Session T18: Turbulence: Wall-Bounded II

Effect of chequerboard-type dynamic roughness on turbulent channel flows – a DNS study

The effect of distributed roughness on turbulent boundary layer flows is a topic of fundamental importance for the elucidating of wall turbulence dynamics and for the advancement of flow control strategies aimed at reducing the frictional drag. Dynamic roughness, generated by moving small areas of the wall surface, can be an entirely new realm of drag control, with parameterizations in terms of the frequency of oscillations and other input parameters such as roughness height, spacing, and shape. In this investigation, we are concerned with the response of wall turbulence to distributed chequerboard-type dynamic roughness, oscillating harmonically at a given frequency. Results from several preliminary direct numerical simulations of turbulent channel flows, featuring dynamic roughness on both walls, will be presented and discussed. By targeting a range of frequencies, spanwise/streamwise wavenumbers, and roughness heights, we will quantify the effect that dynamic roughness has on the skin friction, various turbulent statistics, and turbulent flow structures.   

Non-linear forcing and triadic interactions in flows over spanwise periodic transpiration as a model for wall roughness

Turbulent flows over spanwise periodic surface features are of great interest to many engineering applications, and we seek to shed light on the role of the non-linear terms in these flows. Direct numerical simulations (DNS) with streamwise aligned transpiration boundary conditions (Flores and Jimenez, JFM, 2006) are used to study the effect of spanwise periodicity. DNS of turbulent channel flows with wall transpiration at different spanwise wavenumbers are conducted at friction Reynolds number of 550. Similarities and differences between the flows are examined through the energy spectra of the forcing and the triadic interactions. The forcing spectra show similar structures between the flow with and without transpiration when the 2D mean profiles are used. Additionally, projection coefficients are defined to highlight the relative importance of each triadically compatible pair of wavenumbers. These projection coefficients identify three important regions of interactions between different scales similar to those employed by the generalized quasilinear (GQL) approximation (Marston et al., PRL, 2016).

    

Linearized predictions of secondary flows in turbulent channels with strip-type roughness heterogeneity

Turbulent wall-bounded flows subjected to a lateral roughness heterogeneity develop secondary currents, with strength depending on the surface properties. In this work, secondary flows in pressure-driven channels with strip-type roughness are investigated using Reynolds-Averaged Navier-Stokes (RANS) equations, with the Spalart-Allmaras turbulence model to close the equations. A nonlinear Reynolds stress model is also used to capture the anisotropic Reynolds stresses, required to generate secondary flows. Assuming a small roughness height, linear RANS equations governing secondary flows are obtained.

The flow organization predicted by the linear model agrees with available experimental and numerical data. For increasing strip width, the secondary flows tend to occupy the entire half-height of the channel. Their strength peaks when the spacing between the strips is ~1.4 times the half channel height. This is due to the properties of the Navier-Stokes operator linearised around the turbulent mean profile. Tertiary flows are predicted for wide strips, modifying the flow organization. Similarities and differences between strip- and ridge-type roughness are finally observed. Since the governing equations are linear, a combination of these two effects is possible and will be discussed in the talk.     

Energy cascade in a turbulent boundary layer over spanwise heterogeneous roughness

One of the most attractive features of turbulences is the inter-scale energy transfer from the large energy-containing scales towards the dissipation scales. Recently, Johnson (2020, PRL, 124, 104501) found that the inter-scale energy transfer can be precisely divided into three terms: vorticity stretching, strain self-amplification, and the interaction between strain and vorticity. This brilliant finding makes it possible to characterize the cascade from the contribution of each component. Johnson focused on the homogeneous isotropic turbulence (HIT). Inspired by his work, the decomposition is applied to a heterogenous anisotropic turbulence flow: a turbulent boundary layer over spanwise heterogeneous roughness. By doing so, we try to address the following issues. First, strain self-amplification has been found to be the main cause of the cascade in HIT. Here we verify that this conclusion still hold for such a complicated turbulent flow. Second, both the instantaneous locations of intense strain self-amplification and intense vorticity stretching events are found to be highly related with the local dynamics of the large-scale low-speed motions (L-SMs). Understanding these behaviours could shed new light on the modelling of wall-bounded turbulence.

    

Sparse space-time resolvent analysis

Resolvent analysis has emerged as a common tool for identifying linear amplification mechanisms in a broad range of fluid flows. However, it is in general suited only for the analysis of harmonic forcing and response structures in statistically-stationary systems. Here, we develop a generalized space-time extension of resolvent analysis that can be applied to time-varying systems. In addition, we combine this method with sparsity-promoting methods to identify resolvent modes that are localized in both space and time. Sparsity is achieved by modifying the standard optimization problem associated with the singular value decomposition to include an $L_1$-norm term. This results in a nonlinear eigenproblem, which can be solved using a generalized inverse power method. We first demonstrate this space space-time resolvent analysis on statistically-stationary turbulent channel flow, where it is shown that sparse modes can be identified in both space and time. Next, the method is used to identify time-localized amplification mechanisms in an oscillating turbulent Stokes boundary layer. We will discuss the application of this method to other time-evolving systems, and also comment on how the proposed method relates to harmonic resolvent and transient growth analysis.   

Wavelet-based resolvent analysis of temporally-varying turbulent flows

In this work, we reformulate resolvent analysis and adapt it to the study of transient flows with a time-varying mean state. In our formulation, the resolvent operator links input and output states that have been wavelet-transformed rather than Fourier-transformed in time, which preserves both temporal and frequency information in the system. We validate this methodology for traditional turbulent channel flow and show that the wavelet-based and Fourier-based resolvent analyses are equivalent for statistically-stationary flows. We then apply wavelet-based resolvent analysis to temporally-evolving parallel shear flows such as an oscillating boundary layer and three-dimensional channel flow.   

