Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L4: Stratified Boundary Layers |
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Chair: John R. Taylor, University of Cambridge Room: 103 |
Monday, November 23, 2015 4:05PM - 4:18PM |
L4.00001: Spots and stripes: Isolating the building blocks of intermittent stratified turbulence in plane Couette flow John Taylor, Enrico Deusebio We will describe results from direct numerical simulations (DNS) of stratified plane Couette flow, which we use to explore the boundary between laminar and turbulent flows in a stratified fluid. The flow is described by three nondimensional parameters, the Reynolds (Re), Richardson (Ri), and Prandtl (Pr) numbers. For moderate values of Re and Ri laminar and turbulent flows can co-exist in a spatio-temporally intermittent flow. In large computational domains, laminar and turbulent regions spontaneously form stripes, reminiscent of those seen in transitional unstratified Couette flow at lower Re. We will present two sets of numerical experiments. The first set start with a fully developed stratified turbulent state, and abruptly increase Ri. The flow re-laminarizes for sufficiently large increases in Ri, although turbulent production persists throughout the decay phase. Using insights gained from the decay simulations, a new control scheme is devised, whereby Ri is adjusted based on the rate of change in TKE. Using this strategy, we have isolated localized turbulent spots in stratified turbulence. These newly found flow states lie near the boundary separating laminar and intermittent turbulence and may help describe generic features of stratified turbulence. [Preview Abstract] |
Monday, November 23, 2015 4:18PM - 4:31PM |
L4.00002: Coupling of Interfacial Mixing Events in Stratified Taylor--Couette Flow Jamie Partridge, Anne-Claire Le Bihan, C. P. Caulfield, Stuart Dalziel, Pierre Augier We examine experimentally the coupling of mixing events that occur in stratified Taylor--Couette flow. It has previously been observed that in a density-stratified Taylor--Couette flow consisting of two homogeneous layers there is a periodic mixing event that occurs on the interface separating the two layers. Additionally, if the fluid in the annulus is initially linearly stratified, layers spontaneously form, and an apparently similar quasi-periodic mixing event appears on each of the interfaces. By tracking the mixing event around the annulus we show that the mixing event is not temporally intermittent but is continuously advected around the annulus. Moreover, we demonstrate that the mixing events on adjacent interfaces can couple and become phase locked with an almost constant phase shift between events on each interface. We investigate how robust this coupling is and how it depends on the initial conditions and time evolution of the flow. [Preview Abstract] |
Monday, November 23, 2015 4:31PM - 4:44PM |
L4.00003: Instability onset of the boundary layer on a rotating cylinder in a stratified fluid Jan-Bert Flor, Lionel Hirschberg, Bart Oostenrijk, GertJan van Heijst We consider the instability of the laminar shear layer on a circular cylinder that is impulsively set into rotation about its vertical axis with angular speed $\Omega $. The outer wall of this large gap Taylor-Couette flow is at a radial distance of about 10 times the inner cylinder radius, and the gap is either filled with a homogeneous or linearly stratified fluid. In a homogeneous fluid, the thickness of the boundary layer on the cylinder, d, grows until it becomes centrifugally unstable with a wavelength that is determined by the boundary layer thickness d. In a linearly stratified fluid with stratification N, the flow instability is set by the Froude number F$=\Omega $/N. For F\textgreater 1 the onset of the centrifugal instability is well predicted by the Taylor-G\"{o}rtler number and theory for homogenous fluids. When F$\le $1, the onset of the instability is for a relatively higher Reynolds number, and bifurcates from a vortex regime to a wave regime with a pure inertial wave in the boundary layer. The mechanism of instability is determined by parametric resonance and the generation of waves with subharmonic frequencies typical for Parametric Subharmonic Instability. The results are discussed in view of former results on stratified TC flow. [Preview Abstract] |
Monday, November 23, 2015 4:44PM - 4:57PM |
L4.00004: DNS of stably stratified Ekman flow with surface cooling S. M. Iman Gohari, Sutanu Sarkar Direct numerical simulations of stably stratified Ekman flow are performed to study turbulence in an atmospheric boundary layer under surface cooling. Stability, classified by the normalized Monin-Obukhov (MO) length scale, is varied by imposing a range of cooling fluxes at the surface to mimic ground radiative cooling. The subsequent flow stability, measured by the MO length scale and bulk Richardson number, changes significantly as the flow evolves. We find considerable qualitative differences when a neutrally stratified Ekman flow is exposed to a constant surface cooling rather than a constant temperature, i.e. changes in the veering angle, super-gesotrophic velocity, surface shear velocity and the boundary layer height. Under strongly stable condition, the transient evolution shows the presence of intermittent turbulent patches. These patches contain small-scale, inclined hairpin structures that are organized into near-surface streaks. A low-level jet forms at steady state and the high-shear region between the surface and the low level jet is found to play a vital role in promoting turbulence. Our simplified setup is sufficient to observe turbulence collapse, intermittency and the low-level jet formation, indicating the applicability of this model to atmospheric problems. [Preview Abstract] |
