow events using direct numerical simulation data of turbulent channel flow at Re_τ = 180 and 550. By changing the spanwise size of the computational domain, we observe wide backflow events whose width exceeds 0.1h (where h is the channel-half height), which is an order of the characteristic width of large-scale structures. It is found that wide backflow events originate from a collision between large-scale high-speed and low-speed structures. Due to the difference in convection velocities, the large-scale high-speed structures climb over the low-speed structures. When the incoming high-speed structure aligns with the trailing edge of the low-speed one, a relatively wide shear layer forms near the wall, which subsequently leads to the formation of a strong vortex. As the process evolves, this vortical structure elongates in the spanwise direction with a length scale over 0.1h, which induces a wide backflow region. The collision between large-scale structures and the associated formation of wide backflow events is found to contribute to turbulence production in the near-wall region.   

Direct numerical simulation of one-sided forced thermal convection in square ducts

We perform direct numerical simulations (DNS) of forced thermal convection within one-sided heated square ducts up to friction Reynolds number 2000, comparing the global heat transfer to the academic scenario of uniformly heated walls. Similarly to the case of plane channel flow, and in agreement with early experiments, we find a significant reduction of global heat transfer compared to the uniformly heated case. The reduction of global heat transfer depends on the Reynolds number, and levels off to approximately 10%, at unit Prandtl number. The global heat transfer in square ducts closely parallels that in plane channel flow under similar boundary conditions when we match to the bulk Reynolds number based on the effective diameter. Our results illustrate that the use of traditional engineering formulas, devised for uniform heating scenarios, could potentially introduce substantial uncertainty into global heat transfer coefficient predictions. Consequently, it is essential to consider heat distribution when estimating global heat transfer.   

Numerical simulation of generalized Couette-Poiseuille flow

We present direct numerical simulation (DNS) and modelling of generalized Couette-Poiseuille (GCP) flow in a channel of height 2h defined by three independent parameters (Re,theta,phi). Here (Re,theta) are polar co-ordinates in the space of independent Reynolds numbers (ReC,ReM) associated respectively with the plate velocity difference and fixed volume flow with ReC=Re cos(theta), ReM=Re sin(theta), and phi is the angle between the applied pressure-gradient vector and wall-velocity-difference vector. We will describe DNS of turbulent GCP flow at fixed Re = 6000 with (theta,phi) both in the range zero to 90 degrees. The competition between the Couette-flow shear and the pressure gradient produces a mean velocity profile with directional twist between the confining walls. Results discussed will include four components of the skin friction coefficient with comparison with modeling, mean velocity profiles and pre-multiplied energy spectra.   

Elastically Modulated Vortex Interaction in Taylor-Couette flows

Taylor-Couette flow, between two concentric cylinders, has been used extensively for the case of viscoelastic instabilities, revealing different transitional mechanisms leading to Elasto-Inertial Turbulence (EIT). These mechanisms involve vortex chaotic interaction like vortex merging and splitting (MST/VMS) (Lacassagne et al., 2020; Lopez, 2022). However, visualization techniques or numerical methods are used in most cases.

Implementing Particle Image Velocimetry (PIV) for fluids of different elasticities (El=0.06-El=0.34), we give insight into the fundamental mechanistic differences of vortex interactions based on fluid elasticity on the route to EIT.

Lacassagne, T., Cagney, N., Gillissen, J. J. J., & Balabani, S. (2020). Vortex merging and splitting: A route to elastoinertial turbulence in Taylor-Couette flow. Physical Review Fluids, 5(11), 113303. https://doi.org/10.1103/PhysRevFluids.5.113303

Lopez, J. M. (2022). Vortex merging and splitting events in viscoelastic Taylor-Couette flow. Journal of Fluid Mechanics, 946, A27. https://doi.org/10.1017/jfm.2022.579   

Spatio-temporal quantification of triadic contributions to the turbulent velocities in channel flow

To help clarify the role of the advective nonlinearity in turbulent wall flows, we analyze data from the direct numerical simulation (DNS) of an incompressible turbulent channel flow at a friction Reynolds number of 550 (Flores and Jimenez, JFM 2006). After performing a Reynolds decomposition, the quadratic fluctuation-fluctuation term in the Navier-Stokes equations is treated as a non-linear forcing to the associated linear operator. This forcing is studied in the Fourier domain, in which it becomes a convolution sum over all triadically compatible wavenumber-frequency triplets. The linear resolvent operators (McKeon and Sharma, JFM 2010) are applied to each pair of interacting triplets, and the resulting contributions to the corresponding velocity fields are computed. The results show the importance of interactions involving large streamwise scales. Furthermore, the regions of non-linear interactions permitted under the quasi-linear (QL) and generalized quasi-linear (GQL) reductions (Marston et al., PRL, 2016) are shown to be significant contributors to the velocity fields, providing a possible reason for the success of QL and GQL simulations.