The large scales of forced 2D stratified turbulence are
studied using numerical simulations in a periodic box. As
the buoyancy frequency N is increased from zero, the
transfer of energy to 2D large scales is gradually reduced,
the velocity spectrum is steeper than E(k) \propto
k^-5/3 for scales larger than the forcing scale, and the
density spectrum scales near E_\rho(k) \propto k^-1.
At larger N, the kinetic energy ceases to grow in time.
Further increasing N, the kinetic energy begins once again
to grow, but the transfer of energy is to a 1D layered
pattern of flow, varying mainly in the direction of gravity;
the large-scale (essentially 1D) energy spectrum is
consistent with E(k) \propto k^-3; the density spectrum
is again near E_\rho(k) \propto k^-1. We explore
mechanisms responsible for the transition to 1D flow, and
confirm the importance of resonant triads for early times.
[JB.02] Numerical Simulation of Transpiration Driven Pipe Flows
Kiseok Lee, Robert Moser (Center for Simulation of Advanced Rockets, University of Illinois at Urbana Champaign)
Numerical experiments on the flows in a circular pipe with
the uniform side wall mass flow injection has been
accomplished by solving modified Navier-Stokes equation in a
cylindrical coordinate system. Injection driven pipe flow
undergoes axial acceleration, which in our simulations is
treated using a multi-scale asymptotic formulation, leading
to a modified Navier Stokes equation. In deriving this
formulation, it is assumed that the magnitude of the
turbulence fluctuations scale with the mean velocity. The
resulting equations are solved using a spectral one that
uses Fourier Galerkin approximation in both axial and
azimuthal directions and Chebyshev collocation in radial
direction. Stiffly-stable three-step time splitting method
has been applied. The injection driven flow has increased
centerline axial velocity and decreased the wall shear
compared to the usual pressure-gradient driven flow,
consistent with previous results for injection driven
channel flow. The comparison study of the flows with and
without mass flow injection in the pipe and corresponding
plane channel flow will be presented.
[JB.03] A Direct Numerical Simulation of the Flow Past a Surface-Mounted Mixing Tab
S. Dong, H. Meng (Laser Flow Diagnostics Lab, Dept. of Mechanical and Aerospace Engineering, SUNY at Buffalo, Buffalo, NY14260)
A DNS code based on fractional step scheme and finite volume method is developed for studying the flow past a trapezoidal mixing tab mounted on a flat plate. The flow with an incoming laminar boundary layer is simulated at Re=600 based on the inlet free stream velocity and the tab height. Simulated flow compares very well with experiments by PIV and flow visualization, both conducted at this lab. After an initial transient period vortices are periodically shed from the tab, and a pair of counter- rotating vortices is formed behind the tab. Streamlines indicate that the flow detours the tab and goes in a spiral and wavy pattern in the wake. The vorticity field shows that there exists a 3D shear layer behind the tab which originates from the tab edges and extends downstream. This shear rolls up and forms the sequence of periodically shed vortices. The vorticity iso-surface indicates that vortices shed from the tab have hairpin-like shapes. To understand the source of hairpin vortices several sets of vortex lines are studied, which indicates that the vortex lines close to the wall are pumped up by the flow to a height comparable to the tab height, and then advected downstream. These advected vortex lines form a sequence of hairpin-like shapes. The legs of these hairpin-like vortices intertwine with one another and form the pair of counter- rotating vortices.
[JB.04] DNS of turbulent Couette flow and its comparison with turbulent Poiseuille flow
Hiroshi Kawamura, Kenji Shingai (Science University of Tokyo), Yuichi Matsuo (National Aerospace Laboratory)
A direct numerical simulation (DNS) of turbulent plane
Couette flow (CF, hereafter) is performed. Reynolds number
based on the friction velocity and channel half width is
Re_\tau=180. The obtained statistical quantities are
compared with those of turbulent Poiseuille flows (PF) with
Reynolds numbers of Re_\tau=180 , 395 and 640.
Various statistical quantities are obtained, and the effects
of difference in velocity fields of the two types of flows
are discussed. In the core region of CF, the mean velocity
gradient is not zero unlike in PF. Thus, the turbulent
intensities are much higher in CF than in PF. In the near
wall region, the maximum of the Reynolds normal stresses of
CF are higher than that of PF. This is because the peak of
the turbulence energy production is high and independent of
the Re_\tau in the case of CF, while in PF it decreases
with decreasing Re_\tau. Other turbulent quantities are
also compared for Couette and Poiseuille flows.
[JB.05] Studies of Bypass Transition via Parallel Computing
Paul Durbin, Robert Jacobs, Xiaohua Wu (Stanford University)
When a flat plate boundary layer is subjected to ~ 1% or more free-stream turbulence orderly transition through formation of Tollmein Schlichting waves and subsequent stages of non-linearity does not occur. The process is more complex, but recognizable elements can be identified; they are termed streaks, puffs and spots. Computations showing how these structures occur in perturbed boundary layers will be presented. There were done on highly parallel computing platforms. Two cases will be covered: transition induced by free-stream grid turbulence and transition induced by passing wakes.
In the free-stream turbulence case, a rather intriguing phenomenon occurs: the shear filters the external grid turbulence, causing low-frequency, elongated streaks to appear in the laminar boundary layer. The role of these streaks in transition is unclear. Further downstream turbulent spots appear. They grow and merge with the main turbulent region, thereby maintaining its upstream edge.