Time-localized analytic resolvent analysis

This talk will develop an analytic framework for studying time-localized linear energy amplification mechanisms in wall-bounded turbulent flows. In this approach, the standard Fourier temporal expansion used in the resolvent framework is modified to instead consider localized temporal wavepackets, taking the form of Gabor wavelets. We show that temporal wavepackets with this structure (corresponding to Fourier modes modulated by Gaussian envelopes) naturally emerge when the singular value decomposition used in resolvent analysis is modified to promote sparse-in-time modes. We will demonstrate that an analytic formulation of resolvent analysis can be extended to consider such time-localized wavepackets, and will compare analytic predictions to numerical findings concerning the dependence of mode structure and amplification on the extent of time-localization. We will discuss connections to empirical and theoretical findings concerning the existence of spatial wavepackets with similar structure, and will also comment on the potential application of this method to non-statistically-stationary flows.   

Author not Attending

A fundamental distinction exists between the mechanism of perturbation growth by extracting

energy from the time-independent time mean flow and the mechanism of perturbation growth

by extracting energy from the time-dependent streamwise mean flow. In the former case, the mechanism is transient growth associated with the non-

normality of the structurally invariant eigenvectors of the time mean flow. In the latter case,

perturbation growth can be attributed to contributions to growth arising from two distinct non-

normal processes: growth of each covariant Lyapunov vector in isolation and growth resulting

from non-normal interaction among the covariant Lyapunov vectors. Both of the mechanisms participate in producing perturbation growth and they work together to

determine the excitation of the streamwise mean flow arising from perturbation perturbation nonlinearity. Resolvent analysis is extended to time dependent streamwise mean flow of a turbulent Couette flow at low and moderate Reynolds numbers to analyze and separate these two components of the mechanism of perturbation growth in time dependent flow.   

Wall-bounded turbulence does not need streaks

The streaks of wall-bounded turbulence are typically much longer than the bursts of the cross-plane velocities. Here, the effect of damping long streaks is explored using numerical experiments, and it is shown that they are not required for the self-sustenance of the bursting, which is relatively little affected by their absence. In particular, there are turbulence states in which the fluctuations of the streamwise velocity have approximately the same length as the bursts, and are thus presumably associated with the bursts themselves, while the bursts are essentially indistinguishable from flows in which longer velocity fluctuations are present. This suggests that the long streaks found in natural wall-bounded turbulence may be by-products, rather than active parts of the turbulence regeneration process.

    

Comparison of Turbulence Scales between Internal and External Flow at High Reynolds Number

Data from wall-bounded turbulent flow measured at high Reynolds number was examined to investigate the difference in scaling parameters between internal pipe flow and external turbulent boundary layers. Of particular interest was the degree of agreement between the internal and external flow scaling behavior once the external intermittency of the external flow was accounted for. Results demonstrated that once the external intermittency was accounted for specific parameters describing large-scale characteristics follow similar outer-scaled behavior throughout the flow field for both inner and outer flows. Similarly, scaling parameters for representing dissipative turbulent structure followed similar behavior in inner scaling throughout the flow field for both inner and outer flows. These characteristics were used to produce model one-dimensional homogeneous and isotropic spectra that, when compared to the measured one-dimensional energy spectra, isolated of the difference between the two types of flows in spectral space.   

The spatial changes of the wake of a circular cylinder immersed in a turbulent boundary layer over a flat plate

An experimental study was conducted immersing a small cylinder (D/δ = 0.0478, where D is the cylinder diameter and δ is the boundary layer at 99% of the freestream velocity) in a turbulent boundary layer (TBL) over a flat plate at six wall-normal distances. The cylinder was placed with the longitudinal axis towards the span-wise direction of the test section. Using 2D-2C Time-resolved Particle Image Velocimetry (TR-PIV) measurements were taken immediately downstream of the cylinder obtaining a field of view of 3.7δ-by-2.2δ in the streamwise-wall-normal plane. In this presentation, turbulent statistics for the different cases studied are shown and compared with each other and with experimental data of the canonical TBL i.e., without the cylinder. Statistical trends, including the recovery of the turbulent mean profile downstream of the cylinder disturbance and the evolution of the Reynolds shear stresses downstream of the cylinder wake are reported and compared across the cases. The trends show that for all the cases, the influence of the cylinder on the velocity profile remains strong as the cylinder is placed at a farther distance from the plate. The interactions of the cylinder wake with the turbulent boundary layer coherent structures are analyzed using conditional averaging, including conditional projection averaging (Saxton-Fox et al, 2022). The evolution of the cylinder wake downstream is observed to be affected, in both its amplitude and its advection, by local large-scale turbulent structures.

    

Distortion of Turbulent Pipe Flow by an Axisymmetric Body

To better understand the effects of pressure gradient, streamline convergence/divergence, and streamline curvature on turbulence in wall-bounded flows, a body-of-revolution (BOR) is placed on the axis of the Superpipe at Princeton University. Measurements using a nano-scale thermal anemometry probe (NSTAP) are made in the flow over the body and in the wake recovery region. Mean flow, Reynolds normal stress, and spectra are presented for a pipe flow Reynolds number of 1x10^6 and a BOR with a blockage ratio of 2/9. Spectra show that in the bow region, the largest motions in the turbulence scale with local bulk velocity and the spacing between the pipe wall and BOR. In the stern region, the adverse pressure gradient and expanding flow enhances the turbulence and causes a shift in energy content towards larger scales.