14:00
Stratified Flows 4
14:00
15 mins
#476
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Wall-bounded stably stratified turbulence at large Reynolds number
Francesco Zonta, Pejman Hadi Sichani, Alfredo Soldati
Abstract: Wall-bounded stably stratified turbulent flows are a common occurrence in many industrial and natural processes. Examples include cooling in nuclear reactors, fuel injection and combustion in gasoline engines, the dynamics of the nocturnal atmospheric boundary layer or the transport of organic species in the ocean.
In this work, we focus on stably stratified turbulent channel flow at high shear Reynolds number $Re_{\tau}$. We performed an extensive campaign of pseudo-spectral direct numerical simulations (DNS) of the governing equations (momentum and energy equations written under the OB approximation) in the shear Richardson number space $Ri_{\tau}=Gr/Re^2_{\tau}$, where $Gr$ is the Grashof number. In particular, we fix the Reynolds number $Re_{\tau}=1000$ and we change $Gr$ so to cover a broad range of $Ri_{\tau}$ values.
We recall that $Re_{\tau}$ is the ratio between inertia and viscous forces, whereas $Ri_{\tau}$ is the ratio between buoyancy and inertia forces.
Our results of stratified turbulence indicate that the average and turbulent fields undergo significant variations compared to the case of forced convection, in which temperature is a passive scalar ($Ri_{\tau}=0$). We observe that turbulence is actively sustained only near the boundaries, whereas intermittent turbulence, also flavored by the presence of non-turbulent wavy structures (Internal Gravity Waves, IGW) is observed at the core of the channel.
This situation is clearly visible in Fig.~1, where temperature contours are used to visualized the flow structures on a $(x-z)$ streamwise section for the case $Ri_{\tau}=0$ (top panel) and $Ri_{\tau}=25$ (bottom panel). The flow goes from left to right and is bounded at the bottom and top wall. Internal waves are found in a narrow region around the channel centerline (Fig.~1, bottom panel) and constitute a sort of a thick interface (thermocline) that separates the channel into two parts, a top and a bottom one, which are almost independent and interact only slightly.
Naturally, this alters also the overall transfer rates of momentum and heat, as well as the mixing efficiency of the flow. We believe that the present results may give important contributions to future turbulence parametrization and modeling in this field.
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14:15
15 mins
#629
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Fractal neutral curves in stably-stratified shear flows
Jonathan Healey
Abstract: See uploaded file.
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14:30
15 mins
#219
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Transition and layering in Plane Couette flow with spanwise stratification
Dan Lucas, C.P. Caulfield, Rich Kerswell
Abstract: In this paper we investigate the effect of stable stratification on plane Couette flow when gravity is oriented in the spanwise direction. When the flow is turbulent we observe near-wall layering and associated new mean flows in the form of large scale spanwise-flattened streamwise rolls. The layers exhibit the expected buoyancy scaling $l_z\sim U/N$ where $U$ is a typical horizontal velocity scale and $N$ the buoyancy frequency. We associate the new coherent structures with a stratified modification of the well-known large scale secondary circulation in plane Couette flow. We find that the possibility of the transition to sustained turbulence is controlled by the relative size of this buoyancy scale to the spanwise spacing of the streaks. The transition to turbulence is further complicated by the newly discovered linear instability in this system (Facchini et. al. 2018 {J. Fluid Mech.} vol. 853, pp. 205-234). When wall-turbulence can be sustained the linear instability opens up new routes in phase space for infinitesimal disturbances to initiate turbulence. When the buoyancy scale supresses turbulence the linear instability leads to more ordered nonlinear states, with the possibility for intermittent bursts of secondary shear instability.
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14:45
15 mins
#140
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Controlling the secondary flow in turbulent Taylor--Couette turbulence through spanwise-varying roughness
Pieter Berghout, Dennis Bakhuis, Rodrigo Ezeta, Pim Bullee, Daniel Chung, Roberto Verzicco, Detlef Lohse, Sander Huisman, Chao Sun
Abstract: Highly turbulent Taylor--Couette flow with spanwise-varying roughness is investigated experimentally and numerically to determine the effects of the axial width $\tilde{s}$ of the roughness stripes on the total drag and on the local flow structures. We apply sandgrain roughness, in the form of alternating rough and smooth bands to the inner cylinder. Numerically, the Taylor number is $\mathcal{O}(10^9)$ and the roughness width is varied with $0.47\leq \tilde{s}=s/d \leq 1.24$, where $d$ is the gap width. Experimentally, we explore $\text{Ta}=\mathcal{O}(10^{12})$ and $0.61\leq \tilde s \leq 3.74$. For both approaches the radius ratio is fixed at $\eta = 0.716$. We present how global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacing $\tilde{s}$. Both numerically and experimentally, we find a maximum in the angular momentum transport when $\tilde{s}$ is varied, and we show that this is due to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, which yields turbulent vortices with varying axial wavelengths.
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15:00
15 mins
#264
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Simulating neutrally and stably stratified turbulent Ekman flows with a stochastic turbulence model
Marten Klein, Heiko Schmidt
Abstract: See attached file for the abstract.