Monday, November 23, 2015 4:57PM - 5:10PM |
L4.00005: A Multilevel Kinematic Simulation for the Stratified Surface Layer Aditya Ghate, Sanjiva Lele For problems involving a wide range of spatially disparate scales, Kinematic Simulations (KS) offer a low-cost alternative to LES. This is especially true when the phenomena of interest (Ex. Wind turbine fatigue, pollution dispersion, etc.) are those that are primarily affected by the statistical properties of turbulence. In the proposed KS, Isotropic turbulence is first "rapidly distorted" using an effective mean shear and density gradient (RDT). The temporal advancement of the stochastic fields can then be done using two different models. The first model idealizes the inter-scale interactions as exclusively those due to "sweeping" of smaller eddies by the larger eddies. In the second formulation, the inter-scale "straining" is accounted for using an RDT - like formulation wherein the Gabor transform is used to explicitly enforce separation of scales between successive resolution levels. Both models produce non-Gaussian turbulent fields for the velocity and temperature fluctuations. The KS will be appraised by comparison of cross spectra, space-time correlations, higher order statistics and other attributes of near wall turbulence using higher fidelity results obtained from LES. [Preview Abstract] |
Monday, November 23, 2015 5:10PM - 5:23PM |
L4.00006: High Reynolds number effects on a localized stratified turbulent flow Qi Zhou, Peter Diamessis We report large-eddy simulations (LES) of the turbulent flow behind a sphere of diameter $D$ translating at speed $U$ in a linearly stratified Boussinesq fluid with buoyancy frequency $N$. These simulations are performed using a spectral-multidomain-penalty incompressible Navier-Stokes solver, at Reynolds numbers $Re\equiv UD/\nu \in\{5\times10^3$, $10^5, 4\times10^5\}$ and Froude numbers $Fr \equiv 2U/(ND) \in\{4,16,64\}$. An increasingly richer turbulent fine-structure is observed within the larger-scale quasi-horizontal vortices at later times. Turbulent transport of momentum is examined during the non-equilibrium (NEQ) regime of the turbulent life cycle, with an emphasis on the vertical transport that occurs after the establishment of local buoyancy control. The turbulent viscosities in both horizontal and vertical directions are estimated through the LES data; possible parameterization of the vertical turbulent viscosity with the buoyancy Reynolds number $Re_b=\varepsilon/(\nu N^2)$ (or its easy-to-obtain surrogates) is discussed. The dynamical role of the buoyancy Reynolds number in choosing the vertical turbulence length scales is also investigated. [Preview Abstract] |
Monday, November 23, 2015 5:23PM - 5:36PM |
L4.00007: Internal length scales in rotating and stratified Boussinesq flows Susan Kurien, X.M. Zhai, P.K. Yeung We study the characteristic length scales of the propagating (wave) and non-propagating (vortical) modes, in a suite of simulations of forced, rotating, stably stratified Boussinesq flows. We employ a pseudo-spectral code, periodic boundary conditions and grid resolutions ranging from $512^3$ to $2048^3$ on Blue Gene/Q (Argonne) under DOE's INCITE program. The relative strength of rotation to stratification frequencies is given by the Burger number $Bu$. Integral length scales in the vertical and horizontal directions are chosen as the characteristic scales and their ratio defines an internal aspect ratio. Nominally quasi-geostrophic (QG) scaling of $Bu^{?1}$ is recovered for the vortical scale aspect ratio in the stratification-dominated regime $Bu\gg 4$. Much weaker scaling in $Bu$ emerges for the vortical mode in the rotation-dominated regime $Bu \ll 1/4$. The aspect ratio of the wave modes in both regimes are only weakly dependent on $Bu$. Turbulence affects the wave modes in the strongly rotating case by increasing the aspect ratio systematically but has no impact on the weak $Bu$ dependence. It appears that for unit aspect ratio domains, QG scaling of the vortical mode holds only for stratification-dominated flows irrespective of the strength of rotation. [Preview Abstract] |
(Author Not Attending)
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L4.00008: Laboratory experiments of an atmospheric/oceanic turbulence Adrien Thacker, Olivier Eiff Atmospheric or oceanic turbulence is strongly influenced by the effects of stratification leading to the emmergence of quasi-horizontal layers often described as ``pancake'' structures. The mechanisms of this layering and the selection of the vertical length scale of pancake structures is discussed for one decade whereas it is of a major importance to elucidate the energetic cascade that leads to viscous dissipation. In this present work, we analyze a new series of decaying grid turbulence experiments under the effects of stratification aiming to identify and observe the strongly stratified turbulence regime. The experiments have been performed in a large water towing tank with salt stratification and measurements have been carried out using a scanning correlation imaging velocimetry technique providing instantaneous 3D3C velocity fields along the decaying turbulence. Self similar power laws of the decaying grid turbulence have been assessed and allow the definition of empirical critical time giving transitions to the strongly stratified turbulence regime. A first experimental evidence of overturning process between layers of pancake vortices has been obtained through vorticity fields observation. This observation support the existence of a downscale energy cascade. [Preview Abstract] |
