- Access by Xinjiang University
Production and dissipation of turbulent fluctuations close to a stagnation point
Phys. Rev. Fluids 2, 084601 – Published 4 August, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.084601
Abstract
In this article, we investigate the production and dissipation of turbulence in a region where the mean flow topology presents a stagnation point. Our goal is to understand the generation of anisotropic fluctuations and their influence on production, dissipation, and transport of turbulent kinetic energy. In order to investigate the local turbulent kinetic energy budget, we use a shadow particle tracking velocimetry technique (S-PTV) to track Lagrangian tracers in a large portion of a turbulent von Kármán flow produced by counter-rotating disks. We observe that the flow produced in a square tank is bistable, with each of the two states resembling impinging jets. This stagnation-point topology is responsible for the strong anisotropy of velocity fluctuations observed in these type of flows. The production of turbulence locally exceeds the dissipation rate. As a consequence, the flow is to be considered as strongly inhomogeneous as the fluxes of turbulent kinetic energy are non-negligible when compared to the production and dissipation terms.
Physics Subject Headings (PhySH)
Article Text
References (28)
- U. Frish, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, UK, 1995).
- S. Pope, Turbulent Flows (Cambridge University Press, Cambridge, UK, 2000).
- H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, MA, 1972).
- J.-N. Gence, Linear and nonlinear models of anisotropic turbulence, Ann. Rev. Fluid Mech. 15, 201 (1983).
- A. Reynolds and H. Tucker, The distortion of turbulence by general uniform irrotational strain, J. Fluid Mech. 68, 673 (1975).
- K. Nishino, M. Samada, K. Kasuya, and K. Torii, Turbulence statistics in the stagnation region of an axisymmetric impinging jet flow, Int. J. Heat Fluid Flow 17, 193 (1996).
- L. Marié and F. Daviaud, Experimental measurement of the scale-by-scale momentum transport budget in a turbulent shear flow, Phys. Fluids 16, 457 (2004).
- N. T. Ouellette, H. Xu, M. Bourgoin, and E. Bodenschatz, Small-scale anisotropy in Lagrangian turbulence, New J. Phys. 8, 102 (2006).
- G. A. Voth, A. L. Porta, A. Crawford, J. Alexander, and E. Bodenschatz, Measurement of particle accelerations in fully developed turbulence, J. Fluid Mech. 469, 121 (2002).
- N. Machicoane, J. Bonaventure, and R. Volk, Melting dynamics of large ice balls in a turbulent swirling flow, Phys. Fluids 25, 125101 (2013).
- D. Kuzzay, D. Faranda, and B. Dubrulle, Global vs local energy dissipation: The energy cycle of the turbulent von Kármán flow, Phys. Fluids 27, 075105 (2015).
- G. Zocchi, P. Tabeling, J. Maurer, and H. Willaime, Measurement of the scaling of the dissipation at high Reynolds numbers, Phys. Rev. E 50, 3693 (1994).
- P. Huck, N. Machicoane, and R. Volk, A cost-efficient shadow particle tracking velocimetry setup suitable for tracking small objects in a large volume, Proc. IUTAM 20, 175 (2017).
- R. Volk, N. Mordant, G. Verhille, and J.-F. Pinton, Laser Doppler measurement of inertial particle and bubble accelerations in turbulence, EPL (Europhys. Lett.) 81, 34002 (2007).
- P. K. Yeung and S. B. Pope, Lagrangian statistics from direct numerical simulations of isotropic turbulence, J. Fluid Mech. 207, 531 (1989).
- A. de la Torre and J. Burguete, Slow Dynamics in a Turbulent Von Kármán Swirling Flow, Phys. Rev. Lett. 99, 054101 (2007).
- M. López-Caballero and J. Burguete, Inverse Cascades Sustained by the Transfer Rate of Angular Momentum in a 3d Turbulent Flow, Phys. Rev. Lett. 110, 124501 (2013).
- F. Ravelet, L. Marié, A. Chiffaudel, and F. Daviaud, Multistability and Memory Effect in a Highly Turbulent Flow: Experimental Evidence for a Global Bifurcation, Phys. Rev. Lett. 93, 164501 (2004).
- C. Cambon and J. Scott, Linear and nonlinear models of anisotropic turbulence, Ann. Rev. Fluid Mech. 31, 1 (1999).
- J. Hunt and D. Carruthers, Rapid distorsion theory and the problem of turbulence, J. Fluid Mech. 212, 497 (1990).
- M. M. Rogers and R. D. Moser, Direct simulation of a self-similar turbulent mixing layer, Physics of Fluids 6, 903 (1994).
- H. J. Hussein, S. P. Capp, and W. K. George, Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet, J. Fluid Mech. 258, 31 (1994).
- R. J. Hill, Opportunities for use of exact statistical equations, J. Turbulence 7, N43 (2006).
- N. T. Ouellette, H. Xu, M. Bourgoin, and E. Bodenschatz, An experimental study of turbulent relative dispersion models, New J. Phys. 8, 109 (2006).
- O. Liot and J. Burguete, Bifurcation induced by the aspect ratio in a turbulent von Kármán swirling flow, Phys. Rev. E 95, 013101 (2017).
- N. Machicoane, M. López-Caballero, L. Fiabane, J. F. Pinton, M. Bourgoin, J. Burguete, and R. Volk, Stochastic dynamics of particles trapped in turbulent flows, Phys. Rev. E 93, 023118 (2016).
- G. Rigas, A. S. Morgans, R. D. Brackston, and J. F. Morrison, Diffusive dynamics and stochastic models of turbulent axisymmetric wakes, J. Fluid Mech. 778, R2 (2015).
- Voth et al., Performed Lagrangian measurements at the stagnation point of a von Kármán flow produced in a cylindrical container [9]. They found the flow anisotropy is , and reported the mean gradient tensor is almost diagonal with m, and . This leads to a production term slightly larger than the local value of cm, estimated using the second-order velocity structure function.