Session T37: Turbulence: Environmental and Stratified Flow

Experimental measurements of methane plume transport in a turbulent atmospheric wind tunnel

Methane is a potent greenhouse gas with more than 20 times the global warming potential of carbon dioxide. The US Environmental Protection Agency (US EPA) has recently proposed new guidelines to reduce methane emissions from the oil and natural gas industry. A major obstacle to reducing anthropogenic methane emissions is determining the source location. In this project experimental measurements are taken in a turbulent atmospheric boundary layer wind tunnel to determine the turbulent dispersive methane plume growth one to 20 meters downwind of the leak source. Aeris Technologies sensors are used to determine the plume concentration profile in turbulent background flow speeds of 1 m/s to 6 m/s. The intermittency of the experimental data shows evidence of methane transport due to vortical fissures within the uniform momentum zone of the turbulent wall-bounded flow. Combining a statistical model for vortical fissures with the traditional Gaussian plume growth model is expected to give a good characterization of scalar transport in turbulent environments.   

Simulation-based study on turbulent canopy flows and "Monami" phenomenon

To understand the dynamics of flow and canopy motions and the energy transfer in turbulent canopy flows, we performed a high-fidelity simulation based study using large-eddy simulation. Our simulation employs an immersed boundary method together with a beam model to capture the dynamics of individual filaments in canopy stem arrays. Our simulation resolves the turbulence-induced coherent waving of the stems, which is known  as Monami. A broad range of stem flexibilities are considered in the simulation. Two characteristic scales are identified through spectral analyses. One is the Monami scale which is related to the progressive waving of the canopy, and the other one is the wake scale which is related to the wake behind each filament. A spectral TKE budget analysis indicates that the waving term plays an important role in the inter-scale and wall-normal energy transport processes. Moreover, the spectral shortcut process proposed by previous studies are found to be caused by the waving term.   

Wave-current interactions over coral reef morphology

The exchange of nutrients and dissolved gasses between corals and the surrounding water, which in part dictates how effectively a coral can function, relies on sufficient turbulence-driven mixing. However, the interaction between waves and turbulence is not fully understood when the bottom boundary consists of rough and spatially inhomogeneous surfaces such as coral heads. We employ particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) concurrently in a wave-current laboratory flume to measure velocities and scalar concentrations. 3D-printed, scaled-down coral heads create complex roughness features on the bed of the flume. This allows us to calculate mean quantities such as vertical flux, bottom drag, and energy dissipation, as well as determine phase dependance through phase averaging. More broadly, our results can help with developing models for predicting drag and fluxes over coral reefs.   

The role of turbulent flow on reconfigurable fractal trees: A large eddy simulation (LES) approach

Trees' turbulent boundary layer canopy interaction is usually dominated by large coherent structures, intermittent energetic eddies, and gusts in the flow. This study investigates such interactions using large-eddy simulation (LES). Each tree is modeled as a self-similar fractal branched multibody structure, with each leading mother branch connected to two daughter branches at each branching node. We study the role flexibility, tree spacing, and geometry heterogeneity play in momentum transfer between the inertial sub-layer and the tree canopies. We also investigate the correlation between flow statistics of different large coherent structures and their associated tree deflections. This enables us to identify how trees' static canopy reconfiguration and dynamic oscillations affect the flow's energetic eddies.   

The shape of turbulence generated at highly energetic tidal sites

Turbulence models that assume isotropic turbulence fail to accurately capture the anisotropic characteristics of highly energy tidal sites. Unanticipated anisotropies in the flow could introduce high force fluctuations on tidal energy devices leading to blade/component fatigue and a reduction of the device lifespan. Energy estimates could also be adversely affected. The current study analyzes the anisotropic behavior of turbulence from various tidal energy sites worldwide. Anisotropy for each site is evaluated using a Lumley triangle, a visualization tool that was developed to describe the shape of turbulent eddies (structures) in a flow. The effect of mean flow velocity and turbulence intensity on the shape of the turbulence and the degree of anisotropy at each site will be discussed. Preliminary results suggest the full range of turbulence shape is site-specific, though all sites analyzed demonstrate the majority of data exhibits axisymmetric, oblate spheroid-shaped turbulence. The implications of such turbulence shape and the instances of deviation will be presented.

    

Uniform momentum and temperature zones in unstably stratified turbulent channel flow

In wall-bounded turbulent flows, streamwise momentum organizes into uniform momentum zones (UMZs), separated by intense interfacial gradients. These structural features have received a significant amount of attention in neutrally-stratified flows, but the extent to which UMZs and corresponding uniform temperature zones (UTZs) are modified by unstable thermal stratification remains poorly understood. Using large eddy simulations of unstably stratified turbulent channel flow, we investigate the effects of buoyancy on UMZ and UTZ structure. Statistical properties of UMZs and UTZs (zone depths and interfacial velocity or temperature jumps) give rise to the scaling of the near-wall mean velocity and temperature gradients predicted by Monin-Obukhov similarity theory. Farther from wall, both UMZ and UTZ depth asymptote to a constant fraction of the outer length scale with negligible interfacial jumps, consistent with the well-mixed structure of the convective mixed layer. Conditional averaging reveals that ejections (sweeps) of momentum and warm updrafts (cool downdrafts) are prevalent below (above) UMZ and UTZ interfaces. These results demonstrate a connection between instantaneous structures, turbulence statistics, and scaling laws in these unstably stratified flows.   

