Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session M29: Turbulence: Stratification & BuoyancyConvection Turbulence
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Chair: James Riley, University of Washington Room: 205 |
Tuesday, November 21, 2017 8:00AM - 8:13AM |
M29.00001: Anisotropy in Direct Numerical Simulations of Homogeneous Stratified Turbulence Jeremy Melvin, Robert D. Moser One of the main characteristics of stratified turbulence is the presence of anisotropy. We conduct a series of Direct Numerical Simulations (DNS) of both stable and unstable homogeneous stratified turbulence and investigate the characteristics of anisotropy in length scales and other turbulent statistics. We compare the observed quantities to derived scaling relationships based on the Froude number. Lastly, we discuss the impact of anisotropy on the development of applicable LES models for wind farm simulations. [Preview Abstract] |
Tuesday, November 21, 2017 8:13AM - 8:26AM |
M29.00002: The effect of stable stratification on initially homogeneous, isotripic turbulence James J. Riley, Stephen M. de Bruyn Kops We report on very high resolution direct numerical simulations of the decay of initially isotropic turbulence in a stably-stratified environment. Simulations were carried out at a fixed, low Froude number, but for a range of Reynolds numbers such that, for the high Reynolds number cases, the flows had buoyancy Reynolds numbers in the hundreds, similar to typical oceanic values. A number of aspects of the flows have been studied, including their energetics, the behavior of various length scales describing the flows, their mixing characteristics, and their spectral behavior. It is found, for example, that, as the flows decay, stratification modifies them such that, compared to non-stratified cases, the energy decay rates decreased, the growth rate of the horizontal scales increased, while the growth rates of the vertical scales became negative. These results are consistent with the analysis of Davidson ({\em J.\ Fluid Mech.}, 2010), based upon the behavior of the effects of density stratification on the large-scale motions. It is also found, for example, that the behavior of the spectra of the velocity gradient tensor is consistent with the heuristic arguments of Lilly ({\em J.\ Atmos.\ Sci.}, 1983) and the scaling arguments of Billant \& Chomaz ({\em Phys.\ Fluids}, 2001). [Preview Abstract] |
Tuesday, November 21, 2017 8:26AM - 8:39AM |
M29.00003: Volume Scaling of Intense Mixing Regions in Homogeneous Stratified Turbulence Gavin Portwood, Stephen de Bruyn Kops The spontaneous generation of localized turbulent patches or bursts in otherwise homogeneous flow is a widely accepted characteristic of stratified turbulence and can occur through many mechanisms. Here, we address this spacio-temporal variability in homogeneously forced stationary turbulence across a broad Fr-Re parameter space as realized through pseudo-spectral DNS of Boussinesq turbulence. Using a conditional averaging scheme based on local density gradient inversions, a domain is objectively subdivided into `quiescent regions', `intermittent layers' and `turbulent patches'. We observe that these regions may be characterized by an appropriate locally averaged $\mathrm{Gn} \equiv \epsilon / \nu N^2$ in that they exhibit $\mathrm{Gn} \sim O(1)$, $\mathrm{Gn} \sim O(10)$, and $\mathrm{Gn} \sim O(100)$, respectively. We show that even at nominal bulk $\mathrm{Gn}$, the majority of mixing is confined to small and intense turbulence patches. The volume of these patches scales with the bulk $\mathrm{Gn}^{1/2}$. [Preview Abstract] |
Tuesday, November 21, 2017 8:39AM - 8:52AM |
