Session ZC43: Turbulence: Buoyancy-Driven and Stratified II

Towards generalization of visual anemometry using honami wave theory

Honami is a phenomenon in which wavelike motions propagate downstream along the top of homogeneous canopy fields such as cereal crops, alfalfa fields, rice fields, and grasses. These waves occur when a high momentum coherent fluid parcel, also known as a sweep, is accelerated in the streamwise direction and moves towards the canopy, bending over a group of plant stalks. The phase velocity of honami waves can be interpreted as the frozen histories of gust velocity or the convection velocity of the large eddies with which the gusts are associated. The literature to date has focused on identifying the relationship between the wave properties and mean boundary layer statistics above the canopy and concluded that honami speeds are significantly higher than the mean wind speed at the canopy height. Our research examines the ability of honami speeds to identify instantaneous flow properties and turbulent properties. We will present the relationship between gust speeds and honami phase speeds and compare the results of quadrant analysis for both the canopy and the flow. The combination of these relationships can contribute to the advancement of generalization of visual anemometry, which is the process of inferring wind conditions from visual observations of vegetation kinematics without prior knowledge of the flow or observed canopy.   

Decoupling small-scale turbulence generation from a large-scale domain in direct numerical simulations of Rayleigh-Taylor instabilities

Rayleigh-Taylor (RT) instabilities are buoyant-turbulent phenomena of immense practical value in the areas of wildfire modeling, astrophysics, and inertial confinement fusion. Unfortunately, direct numerical simulations (DNS) of the full domain of RT flow, including both reservoirs of heavy and light fluid, may be an inefficient use of computational resources when most turbulence generation is confined to small-scale eddies in the central mixing layer. To isolate these effects in a smaller domain, this study relies on a Reynolds-decomposition of the governing equations into mean and fluctuations. The fluctuations are transformed into variables verified to be spatially homogeneous by leveraging results of previous DNS of RT instabilities, allowing the use of a 3D periodic box for boundary conditions. The equations are closed by assuming the mean flow to be of a form known from previous DNS, resulting in a set of equations similar to Navier-Stokes but with a few additional source terms. These terms act to maintain the turbulent kinetic energy and mixture fraction variance, emulating the effect of the larger-domain flow without having to resolve it in a full-scale simulation. The equations are then implemented in the periodic box DNS and the resulting statistics are compared with those found in a full DNS of RT instabilities.   

Understanding the effect of Prandtl number on momentum and scalar mixing rates in neutral and stably stratified flows using gradient field dynamics

Recent DNS of stably stratified turbulence show that when increasing the Prandtl number ($Pr$) from 1 to 7, the mean turbulent potential energy dissipation rate (TPE-DR) drops dramatically, while the mean turbulent kinetic energy dissipation rate (TKE-DR) increases significantly. Through an analysis of the equations governing the fluctuating velocity gradients (FVG) and fluctuating density gradients (FDG) we provide a mechanistic explanation for this surprising behavior. We show that the mean density gradient gives rise to a mechanism that opposes the production of FDG and is connected to the emergence of ramp-cliffs. An equal but opposite term appears in the FVG equation, corresponding to the contribution from buoyancy, and this is ultimately the reason why the TPE-DR reduces while the TKE-DR increases with increasing $Pr$. Our analysis predicts that the effects of buoyancy on the FVG become stronger as $Pr$ is increased, which is confirmed by our DNS data. Due to this, the buoyancy Reynolds number does not correctly estimate the impact of buoyancy on FVG when $Pr eq 1$, and we derive a suitable alternative parameter. Finally, an analysis of the filtered gradient equations reveals that the buoyancy term acts as a source for FVG at small scales, but as a sink at large scales.   

Lagrangian irreversibility in rotating-stratified turbulent flows

In homogeneous and isotropic turbulence (HIT), two tracer particles separate faster backward than forward in time, a manifestation of the irreversibility induced by the energy flux from large to small scales. We establish that this property extends to flows of geophysical relevance, with broken isotropy. Specifically, we study turbulence in the presence of both solid body rotation (ROT, Coriolis parameter f) and stable stratification (STRAT, Brunt-Väisälä frequency N). At the fixed relative strength of ROT and STRAT N/f = 5, we perform a series of direct numerical simulations (DNS) with increasing strength of both ROT and STRAT from flows that are close to HIT to wave-dominated flows. 

We revisit the energy budget in such flows to account for the potential energy induced by stratification and extend the Karman-Howarth-Monin relations for ROTSTRAT turbulence in the Lagrangian framework. When the flow is forced mechanically, we observe a net flux from kinetic to potential energy at large scales, and surprisingly, from potential to kinetic energy at smaller scales. Finally, we discuss the implications of the flow anisotropy for the relative separation of two particles.    