In the wake case, puffs are observed just upstream of the wake. Turbulent spots eventually emerge inside these puffs. In both cases `backward jets' were observed as spot precursors. These undergo highly localized instabilities that become turbulent spots at a macroscopic level.
The DNS provide insights into the transition mechanism
cannot be obtained by laboratory measurements because of the
amount of space-time data needed and the high resolution of
velocity required to see the early stages of interaction
between the boundary layer and external perturbation.
[JB.06] Simulations of a Two-Scale Richtmyer-Meshkov Instability
D. E. Eliason, L. Cloutman, R. H. Cohen, W. P. Dannevik, A. M. Dimits, A. A. Mirin, T. A. Peyser, O. Schilling (Lawrence Livermore National Laboratory), D. H. Porter, P. R. Woodward (U. Minnesota)
A series of simulations of a shocked, Richtmyer-Meshkov unstable interface with a two-scale initial perturbation, qualitatively similar to the Vetter-Sturtevant shock-tube experiments, was performed and studied. A sequence of three-dimensional simulations with increasing resolution up to a maximum resolution of 2048^2\times 1920 was compared to a corresponding two-dimensional sequence, as well as a series of three-dimensional single mode simulations which were periodic at the shorter of the two scales. Visualizations and analysis of the kinetic energy spectra suggest a transition from well-defined bubbles and spikes to turbulent flow as the effective Reynolds number (related to numerical dissipation) is increased. A forward transfer of kinetic energy is exhibited in the three-dimensional results, whereas in comparison the two-dimensional simulations indicate an inhibition. Contrasting the results from the two-scale simulations with those from the single shorter-mode simulations suggests that two-scale coupling breaks up much of the shorter-scale structure.
[JB.07] Interaction of Vorticity, Rate of Strain, and Scalar Gradient in Stably Stratified Homogeneous Sheared Turbulence: the Effect of Initial Scalar Fluctuations
Peter J. Diamessis, Keiko K. Nomura (University of California, San Diego)
The fully coupled, triadic interaction of vorticity \boldmath ømega, rate-of-strain \sf S, and scalar (density fluctuation) gradient \boldmath G \equiv \boldmath \nabla \rho' in stably stratified sheared turbulence is investigated.\, Results from direct numerical simulations of homogeneous sheared turbulence with (ISF) and without (NISF) initial scalar fluctuations (turbulent potential energy) for differing degrees of (supercritical) stratification are presented.\, Key physical processes and feedback mechanisms are identified.\, In the case of strong stratification (Ri=1) and ISF, there is a transient phase of evolution in which the buoyancy force acts in collaboration with the shear to temporarily sustain the interaction of \boldmath ømega and \sf S.\, However, eventually, the behavior of \boldmath ømega, \sf S, and \boldmath G tends towards that of NISF as the flow settles into a similar state of decay.\, The NISF dynamics are characterized by an inherent negative feedback between baroclinic torque and reorientation of \boldmath G by \boldmath ømega and a positive feedback between differential acceleration and scalar gradient amplification by compressive straining.\, The latter results in persistent \boldmath G^2 in the case of ISF.\, It is suggested that in a slightly supercritical flow, sufficiently large initial potential energy is capable of overcoming the damping effects of mean stratification thereby sustaining the interaction of \mathbfømega and \sf S of neutrally stratified flow well into the asymptotic state.\,
[JB.08] Direct Numerical Simulations of Decaying Isotropic Compressible Turbulence
Ravi Samtaney, D. I. Pullin, Branko Kosovic (GALCIT, Caltech), D. I. Meiron (Applied Math., Caltech)
We describe 256^3 direct numerical simulations (DNS) of
decaying compressible isotropic turbulence at
fluctuation Mach numbers of M_t\sim 0.5 and at Taylor
Reynolds numbers Re_\lambda = O(100). Regions of
high-negative divergence are indicative of the presence of
eddy shocklets in these simulations. A quantitative analysis
of shocklets will be presented. Furthermore, the issue of
initial conditions for these simulations will be discussed.
Comparisons of the decay of the turbulent kinetic energy
obtained from the DNS with large-eddy simulations at 32^3
resolution are the subject of another presentation at this
conference.
[JB.09] Enstrophy Cascade in Forced 2D Turbulence
Mei-Jiau Huang (Mechanical Engineering Department/National Taiwan University)
Direct simulations of 2D turbulence are performed. The turbulence is forced with the so-called frozen method and a ``stationary" state is said to be obtained when the Reynolds number defined based on the enstrophy and enstrophy dissipation rate reaches steady. It is observed that a Kolmogorov's spectrum is built gradually in front of the forced wave numbers and the Saffman's(1971) spectrum after. Moreover, corresponding to the Kolmogorov's spectrum, a zero enstrophy transfer spectrum and a constant energy transfer spectrum seemingly exists. Kraichnan's spectrum (1971) is observed also with a Kraichnan's constant \approx 2.390 when the forcing is applied to very low wave numbers.
Two eddy viscosities associated with the nonlinear enstrophy cascade are defined and explored by taking advantage of the direct numerical simulation data. One is statistically defined in the wave space and is found not always being positive. The other is defined in the physical space and is of Smagorinsky-type. Correlations of these eddy viscosities with the cut-off wave number and cut-off enstrophy are investigated.