M29.00004: Characteristics of the Residual Stress tensor when filter width is larger than the Ozmidov scale. Felipe Augusto de Bragança Alves, Stephen de Bruyn Kops In stratified turbulence, the residual stress tensor is statistically anisotropic unless the smallest resolved length scale is smaller than the Ozmidov scale and the buoyancy Reynolds number is sufficiently high for there to exist a range of scales that is statistically isotropic. We present approximations to the residual stress tensor that are derived analytically. These approximations are evaluated by filtering data from direct numerical simulations of homogeneous stratified turbulence, with unity Prandtl number, resolved on up to $8192 \times 8192 \times 4096$ grid points along with an isotropic homogeneous case resolved on $8192^3$ grid points. It is found that the best possible scaling of the strain rate tensor yields a residual stress tensor (RST) that is less well statistically aligned with the exact RST than a randomly generated tensor. It is also found that, while a scaling of the strain rate tensor can dissipate the right amount of energy, it produces incorrect anisotropic dissipation, removing energy from the wrong components of the velocity vector. We find that a combination of the strain rate tensor and a tensor related to energy redistribution caused by a Newtonian fluid viscous stress yields an excellent tensorial basis for modelling the RST. [Preview Abstract] |
Tuesday, November 21, 2017 8:52AM - 9:05AM |
M29.00005: Inclined vortex rings interacting with a density interface Benjamin Jackson, Stuart Dalziel The interaction between a vortex ring and a density interface is a canonical problem for studying turbulence in stratified environments. Localised coherent structures containing highly vortical motion are often associated with turbulence. Vortex rings provide a simple analogy for such structures to study small scale mixing processes, allowing insight into energy transfers within the turbulence and entrainment across the interface. Since Linden's introduction of the problem over 40 years ago, most studies have been restricted to the case of vortex rings propagating normal to a density interface. Recently, Olsthoorn and Dalziel showed the development of symmetry-breaking instabilities during such an interaction are of critical importance to the resultant mixing. Here we consider the problem of vortex rings impinging at other angles. We present key results on how breaking the axisymmetry of the problem impacts the dynamics of the interaction and the mixing that ensues. [Preview Abstract] |
Tuesday, November 21, 2017 9:05AM - 9:18AM |
M29.00006: Self-similar mixing in stratified plane Couette flow for varying Prandtl number C. P. Caulfield, Qi Zhou, John Taylor We investigate fully developed turbulence in statically stable stratified plane Couette flows (the flow between two horizontal plates a distance $2h$ apart moving at velocities $\pm U_0$ and held at densities $\rho_a \mp \rho_0$) using direct numerical simulations at a range of Prandtl numbers $Pr \equiv \nu/\kappa \in \{0.7,7,70\}$ and Reynolds numbers $Re\equiv U_0 h/\nu \in [865,280000]$. We observe significant effects of $Pr$ on the heat and momentum fluxes across the channel gap and on the mean temperature and velocity profile, which can be described through a mixing length model using Monin-Obukhov (M-O) similarity theory. We employ M-O theory to formulate similarity scalings for various flow diagnostics in the gap interior. The mid-channel-gap gradient Richardson number $Ri_g$ is determined by the length scale ratio $h/L$, where $L$ is the Obukhov length scale. When $h/L \gg 1$, $Ri_g$ asymptotes to a maximum characteristic value of approximately 0.2, for very high $Re$ and for a range of $Pr$ and bulk Richardson number $Ri=g \rho_0 h/(\rho_a U_0^2)$. The flux Richardson number $Ri_f \simeq Ri_g$, implying that such turbulent flows do not access the (strongly) `layered anisotropic stratified turbulence' regime, and that the turbulent Prandtl number is approximately one. [Preview Abstract] |
Tuesday, November 21, 2017 9:18AM - 9:31AM |
M29.00007: Stably-stratified wall-bounded turbulence Pejman Hadi Sichani, Francesco Zonta, Aleksandr Obabko, Alfredo Soldati Stably-stratified (bottom-up cooling) turbulent flows are encountered in a number of industrial applications, environmental processes and geophysical flows. Turbulent entrainment and mixing across density interfaces in terrestrial water bodies (oceans, lakes and rivers) and in industrial heat transfer equipments are just some important examples of stably-stratified flows. In this work we use Direct Numerical Simulation to investigate the fundamental physics of stably-stratified channel turbulence under Boussinesq and Non-Oberbeck-Boussinesq (NOB) conditions. Compared to the neutrally-buoyant case, in the stably-stratified case active turbulence survives only in the near-wall region and coexists with internal gravity waves (IGW) moving in the core region of the channel. This induces a general suppression of turbulence levels, momentum and buoyancy fluxes. Our results show also that NOB effects may be important when the flow is subject to large temperature gradients. The most striking feature observed in case of NOB conditions is the generation of a strong flow asymmetry with possible local flow laminarization in the near wall region. [Preview Abstract] |