Irreversible mixing in stably-stratified turbulence under momentum and scalar forcing: beyond the turbulent Froude number

Mixing coefficient (Γ) parameterizations play a key role in estimating vertical diffusivities of buoyancy (e.g., Osborn model, 1980) in general circulation models. Because of this, there has been continued interest in finding universal descriptions of Γ for stratified turbulent flows. Notably, Γ has been long studied as a function of the buoyancy Reynolds number and, more recently, as a function of the turbulent Froude number with varying degrees of success. In this study, we conducted direct numerical simulations (DNS) of stably-stratified turbulence with both momentum and scalar forcing. Momentum and scalar forcing were linear in the velocity and scalar fields, respectively. In the absence of scalar forcing, Γ from our DNS generally agrees with the turbulent Froude number scalings from Garanaik and Venayagamoorthy (2019). When scalar forcing is present, however, Γ exhibits large variations at fixed values of the turbulent Froude number, indicating that additional parameters need to be considered. We study the turbulence energetics as a function of the relative strengths of momentum and scalar forcing to the background stratification and explore other candidate parameters for collapsing Γ. We also show that Γ can be kept constant by temporally varying the momentum and scalar forcing. Taken together, these results emphasize that the mixing efficiency is strongly influenced by the specific details of the turbulence generation mechanism.   

Linear logistic regression with weight thresholding for flow regime classification of a stratified wake

A stratified wake has multiple flow regimes, and exhibits different behaviors in these regimes. We aim at automated classification of the weakly stratified and the strongly stratified turbulence flow regimes based on information available in a full Reynolds stress model. We first generate a direct numerical simulation (DNS) database covering a Reynolds number range from 10 000 to 50 000 and a Froude number range from 2 to 50. 80 to 100 independent realizations of temporal evolving simulations are computed to get converged flow statistics. These data are used for training and testing purposes. Next, we train a linear logistic regression classifier with weight thresholding for automated flow regime classification. The classifier is designed to identify the physics critical to the classification task. Trained against data at one case, the classifier is found to generalize well to other Reynolds and Froude number combinations. We come to two conclusions from the trained classifier results. First, the physics governing wake evolution is universal, and second, the classifier captures that physics. The novelty of this work lies in the new DNS database and the development of a new machine learning tool.

    

Exponential-like decay of the centerline velocity deficit and budget analysis in stratified wake

Thermal stratification and stratified flow are ubiquitous in nature. We conduct direct numerical simulations (DNSs) for temporally evolving stratified wake flows at Re=10,000 to Re=50,000 and Fr = 2 to 50, where Re is the Reynolds number and Fr is the Froude number. Unlike previous DNS studies, 80 to 100 realizations are used for ensemble average to make sure the convergence of higher order statistics. All DNSs continue until the wakes are strongly stratified. The many realizations allow us to get converged statistics and compare these statistics to the previously established scalings. Special attention is given to the decay of the centerline velocity deficit U₀. Instead of a power law decay U₀∼t^0.25,U₀∼t^0.76 in the non-equilibrium regime (NEQ) and the quasi-two-dimensional regime (Q2D) as suggested by the previous studies, our data suggests an exponential-like decay U₀∼exp(-0.008Nt) in two regimes. The budget analysis also supports a unified description of the late NEQ regime and the early Q2D regime.

    

On the Modeling of Dissipation Anisotropy, Pressure Diffusion and Coherent Structures in Stratified Wakes Using Second Moment Closure

Simulation of wake flows encountered in the environment, which are often characterized by high Reynolds and Froude numbers, requires considerable computational resources, prohibiting the use of DNS/LES. Second-Moment Closure (SMC) is suitable for such complex flows. Recent DNS studies by the authors have highlighted important inconsistencies/errors in conventional SMC^1,2,3. Specifically, we have identified the lack of suitable dissipation anisotropy and pressure diffusion modeling as critical shortcomings in these 11-equation models. This presentation summarizes our recent work to develop and validate models for these important Reynolds stress and density flux transport mechanisms. To this end, we use DNS, physical reasoning, and machine learning tools.

[1] Jain, Naman, et al. "Insights into second-moment closure modelling performance for stratified wakes from DNS ensembles." Bulletin of the American Physical Society 66 (2021)

[2] Jain, Naman, et al. "Second Moment Closure Modeling and Direct Numerical Simulation of Stratified Shear Layers." Journal of Fluids Engineering

[3] Jain, Naman, et al. "A Study of Second Moment Closure Modeling for Stratified Wakes Using DNS Ensembles." Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2022

    

Spectral analysis of the nonlinear terms in stratified wall turbulence

The quadratic nonlinearity in the Navier-Stokes equations redistributes energy across scales and plays a central role in the dynamics of wall turbulence. Introducing stable stratification can have a qualitative impact on the flow, even in the weakly stratified regime. In this work, we adapt a recent spectral analysis of the nonlinear terms that was performed for isothermal flows (Morra et al., J. Fluid Mech. (2021), vol. 907, A24) to include the influence of buoyancy. The data are obtained from direct numerical simulations of channel flow, for multiple Richardson numbers. We report the cross-spectral densities of the nonlinear terms, both in the momentum and scalar transport equations. The results are discussed with reference to the dynamics of the underlying stratified flow.