Mixing efficiency in shearless, inhomogeneous, and stably stratified turbulence

Large scale simulations of the Earth’s oceans and atmosphere rely on crude parameterizations of turbulent processes using bulk quantities due to the prohibitive mesh resolution required to capture these processes directly. An interesting flow regime useful for evaluating existing models is one in which shearless turbulence, generated in a localized region of space, decays and interacts with background stratification, a scenario common in geophysical settings.

 

We propose a series of high-resolution large eddy simulations (1 – 8.5 billion mesh points) to investigate this problem with the goal of identifying limitations of popular models of the mixing efficiency and propose improvements that can handle this highly nonlinear regime. The code we will use is a high order incompressible Navier Stokes solver using a combination of pseudo-spectral and compact difference schemes. The flow is driven by a spatially localized body force which generates negligible mean flow. We have run a series of low-resolution cases (2 million mesh points) to validate the forcing method and determine the parameter space of interest which includes the energy dissipation rate, integral length scale, Reynolds number, Froude number, RMS velocities (stream- and span-wise), and turbulence kinetic energy as functions of distance from the forcing layer.   

The characteristics of the meandering effect in a stratified wake

In a stratified wake, the near-wake flow is similar to its non-stratified equivalent, and the buoyancy effect grows stronger as the flow develops downstream. The flow starts with initial vortex shedding. Then, the vertical motions get suppressed and large horizontal structures are observed in the late wake. The evolving flow structures bring in meandering behavior in the wake regime. We aim at understanding how the meandering impacts the flow behavior, especially the scaling of the deficit velocity. 

In this work, we study the meandering effect by the decomposition of the stationary behavior and the pure meandering behavior. A large direct numerical simulation (DNS) database is set up for a wide range of Reynolds numbers and Froude numbers. The meandering effect can be characterized by extracting the center location from a large number of instantaneous snapshots. We find similar horizontal expansion in the meandering of the center location as in the size expansion of flow structures. We established self-similarity theory in the stratified wake and obtain the conservation law. We find that the meandering has little effect on changing the scaling of the mean velocity, but it is one of the main reasons for possible deviation from the Gaussian assumptions.    

Assessment of subgrid-scale models in large-eddy simulations of decaying rotating stratified turbulence

We report the results of large eddy simulation (LES) using three subgrid scale models, namely: constant coefficient Smagorinsky, dynamic Smagorinsky, and a non-linear model, for rotating stratified turbulence in the absence of forcing using large-scale isotropic initial condition. The LES results are compared to in-house direct numerical simulation (DNS) for establishing grid-independence requirements. Three cases with varying ratios of Brunt-Vaisala frequency to the inertial wave frequency, $mathcal{N}/f$, have been chosen to evaluate the performance of LES models. The Reynolds number and N/f are chosen as (a) Run1: Re=3704, N/f=5, (b) Run2: Re=6667, N/f=40 and, (c) Run3: Re=6667, N/f=138. This framework is used to illustrate the relative magnitudes of the stratification and rotation which is observed in geophysical flows. Various quantities including turbulent kinetic energy (tke), turbulent potential energy (tpe), total dissipation, potential & total energy spectra, and their fluxes, are analyzed to understand the predictive capability of the various LES models. Results showed that all the SGS model predictions were very similar to each other with the classical Smagorinsky model displaying the highest deviation in comparison to DNS. The effect of an increase in value of N/f was also seen in the results of LES with an increase in the oscillation observed in the evolution of tke and tpe, and reduction in dissipation, which is exhibited by DNS. The spectral analysis shows that the non-linear and dynamic Smagorinsky models predict the large-scale physics ($kappa < 10$), while the small scales (10< κ< 64) energy is under-predicted.    

Linear and nonlinear effects in stably stratified turbulent channel flow

Even small levels of stable stratification significantly alter the dynamics of wall-bounded turbulent flows. The observed changes are due to (i) modifications to the linear dynamics and (ii) spectral and wall-normal redistribution of energy in the nonlinear terms. This work examines the two from an input-output perspective, at moderate Reynolds number. The linear dynamics are described by the resolvent operator where the effect of stratification is represented by changes in the forcing-response relation, due to the modified mean flow profiles and bulk Richardson number. As for the nonlinear terms, their statistics are computed from direct numerical simulations, and contrasted for the isothermal and weakly-stratified cases. Numerical experiments where we modify the resolvent operator and the nonlinear forcing in isolation differentiate the contributions of the linear and nonlinear effects. The analysis draws attention to the channel center where the influence of stratification is most evident.