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15:15
15 mins
#541
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Identification and parametrisation of spontaneous Kelvin-Helmholtz instabilities in stratified turbulence via convolutional neural networks
Gavin Portwood, Juan Saenz, Stephen de Bruyn Kops
Abstract: When a flow is subjected to a stabilizing density gradient, it tends to self-organize into horizontal layers with thickness such that the layers are continually susceptible to instability via spontaneous Kelvin-Helmholtz (K-H) and other shear mechanisms [1, 3]. As a consequence, understanding the prevalence of spontaneous K-H instabilities, in particular those that transition to turbulence, is central to understanding turbulence and mixing in the deep ocean, stratosphere, and portions of the atmospheric boundary layer [5]. In order to develop predictive models for stratified turbulence, it is essential to
parametrize K-H instabilities in terms of non-dimensional flow parameters. Fortunately, the K-H mechanism triggers characteristic billows that are good candidates for automated and robust detection, which encourages the thought that machine learning can be vastly superior to human observation for the quantification and parametrization of this important turbulence production mechanism.
Here we use convolutional neural networks (CNNs) to identify localized K-H billows in direct numerical simulations of stratified turbulence. By identifying local regions in the flow that are subject to these shear instabilities, we perform conditional averages in order to dynamically assess their influence in the broader flow. We then characterize them both in terms of classical non-dimensional parameters and as emerges to be relevant and distinguishing by analysis of a trained CNN model. CNNs have emerged as a robust approach for object detection and classification due to their ability to learn
complex spatial relationships in image processing, relationships which can be exposed by model analysis to improve our understanding these instabilities. Our approach is to train classification networks on perturbed K-H simulations then apply them to detect spontaneous K-H in homogeneous flows at many scales in a quasi-supervised way.
Using this methodology, decaying stratified turbulence is considered with direct numerical simulation then analysed. Most fundamentally, we confirm scaling analysis, as shown in figure 1 with homogeneous stratified sheared turbulence, which suggests that K-H billows cannot develop spontaneously when Reb = U^3/(Lhnu N^2) < O(1), where nu is the kinematic viscosity, N is the buoyancy frequency and Uh, Lh are the horizontal velocity and integral length scales, respectively [2]. In flows subject to mean shear (c.f. [4]), we show (1) that shear instabilities develop even which subject to gradient Richardson numbers greater than the Miles-Howard criterion, (2) note an apparent Richardson number trend in the transitional Reb value, and (3) present conditional statistics which parametrise the spontaneous billows.
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15:30
15 mins
#197
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Filter Approach for Variable Density Flows
Robert Ecke
Abstract: Variable density flows occur in physical systems including stably-stratified shear flows associated with oceanic overflows and in jets of one density fluid into another as in volcanic eruptions. An analysis approach for such systems is related to the simulation method known as Large Eddy Simulation (LES): by applying a spatial filter to a turbulent field such as velocity, one can divide up the flow into large and small scale components that pass, for example, energy between scales [1]. Eyink [2] used this formalism to analyze turbulent flow by measuring the coupling terms in highly resolved DNS or similar experiments. One application of this approach was in two-dimensional experimental turbulent flows [3]. The scale decomposition has also been applied to compressible flows that include large density variations [4]. We present the application of the filtering approach to variable-density flows, taking two example systems. The first is an experiment on stably-stratified shear flow [5] where a Boussinesq approximation is adequate. In the second experiment, there are order one variations in density for a buoyant jet of SF6 into co-flowing air [6].
For the stably-stratified shear flow [5], the velocity field is characterized by the Navier-Stokes (NS) equation in the Boussinesq approximation with an additional advection equation for the density difference. After filtering the NS equation, a filtered equation for the energy: \partial_t |\overbar \u_\ell|^2 + \nabla \cdot {\bf J}_\ell = - \pi_\ell + ... where energy flux is \pi and transport terms are \nabla•J_\ell (additional terms are not included). In Figs. 1a,b we show, respectively, an instantaneous density field (heavier fluid on bottom) and the corresponding energy flux field.
For flows with order-one density variations [6], one needs, for example, Favre averaging (indicated by ~ over quantity) for the velocity. One then has an equation of the form: \partial_t {\overbar \rho}_\ell {|{\tilde u}_\ell|^2 + \nabla \cdot {\bf J}_\ell = - \pi_\ell + D_\ell + ... where transport and flux have different specific definitions [4] but reflect similar processes as for the Boussinesq flow. In Fig. (2), we show mean quantities and energy flux and dissipation fields.
References
[1] M. Germano, Turbulence-The filtering approach, J. Fluid Mech. 238, 325 (1992).
[2] G. Eyink, Local energy flux and the refined similarity hypothesis, J. Stat. Phys. 78, 335 (1995).
[3] M.K. Rivera, H. Aluie, and R.E. Ecke, The direct enstrophy cascade of two-dimensional soap film flows, Phys. Fluids 26, 055105 (2014).
[4] H. Aluie, Scale decomposition in compressible turbulence, Physica D 247, 54 (2013).
[5] P. Odier and R.E. Ecke, Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow, J. Fluid Mech. 815, 243 (2017).
[6] J.J. Charonko and K. Prestridge, Variable-density mixing in turbulent jets with coflow, J. Fluid Mech. 825, 887 (2017).
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