Abstract
The main aim of this article is to explore the relationship of vorticity and stretching in flows having a simple configuration forced by their geometry. Using Taylor’s four rollers mill experiment the stability of a region of pure strain (a 3D hyperbolic flow having a linear stagnation line) is first investigated. In agreement with previous theoretical predictions this flow is shown to be unstable and to give rise to a periodic pattern of alternate vortices aligned in the direction of stretching. It is demonstrated that the vortices which have been amplified by the stretching react on the strain so that the longitudinal velocity gradient is weakened in their core. This effect is also observed in another experiment where a vortex is formed in a cylindrical tank having a rotating bottom and submitted to an axial pumping. This later experiment demonstrates that the reduction of the stretching can be ascribed to the bidimensionalization induced by the vortex rotation.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
Andreotti B., (1997): Studying simple models to investigate the significance of some statistical tools used in turbulence. to appear in Physics of Fluids, March 1997.
Aryshev, Y. A., Golovin, V. A. and Ershin, S., A. (1981): Stability of colliding flows. Fluid Dyn. 16(5) 755–759.
Ashurst W. T., Kerstein A. R., Kerr R. M. and Gibson C. H., (1987): Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30, 3243–3253.
Cadot, O., Douady, S. and Couder, Y., (1995): Characterization of the low-pressure filaments in a 3-dimensional turbulent shear flow. Phys. Fluids. 7, 1–15.
Constantin P. and Procaccia I. (1995): Scaling in fluid turbulence—A geometric theory. Phys. Rev. E 51, 3207–3222.
Donaldson C. D. and Sullivan R.D., (1960): Behaviors of solutions of Navier Stokes equations for a complete class of three dimensionnal vortices. Proceedings of Heat Transfer and Fluid Mechanics Instabilities, 16–30 Stanford University.
Douady S., Couder Y. and Brachet M. E., (1991): Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983.
Escudier, M. P., (1984): Vortex breakdown: observations and explanations. Exp. Fluids, 2, 189–196.
Fauve S., Laroche C. and Castaing B., (1993): Pressure fluctuations in swirling turbulent flows. J. Phys. II France 3, 271–278.
Galanti B., Procaccia I. and Segel D., (1996): Dynamics of vortex lines in Turbulent flows Preprint.
Jimenez J., Wray A. A., Saffman P. G. and Rogallo R. S., (1993): The Structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.
Kerr O. and Dold, J. W. (1994): Periodic steady vortices in a stagnation-point flow. Fluid Mech. 276, 307–325.
Kerr R. M., (1987): Histograms of helicity and strain in numerical turbulence. Phys. Rev. Lett. 59, 783.
Lagnado, R. R., Phan Thien, N. and Leal, L. G., (1984): The stability of two-dimensional linear flows. Phys. Fluids, 27, 1094–1101.
Lagnado, R. R. and Leal, L. G., (1990): Visualization of 3-dimensional flow in a 4-roll mill. Exp. Fluids, 9, 25–32.
Lin S. J. and Corcos G. M., (1984): The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139.
Moffat H. K., Kida S. and Okhitani K., (1994): Stretched vortices-The sinews of turbulence-Large Reynolds number asymptotics J. Fluid Mech. 259, 241–264.
Mory, M. and Yurchenko N., (1993): Vortex generation by suction in a rotating tank. Eur. J. Mech. B / Fluids 12(6), 729–747.
Neu J. C., (1984): The dynamics of stretched vortices. J. Fluid Mech. 143, 253–276.
Nomura K.K. (1995): On the nature of the pressure Hessian in Homogeneous Turbulence. Bulletin of APS 40(12), 1973.
Ohkitani, K. (1994): Kinematics of vorticity-Vorticity-strain conjugation in incompressible fluid flows. Phys. Rev. E, 50, 5107–5110.
Ohkitani, K. and Kishiba, S. (1995): Nonlocal nature of vortex stretching in an inviscid fluid. Phys. Fluids, 7, 411–421.
Raynal F., (1996): Exact relation between spatial mean enstrophy and dissipation in confined incompressible flows. Phys. Fluids, 8, 2242–2245.
Siggia E. D., (1981): Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech., 107, 375.
Tanaka, M. and S. Kida, (1993): Characterization of vortex tubes and sheets. Phys. Fluids A 5, 2079–2082.
Taylor, G. I., (1934): The formation of emulsions in definable fields of flow. Proc. Roy. Soc. A 146, 501–523.
Taylor, G. I. (1938): Production and dissipation of vorticity in a turbulent fluid. Proc. Roy. Soc. A 164, 15–23.
Tsinober A., Kit E. and Dracos T., (1992): Experimental investigation of the field of velocity gradients in turbulent flows. J. Fluid Mech. 242, 169–192.
Turner, (1966): The constraints imposed on tornado-like vortices by the top and bottom boundary conditions. J. Fluid Mech. 25, 377–386.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag
About this paper
Cite this paper
Andreotti, B., Douady, S., Couder, Y. (1997). About the interaction between vorticity and stretching in coherent structures. In: Boratav, O., Eden, A., Erzan, A. (eds) Turbulence Modeling and Vortex Dynamics. Lecture Notes in Physics, vol 491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105032
Download citation
DOI: https://doi.org/10.1007/BFb0105032
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63051-7
Online ISBN: 978-3-540-69119-8
eBook Packages: Springer Book Archive