Session T22: Turbulence: Buoyancy-driven Flows, Stratification, Rotation and Magnetic Fields

Reynolds and Richardson Number Dependence of Near-Field Flow Behavior for Axisymmetric Buoyant Jets and Plumes

The large-scale structures that form in the near-field of axisymmetric buoyant jets and plumes play an important role in the entrainment and mixing properties of the flow. As such, characterizing the dynamics of these structures is essential to building reduced-order models (ROMs) that accurately capture these dynamics without resolving the broad range of scales that occur in the flow. With accurate ROMs, we will be able to better predict flow properties and optimize flow configurations. In order to do this, here we conduct high-resolution numerical simulations using adaptive mesh refinement of axisymmetric non-reacting helium jets and plumes spanning different Richardson (Ri) and Reynolds (Re) numbers. We first review the flow kinematics, showing that, as the flow becomes more turbulent via increases in Ri and Re, the ambient fluid penetrates further into the core of the flow, ultimately with sufficient strength to form a mean recirculation zone just above the inlet. We then explore the dynamics through the mean and turbulent kinetic energy transport equations, which allows us to probe the dynamical causes of the production, transport, and removal of kinetic energy. The balance between budget terms is compared for each simulation and examined for different Ri and Re.   

Vortical structures in turbulent buoynat plumes

Turbulent buoyant plumes are an important phenomenon

to energy transfer and scalar transport

in natural and engineering systems.

We study the statistical stationary state of turbulent fluctuations

in buoyant plumes

using large eddy simulations.

The plume is generated from a heat source

and sustained by buoyancy and entrainment.

Scaling laws are proposed

for various turbulent properties

evolving across the plume.

Budget analysis identifies the leading mechanisms

for the transport of those turbulent properties.

Furthermore,

the probability distribution function

reveals some other details regarding

the characteristics of vorticity.

Near the source,

vorticity is mainly aligned with transverse direction

and return-to isotropy is observed downstream.

Within the plume,

the competition of strain and rotation is compared

and the corresponding alignment of vorticity is analyzed.

Finally,

based on the change of the plume characteristics,

plume structure is categorized into different regions.   

Measures for Defining the Turbulent/non-Turbulent Interface of a Steady Round Plume: A DNS Study

Free shear flows such as plumes and jets are characterized by a turbulent/non-turbulent interface (TNTI) which forms a part of the convoluted thin boundary that separates the turbulent flow from the irrotational ambient. Existing literature delineates several methods to identify the TNTI in such types of flows. We performed direct numerical simulation (DNS) of a turbulent plume at a Reynolds number (defined using base scales) of 2000 to show that additional insightful measures can be used to determine the TNTI. A code named Megha 3, used for the simulation, solves the Boussinesq approximation of the three-dimensional continuity and Navier-Stokes equations. We identify the TNTI using independent thresholds on three different variations of the vorticity field, including scaled vorticity and the impact of strain field on the vorticity. Each one of such measures is not merely a number. Instead, they seem to capture subtle differences in the flow field, which can be used to capture the turbulent nature of the flow more accurately. For example, the scaling based on self-similarity seems to reflect some aspects of coherent structures present in the flow. In contrast, the scaling based on time-averaged geometric and kinematic quantities makes the TNTI well-defined at all vertical levels.   

Mechanisms of Buoyancy-Modified Entrainment in Plumes: Theoretical Analysis

We present a theoretical analysis, based on the self-similar velocity and buoyancy profiles for plumes in the far field region, to show how buoyancy dually shapes the flow behavior. In particular, we show that while buoyancy flux makes a positive contribution to mean kinetic energy flux, buoyancy also enhances the mean velocity gradients so that the loss of mean kinetic energy to turbulent kinetic energy is amplified. The ability of buoyancy to increase the separation between the large and small length scales of the flow is discussed in terms of its impact on the evolutionary dynamics of the flow structures. It is also shown, as a result of the scaling laws that follow from the analysis, that the ability of buoyancy to strengthen the eddy vorticity in plumes is primarily through its leading order effect of enhancing the mean velocity gradients, and less so through its lower order contributions to the baroclinic component of torque. We then provide a perspective on how the small-scale nibbling contribution to the entrainment process is affected by such buoyancy-induced modifications to the mean flow. Finally, we juxtapose key takeaways from the analysis with the contemporary view provided by the literature on the entrainment process to propose a mechanistic picture of buoyancy-modified entrainment in plumes.   

Effect of Roughness on Entrainment of Turbulent Buoyant Flows

Interaction of heavy density fluid with a buoyant, ambient environment results in the formation of bottom-propagating 3D turbulent density current. A large-eddy simulation (LES) is performed for lock-exchange release density currents over rough walls to better understand the effect of roughness on turbulent density currents. A finite volume method is implemented to solve Navier-Stokes equations using Boussinesq approximations. A special case of the immersed-boundary method called volume-penalization is performed to comprehend the bottom-mounted rough topology. The effect of regular and irregular roughness shapes is investigated for cubical and cylindrical roughness elements.  The effect of Reynold’s number, frictional Reynolds number, and Froude’s number on the entrainment coefficient has been studied to provide a universal framework on the effect of roughness in entrainment.   

