5 results
Evolution of the density self-correlation in developing Richtmyer–Meshkov turbulence
- C. D. Tomkins, B. J. Balakumar, G. Orlicz, K. P. Prestridge, J. R. Ristorcelli
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- Journal:
- Journal of Fluid Mechanics / Volume 735 / 25 November 2013
- Published online by Cambridge University Press:
- 24 October 2013, pp. 288-306
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Turbulent mixing in a Richtmyer–Meshkov unstable light–heavy–light (air–${\mathrm{SF} }_{6} $–air) fluid layer subjected to a shock (Mach 1.20) and a reshock (Mach 1.14) is investigated using ensemble statistics obtained from simultaneous velocity–density measurements. The mixing is driven by an unstable array of initially symmetric vortices that induce rapid material mixing and create smaller-scale vortices. After reshock the flow appears to transition to a turbulent (likely three-dimensional) state, at which time our planar measurements are used to probe the developing flow field. The density self-correlation $b= - \langle \rho v\rangle $ (where $\rho $ and $v$ are the fluctuating density and specific volume, respectively) and terms in its evolution equation are directly measured experimentally for the first time. Amongst other things, it is found that production terms in the $b$ equation are balanced by the dissipation terms, suggesting a form of equilibrium in $b$. Simultaneous velocity measurements are used to probe the state of the incipient turbulence. A length-scale analysis suggests that an inertial range is beginning to form, consistent with the onset of a mixing transition. The developing turbulence is observed to reduce non-Boussinesq effects in the flow, which are found to be small over much of the layer after reshock. Second-order two-point structure functions of the density field exhibit a power-law behaviour with a steeper exponent than the standard $2/ 3$ power found in canonical turbulence. The absence of a significant $2/ 3$ region is observed to be consistent with the state of the flow, and the emergence of the steeper power-law region is discussed.
Turbulent mixing in a Richtmyer–Meshkov fluid layer after reshock: velocity and density statistics
- B. J. Balakumar, G. C. Orlicz, J. R. Ristorcelli, S. Balasubramanian, K. P. Prestridge, C. D. Tomkins
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- Journal:
- Journal of Fluid Mechanics / Volume 696 / 10 April 2012
- Published online by Cambridge University Press:
- 07 March 2012, pp. 67-93
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The properties of turbulent mixing in a Richtmyer–Meshkov (RM) unstable fluid layer are studied under the impact of a single shock followed by a reshock wave using simultaneous velocity–density measurements to provide new insights into the physics of RM mixing. The experiments were conducted on a varicose fluid layer (heavy fluid) interposed in air (light fluid) inside a horizontal shock tube at an incident Mach number of 1.21 and a reflected reshock Mach number of 1.14. The light–heavy–light fluid layer is observed to develop a nonlinear growth pattern, with no transition to turbulence upon impact by a single shock (up to ). However, upon reshock, enhanced mixing between the heavy and light fluids along with a transition to a turbulent state characterized by the generation of significant turbulent velocity fluctuations () is observed. The streamwise and spanwise root-mean-squared velocity fluctuation statistics show similar trends across the fluid layer after reshock, with no observable preference for the direction of the shock wave motion. The measured streamwise mass flux () shows opposing signs on either side of the density peak within the fluid layer, consistent with the turbulent material transport being driven along the direction of the density gradient. Measurements of three of the six independent components of the general Reynolds stress tensor () show that the self-correlation terms and are similar in magnitude across much of the fluid layer, and much larger than the cross-correlation term . Most importantly, the Reynolds stresses () are dominated by the mean density, cross-velocity product term (), with the mass flux product and triple correlation terms being negligibly smaller in comparison. A lack of homogeneous mixing (and, possibly, a long-term imprint of the initial conditions) is observed in the spanwise turbulent mass flux measurements, with important implications for the simulation and modelling of RM mixing flows.
Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer
- C. D. TOMKINS, R. J. ADRIAN
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- Journal:
- Journal of Fluid Mechanics / Volume 545 / 25 December 2005
- Published online by Cambridge University Press:
- 02 December 2005, pp. 141-162
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The influence of large-scale outer-region motions on the properties and processes of the inner layer remains an open issue in wall turbulence research. In the present work, two-dimensional power spectra of the streamwise component are measured in streamwise-spanwise planes throughout the logarithmic region of smooth flat-plate turbulent boundary layers at $Re_\theta\,{=}\,1015$ and 7705. The spectra are based on PIV measurements with a wide spanwise view ($z/\delta\,{>}\, 2.5$), and the spanwise energy distribution is emphasized. The spectra reveal that the mode associated with the spacing of the low-speed streaks near the wall, $\lambda_z^+ \,{\approx}\, 100$, contains surprisingly little energy relative to modes in the range $\lambda_z^+ \,{\approx}\,$200–400 at $y^+ \,{=}\, 21$. This result is consistent with measurements in a channel flow (Liuet al. 1996) at a similar height. Further from the wall, large-scale structures that scale with outer variables organize with spacing $\lambda_z/\delta\,{=}\,$0.75–0.9, and these motions dominate the spanwise distribution of streamwise energy throughout the logarithmic region. The large spanwise modes are associated with the large streamwise modes on average, as the median energetic spanwise mode increases roughly linearly with increasing streamwise mode up to approximately $\lambda_{z,\mathrm{med}}/\delta \,{\approx}\, 0.8$, and then remains roughly constant for larger streamwise modes. The aspect ratio $\lambda_x / \lambda_{z,\mathrm{med}}$ decreases with increasing distance from the wall, suggesting that the most streaky structures remain buried near the wall.
Spanwise structure and scale growth in turbulent boundary layers
- C. D. TOMKINS, R. J. ADRIAN
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- Journal:
- Journal of Fluid Mechanics / Volume 490 / 10 September 2003
- Published online by Cambridge University Press:
- 19 August 2003, pp. 37-74
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Spanwise structure and growth mechanisms in a turbulent boundary layer are investigated experimentally. PIV measurements are obtained in the streamwise–spanwise ($x$–$z$)-plane from the buffer layer to the top of the logarithmic region at Re$_\theta = 1015$ and 7705. The dominant motions of the flow are shown to be large-scale regions of momentum deficit elongated in the streamwise direction. Throughout the logarithmic layer, the regions are consistently bordered by vortices organized in the streamwise direction, offering strong support for a vortex packet model. Additionally, evidence is presented for the existence and organization of hairpin vortices in the region $y^+ < 60$. Statistical evidence is also presented for two important aspects of the vortex packet paradigm: vortex organization in the streamwise direction, and the clear association of the hairpin signature with local minima in streamwise velocity. Several spanwise lengthscales are shown to vary linearly with distance from the wall, revealing self-similar growth of spanwise structure in an average sense. Inspection of the data, however, suggests that individual structures do not grow strictly self-similarly in time. It is proposed that additional scale growth occurs by the merging of vortex packets on an eddy-by-eddy basis via a vortex re-connection mechanism similar to that suggested by Wark & Nagib (1989). The proposed mechanism provides a link between vortex-pairing concepts and the observed coalescence of streaky low-speed regions in the inner layer.
Vortex organization in the outer region of the turbulent boundary layer
- R. J. ADRIAN, C. D. MEINHART, C. D. TOMKINS
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- Journal:
- Journal of Fluid Mechanics / Volume 422 / 10 November 2000
- Published online by Cambridge University Press:
- 06 November 2000, pp. 1-54
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The structure of energy-containing turbulence in the outer region of a zero-pressure- gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 < Reθ < 6845 show that the boundary layer is densely populated by velocity fields associated with hairpin vortices. (The term ‘hairpin’ is here taken to represent cane, hairpin, horseshoe, or omega-shaped vortices and deformed versions thereof, recognizing these structures are variations of a common basic flow structure at different stages of evolution and with varying size, age, aspect ratio, and symmetry.) The signature pattern of the hairpin consists of a spanwise vortex core located above a region of strong second-quadrant fluctuations (u < 0 and v > 0) that occur on a locus inclined at 30–60° to the wall.
In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian & Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12°, and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart & Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent ‘bursts’, and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.
In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.