Monday, November 23, 2015 5:49PM - 6:02PM |
L4.00009: Characteristics of the residual stress tensor as a function of length scale in simulations of stably stratified turbulence Felipe Augusto de Braganca Alves, Stephen de Bruyn Kops \emph{A priori} analysis of the relationships between the deviatoric residual stress tensor $\tau^r$ and kinematic tensors is made for stably stratified Boussinesq turbulence. Two data sets from direct numerical simulation are used for the analyses: the decaying Taylor-Green simulations of Riley and de Bruyn Kops(2003), and the forced homogeneous stratified turbulence simulations of Almalkie and de Bruyn Kops(2012) resolved on up to $8192 \times 8192 \times 4096$ grid points. The data sets are filtered using a Gaussian kernel with filter widths up to the buoyancy scale. Through tensor decomposition theorems described in Thompson et al.(2010) the relationship between the strain rate tensor and the residual stress is quantified for each filter width and case. This is also done for the tensor formed by the Lie product between the strain rate and rate of rotation tensors. The role of each tensor, seen as a part of the residual stress tensor, is analyzed, in particular with respect to filtered kinetic energy budget equation. [Preview Abstract] |
Monday, November 23, 2015 6:02PM - 6:15PM |
L4.00010: Energy transfer in stably stratified turbulence Yoshifumi Kimura, Jackson Herring Energy transfer in forced stable stratified turbulence is investigated using pseudo-spectral DNS of the Navier-Stokes equations under the Boussinesq approximation with $1024^3$ grid points. Making use of the Craya-Herring decomposition, the velocity field is decomposed into vortex $(\Phi_1)$ and wave $(\Phi_2)$ modes. To understand the anisotropy of stably stratified turbulence, the energy flues in terms of the spherical, the horizontal and the vertical wave numbers, are investigated for the total kinetic, $\Phi_1$, $\Phi_2$ energies, respectively. Among the three fluxes, the spherical and the horizontal look similar for strong stratification, and $\Phi_1$ flux shows a wave number region of constant value, which implies Kolmogorov's inertial range. The corresponding spectral power are, however, $k^{-5/2}$ for the spherical and $k_{\perp}^{-5/3}$ for the horizontal cases. In contrast to these, the vertical energy fluxes show completely different features. We have observed the saturation spectrum $E(k_z) \sim CN^2k_z^{-3}$ for strong stratification as before$^{[1]}$, but the mechanism to produce this spectrum seems different from the Kolmogorov picture. \\\noindent [1] Y. Kimura \& J.R. Herring: Energy spectra of stably stratified turbulence, {\it JFM}, {\bf 698} 19--50 (2012) [Preview Abstract] |
Monday, November 23, 2015 6:15PM - 6:28PM |
L4.00011: LES of oscillating boundary layers under neutrally stratified and unstably stratified conditions Mario Juha, Jie Zhang, Andres Tejada-Martinez Results are presented from LES of open channel flow driven by an oscillating pressure gradient with zero surface shear stress. The flow is representative of an oscillating tidal boundary layer. Under neutrally stratified conditions, during certain phases of the oscillating pressure gradient, the flow develops large scale secondary structures, characterized by full-depth regions (or limbs) of negative and positive wall-normal velocity fluctuations. These structures are similar but less coherent than the classical Couette cells found in Couette flow driven by parallel no-slip plates moving in opposite direction. Unstable stratification will be imposed by a constant cooling flux at the surface and an adiabatic bottom wall. The effect of the surface cooling on the large scale secondary structures and the overall turbulence statistics will be investigated. The analysis will be performed in terms of the Rayleigh number (Ra), representative of the importance of surface buoyancy relative to shear, and the Rossby number (Ro), representative of the importance of the turbulence throughout the water column. For example, in unstratified conditions, if Ro is relatively small, turbulence stress is expected to be important only near the bottom of the boundary layer. [Preview Abstract] |
Monday, November 23, 2015 6:28PM - 6:41PM |
L4.00012: Turbulent flows over a modeled steep topography in a thermally-stratified boundary layer. Wei Zhang, Corey Markfort, Fernando Port\'e-Agel Turbulent flows with features of separation and reattachment, induced by topography of steep slopes, have been very challenging to predict using numerical models. The geometry of the topography, surface roughness and temperature along with the inflow characteristics (velocity, turbulence level, and atmospheric thermal stability) play important roles in determining onset of separation, reattachment location and momentum and heat flux distribution. To address the coupled effects of steep slope and thermal stability on turbulent flows over topography, series of wind-tunnel measurements of velocity fields, temperature and heat fluxes will be presented. Results will demonstrate the turbulent flow properties, including the size of the separation bubble, separated shear layers and the boundary layer recovery in different cases. Focus will be placed on correlation of momentum and heat flux distribution in the wake and turbulent kinetic energy transport. [Preview Abstract] |
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