Tuesday, November 21, 2017 9:31AM - 9:44AM |
M29.00008: Density-ratio effects on buoyancy-driven variable-density turbulent mixing Denis Aslangil, Daniel Livescu, Arindam Banerjee Density-ratio effects on the turbulent mixing of two incompressible, miscible fluids with different densities subject to constant acceleration are studied by means of high-resolution Direct Numerical Simulations. In a triply periodic domain, turbulence is generated by stirring in response to the differential buoyancy forces within the flow. Later, as the fluids become molecularly mixed, dissipation starts to overcome turbulence generation by bouyancy. Thus, the flow evolution includes both turbulence growth and decay, and it displays features present in the core region of the mixing layer of the Rayleigh-Taylor as well as Richtmyer-Meshkov instabilities. We extend the previous studies by investigating a broad range of density-ratio, from 1-14.4:1, corresponding to Atwood numbers of 0.05-0.87. Here, we focus on the Atwood number dependence of mixing-efficiency, that is defined based on the energy-conversion ratios from potential energy to total and turbulent kinetic energies, the decay characteristics of buoyancy-assisted variable-density homogeneous turbulence, and the effects of high density-ratios on the turbulence structure and mixing process. [Preview Abstract] |
Tuesday, November 21, 2017 9:44AM - 9:57AM |
M29.00009: Two-point spectral model for variable density homogeneous turbulence Nairita Pal, Susan Kurien, Timothy Clark, Denis Aslangil, Daniel Livescu We present a comparison between a two-point spectral closure model for buoyancy-driven variable density homogeneous turbulence, with Direct Numerical Simulation (DNS) data of the same system. We wish to understand how well a suitable spectral model might capture variable density effects and the transition to turbulence from an initially quiescent state. Following the BHRZ model developed by Besnard et. al (1990), the spectral model calculation computes the time evolution of two-point correlations of the density fluctuations with the momentum and the specific-volume. These spatial correlations are expressed as function of wavenumber $k$ and denoted by ${\bf{a}}(k)$ and $b(k)$, quantifying mass flux and turbulent mixing respectively. We assess the accuracy of the model, relative to a full DNS of the complete hydrodynamical equations, using ${\bf{a}}$ and $b$ as metrics. [Preview Abstract] |
Tuesday, November 21, 2017 9:57AM - 10:10AM |
M29.00010: Upper bounds on the heat flux in 2D Rayleigh-Bénard convection using a 2D background field method Zijing Ding, Rich Kerswell The background method [1] has proved a popular and effective technique for estimating the maximal heat flux possible in turbulent Rayleigh-Benard convection. In this method, the temperature is non-uniquely decomposed into a background field which satisfies the physical boundary conditions and a fluctuation field satisfying homogenous boundary conditions. So far, only a 1D background field (just varying with the wall normal direction) has been studied which has the effect of only imposing the horizontal average of the heat equation as a constraint [2]. Here we consider a 2D background field, which imposes the full heat equation, to bound the heat flux in 2D Rayleigh-Benard convection. The results of applying a time-stepping method, which has recently proved successful for the 1D background field case [3], to the extended variational problem will be discussed. References [1] C. R. Doering {\&} P. Constantin, Phys. Rev. Lett., \textbf{69}, 1648-1651, (1992) [2] C. R. Doering {\&} P. Constantin, Phys. Rev. E, \textbf{53}, 5957-5981 (1996) [3] B. Wen, G.P. Chini, R.R. Kerswell and C.R. Doering, Phys. Rev. E. \textbf{92 }043012 (2015) [Preview Abstract] |
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