4 results
Similarity scaling and vorticity structure in high-Reynolds-number stably stratified turbulent wakes
- PETER J. DIAMESSIS, GEOFFREY R. SPEDDING, J. ANDRZEJ DOMARADZKI
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- Journal:
- Journal of Fluid Mechanics / Volume 671 / 25 March 2011
- Published online by Cambridge University Press:
- 07 March 2011, pp. 52-95
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The mean velocity profile scaling and the vorticity structure of a stably stratified, initially turbulent wake of a towed sphere are studied numerically using a high-accuracy spectral multi-domain penalty method model. A detailed initialization procedure allows a smooth, minimum-transient transition into the non-equilibrium (NEQ) regime of wake evolution. A broad range of Reynolds numbers, Re = UD/ν ∈ [5 × 103, 105] and internal Froude numbers, Fr = 2U/(ND) ∈ [4, 64] (U, D are characteristic velocity and length scales, and N is the buoyancy frequency) is examined. The maximum value of Re and the range of Fr values considered allow extrapolation of the results to geophysical and naval applications.
At higher Re, the NEQ regime, where three-dimensional turbulence adjusts towards a quasi-two-dimensional, buoyancy-dominated flow, lasts significantly longer than at lower Re. At Re = 5 × 103, vertical fluid motions are rapidly suppressed, but at Re = 105, secondary Kelvin–Helmholtz instabilities and ensuing turbulence are clearly observed up to Nt ≈ 100. The secondary motions intensify with increasing stratification strength and have significant vertical kinetic energy.
These results agree with existing scaling of buoyancy-driven shear on Re/Fr2 and suggest that, in the field, the NEQ regime may last up to Nt ≈ 1000. At a given high Re value, during the NEQ regime, the scale separation between Ozmidov and Kolmogorov scale is independent of Fr. This first systematic numerical investigation of stratified turbulence (as defined by Lilly, J. Atmos. Sci. vol. 40, 1983, p. 749), in a controlled localized flow with turbulent initial conditions suggests that a reconsideration of the commonly perceived life cycle of a stratified turbulent event may be in order for the correct turbulence parametrizations of such flows in both geophysical and operational contexts.
Direct numerical simulation of transition to turbulence in Görtler flow
- Wei Liu, J. Andrzej Domaradzki
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- Journal:
- Journal of Fluid Mechanics / Volume 246 / January 1993
- Published online by Cambridge University Press:
- 26 April 2006, pp. 267-299
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Using direct numerical simulation techniques we investigate transition to turbulence in a boundary-layer flow containing two large-scale counter-rotating vortices with axes aligned in the streamwise direction. The vortices are assumed to have been generated by the Görtler instability mechanism operating in boundary-layer flows over concave walls. Full, three-dimensional Navier–Stokes equations in a natural curvilinear coordinate system for a flow over concave wall are solved by a pseudospectral numerical method. The simulations are initialized with the most unstable mode of the linear stability theory for this flow with its amplitude taken from the experimental measurements of Swearingen & Blackwelder (1987). The evolution of the Görtler vortices for two different spanwise wavenumbers has been investigated. In all cases the development of strong inflexional velocity profiles is observed in both spanwise and vertical directions. The instabilities of these velocity profiles are identified as a primary mechanism of the transition process. The results indicate that the spanwise shear plays a more prominent role in the transition to turbulence than the vertical shear, in agreement with the hypothesis originally proposed by Swearingen & Blackwelder (1987). The following features of the transition, consistent with this hypothesis, were observed. Instability oscillations start in the spanwise direction and are followed later by oscillations in the vertical direction. A two-dimensional linear stability analysis predicts that the maximum growth rates of perturbations associated with the spanwise profiles are greater than those associated with the vertical profiles. Regions of high perturbation velocity correlate well with the regions of high spanwise shear and no obvious correlation with the vertical shear regions is observed. Finally, the analysis of the kinetic energy balance equation reveals that most of the perturbation energy production in the initial stages of transition occurs in the region characterized by large spanwise shear created by the action of the vortices moving low-speed fluid away from the wall. Our results are consistent qualitatively and quantitatively with other experimental, theoretical, and numerical investigations of this flow.
Direct numerical simulations of the effects of shear on turbulent Rayleigh-Bénard convection
- J. Andrzej Domaradzki, Ralph W. Metcalfe
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- Journal of Fluid Mechanics / Volume 193 / August 1988
- Published online by Cambridge University Press:
- 21 April 2006, pp. 499-531
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The interaction between shear and buoyancy effects for Bénard convection in plane Couette flow is studied by performing direct numerical simulations. At moderate Rayleigh number (≈10000−50000), shear tends to organize the flow into quasi-two-dimensional rolls parallel to the mean flow and can enhance heat transfer, while at higher Rayleigh number (>150000), shear tends to disrupt the formation of convective plumes and can reduce heat transfer. A significant temporal oscillation in the local Nusselt number was consistently observed at high Rayleigh numbers, a factor that may contribute to the scatter seen in experimental data. This effect, plus the time-varying reversal of the mean temperature gradient in the middle of the channel, is consistent with a flow model in which the dynamics of large-scale, quasi-two-dimensional, counter-rotating vortical cells are alternately driven by buoyancy and inertial effects. An analysis of the energy balance in the flow shows that the conservative pressure diffusion term, which has been frequently neglected in turbulence models, plays a very important dynamical role in the flow evolution and should be more carefully modelled. Most of the turbulent energy production due to mean shear is generated in the boundary layers, while the buoyant production occurs mainly in the relatively uniform convective core. The simulations and the laboratory experiments of Deardorff & Willis (1967) are in very reasonable qualitative agreement, suggesting that the basic dynamics of the flow are being accurately simulated.
Direct numerical simulations of passive scalars with Pr>1 advected by turbulent flow
- DAREK BOGUCKI, J. ANDRZEJ DOMARADZKI, P. K. YEUNG
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- Journal:
- Journal of Fluid Mechanics / Volume 343 / 25 July 1997
- Published online by Cambridge University Press:
- 25 July 1997, pp. 111-130
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Direct numerical simulations of passive scalars, with Prandtl numbers Pr=3, 5, and 7, advected by turbulence at three low Reynolds numbers were performed. The energy spectra are self-similar under the Kolmogorov scaling and exhibit behaviour consistent with many other investigations: a short inertial range for the highest Reynolds number and the universal exponential form of the spectrum for all Reynolds numbers in the dissipation range. In all cases the passive scalar spectra collapse to a single self-similar curve under the Batchelor scaling and exhibit the k−1 range followed by an exponential fall-off. We attribute the applicability of the Batchelor scaling to our low-Reynolds-number flows to the universality of the energy dissipation spectra. The Batchelor range is observed for wavenumbers in general agreement with experimental observations but smaller than predicted by the classical estimates. The discrepancy is caused by the fact that the velocity scales responsible for the generation of the Batchelor range are in the vicinity of the wavenumber of the maximum energy dissipation, which is one order of magnitude less than the Kolmogorov wavenumber used in the classical theory. Two different functional forms of passive scalar spectra proposed by Batchelor and Kraichnan were fitted to the simulation results and it was found that the Kraichnan model agrees very well with the data while the Batchelor formula displays systematic deviations from the data. Implications of these differences for the experimental procedures to measure the energy and passive scalar dissipation rates in oceanographic flows are discussed.