Buoyancy-Driven Homogeneous Turbulence Under Sharp Acceleration Changes

The effects of sharp acceleration changes on variable-density mixing are investigated using direct numerical simulations of buoyancy-driven homogeneous variable-density turbulence (HVDT). Such sharp changes, including acceleration reversal or a total removal of the acceleration field, occur in the high-energy-density applications such as inertial confinement fusion, blast waves, and astrophysical flows. HVDT is known to mimic the core regions of the mixing layers produced by the acceleration-driven Rayleigh-Taylor and the shock-driven Richtmyer-Meshkov instabilities by isolating the problem from edge effects. In this study, we explore the effects of acceleration switches on variable-density mixing in HVDT.  The flow contains unique coupled transitory effects between the turbulent mixing and turbulence intensity which arise due to the sharp acceleration switches. These effects will be discussed in detail benefiting from the joint probability density functions (jPDF) of the density and momentum fields. Finally, the short- and long-term similarities between the effects of acceleration reversal on the Rayleigh-Taylor instability and HVDT will be discussed.   

Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence

The budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales in sheared, stably stratified turbulence (SSST) are analyzed using a filtering approach together with data from direct numerical simulations. Fluctuations of the flow about the mean-field state are shown to be strong, and at larger scales, buoyancy is almost never observed to be positive, such that buoyancy always acts to convert TKE to TPE at these scales. As the filter length is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. Recent analytical results are used to investigate the physical mechanisms governing the TKE and TPE fluxes between scales. These TKE and TPE fluxes exhibit large fluctuations about their mean values and are positively correlated, but weakly so, and this is shown to be due to the fact that fundamentally different physical mechanisms govern the two fluxes. Moreover, the contribution to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain-rate self-amplification, vortex stretching, and density gradient amplification by the strain-rate field.    

Scaling of Turbulent Viscosity and Resistivity: Extracting a Scale-dependent Turbulent Magnetic Prandtl Number

Turbulent viscosity μ_t and resistivity η_t are perhaps the simplest models for turbulent transport of angular momentum and magnetic fields, respectively. The associated turbulent magnetic Prandtl number Pr_t = μ_t/η_t has been well recognized to determine the final magnetic configuration of accretion disks. Here, we present an approach to determining these "effective transport" coefficients acting at different length-scales using coarse-graining and recent results on decoupled kinetic and magnetic energy cascades. By analyzing the kinetic and magnetic energy cascades from a suite of high-resolution simulations, we show that our definitions of μ_t, η_t, Pr_t  have power-law scalings in the "decoupled range." We observe that Pr_t ≈1 to 2 at the smallest inertial-inductive scales, increasing to ≈5 at the largest scales. However, based on physical considerations, our analysis suggests that Pr_t has to become scale-independent and of order unity in the decoupled range at sufficiently high Reynolds numbers (or grid-resolution), and that the power-law scaling exponents of velocity and magnetic spectra become equal. In addition to implications to astrophysical systems, the scale-dependent turbulent transport coefficients offer a guide for large eddy simulation modeling.   

Effect of plasmoid instability on energy spectra at high magnetic Reynolds number 3D-magnetohydrodynamic turbulence using large eddy simulation

Plasmoid instability in evolving current sheets has been studied in the past using 2D magnetohydrodynamic (MHD) simulations. The combined effect of reconnection and thin current sheets at the point of maximum current density during the evolution of flow, at large magnetic Reynolds number (Re_m), is favorable for the formation of plasmoid leading to disruption of current sheets. This causes emergence of plasmoid-mediated regime within the inertial sub-range with a slope steeper than -3/2. Previously conducted direct numerical simulations (DNS) show a slope of -2 in the inertial sub-range at small scales for Re_m ≅ 9200. To analyze plasmoid effects on the properties of three-dimensional (3D) flow, simulations at Re_m of Ο(10⁴) or higher need to be performed. Since high-Re_m DNS is limited by computational resources required to carry out the simulation, numerical analysis of incompressible decaying MHD turbulence at high Reynolds number using LES is a feasible alternative. The current study uses LES to analyze 3D high Re_m MHD turbulent flow at Re_m of 10⁴. The grid resolution in LES is such that the inertial subrange is resolved completely, so that the effect of plasmoid instability on the energy cascade and energy spectra at high Reynolds number can be demonstrated.   

Comparison between time-evolution of centroids and local-flux vectors flor localized initial conditions in wavenumber space

Although energy flux in the wavenumber space (k space) is the most fundamental problem in turbulence analyses, no identification method of it in anisotropic turbulence has been established due to its vectorial property. We have proposed a simple method to determine local-flux vectors of inviscid invariants and applied it to various turbulent fields[1][2]. The results were consistent with previous studies. Nazarenko and Quinn [3] examined triple cascade in Charney-Hasegawa-Mima (CHM) turbulence, where an additional positive quadratic invarinant called zonostrphy exists together with the energy and the enstrophy. They performed direct numerical simulations (DNSs) started from the initial condition localized in the k space and also applied a generalized FjΦrtoft argument to predict k-space paths of the three invariants. They inferred the cascade of the invariants from the time-evolution of their centroids in the k space owing to its analogy to the motions of the masses of the invariants, though its relation to the cascade in turbulence, where their spectra are continuously distributed in the whole k space, is not clear. It should be noted that the difference among the motions of invariants comes from the distribution of the spectra even in their simulations.

Our proposed method can be applied to such initial-value problem and directly compared with their results, which may access the adequacy of the proposed method. We performed DNSs of CHM equation with similar localized initial conditions. The results are consistent with those by Nazarenko and Quinn [3]. Since high-wavenumber modes are excited rapidly and the smoothness of the field is lost in inviscid DNSs, the importance of (hyper-)viscosity will be discussed.

¹ N.Yokoyama and M.Takaoka, J.Fluid Mech.908(2021)A17

² M.Takaoka, N.Yokoyama, and E.Sasaki, submitted to Phys.Rev.Fluid

³ S.Nazarenko and B.Quinn, Phys.Rev.Lett.103(2009)118501