Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-17T15:48:25.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Predicting vortex merging and ensuing turbulence characteristics in shear layers from initial conditions

Published online by Cambridge University Press:  17 September 2019

Anirban Guha Open the ORCID record for Anirban Guha [Opens in a new window]  and
Mona Rahmani Open the ORCID record for Mona Rahmani [Opens in a new window]
Anirban Guha*
Affiliation:
Institute of Coastal Research, Helmholtz-Zentrum Geesthacht, Geesthacht 21502, Germany School of Science and Engineering, University of Dundee, Dundee DD1 4HN, UK
Mona Rahmani
Affiliation:
Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, British Columbia V6T 1Z2, Canada
*
†Email address for correspondence: anirbanguha.ubc@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Unstable shear layers in environmental and industrial flows roll up into a series of vortices, which often form complex nonlinear merging patterns such as pairs and triplets. These patterns crucially determine the subsequent turbulence, mixing and scalar transport. We show that the late-time, highly nonlinear merging patterns are predictable from the linearized initial state. The initial asymmetry between consecutive wavelengths of the vertical velocity field provides an effective measure of the strength and pattern of vortex merging. The predictions of this measure are substantiated using direct numerical simulations. We also show that this measure has significant implications in determining the route to turbulence and the ensuing turbulence characteristics.

JFM classification

Instability: Transition to turbulence Turbulent Flows: Shear layer turbulence Vortex Flows: Vortex interactions
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 878 , 10 November 2019 , R4
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arbey, H. & Williams, J. E. F. 1984 Active cancellation of pure tones in an excited jet. J. Fluid Mech. 149, 445–454.Google Scholar
Batchelor, G. K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Baty, H. & Keppens, R. 2006 Kelvin–Helmholtz disruptions in extended magnetized jet flows. Astron. Astrophys. 447 (1), 9–22.Google Scholar
Bluestein, D., Rambod, E. & Gharib, M. 2000 Vortex shedding as a mechanism for free emboli formation in mechanical heart valves. J. Biomed. Engng 122 (2), 125–134.Google Scholar
Bridges, J. E. & Hussain, A. K. M. F. 1987 Roles of initial condition and vortex pairing in jet noise. J. Sound Vib. 117 (2), 289–311.Google Scholar
Broze, G. & Hussain, A. K. M. F. 1994 Nonlinear dynamics of forced transitional jets: periodic and chaotic attractors. J. Fluid Mech. 263, 93–132.Google Scholar
Buban, M. S. & Ziegler, C. L. 2016 The formation of small-scale atmospheric vortices via horizontal shearing instability. J. Atmos. Sci. 73 (5), 2061–2084.Google Scholar
Caulfield, C. P. & Peltier, W. R. 2000 The anatomy of the mixing transition in homogeneous and stratified free shear layers. J. Fluid Mech. 413, 1–47.Google Scholar
Cho, S. K., Yoo, J. Y. & Choi, H. 1998 Vortex pairing in an axisymmetric jet using two-frequency acoustic forcing at low to moderate Strouhal numbers. Exp. Fluids 25 (4), 305–315.Google Scholar
Corcos, G. M. & Sherman, F. S. 1984 The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and the two-dimensional flow. J. Fluid Mech. 139, 29–65.Google Scholar
Demare, D. & Baillot, F. 2001 The role of secondary instabilities in the stabilization of a nonpremixed lifted jet flame. Phys. Fluids 13 (9), 2662–2670.Google Scholar
Dong, W., Tedford, E. W., Rahmani, M. & Lawrence, G. A. 2019 Sensitivity of vortex pairing and mixing to initial perturbations in stratified shear flows. Phys. Rev. Fluids 4, 063902.Google Scholar
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Flament, P., Lumpkin, R., Tournadre, J. & Armi, L. 2001 Vortex pairing in an unstable anticyclonic shear flow: discrete subharmonics of one pendulum day. J. Fluid Mech. 440, 401–409.Google Scholar
Hajj, M. R., Miksad, R. W. & Powers, E. J. 1993 Fundamental–subharmonic interaction: effect of phase relation. J. Fluid Mech. 256, 403–426.Google Scholar
Ho, C.-M. & Huang, L.-S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443–473.Google Scholar
Husain, H. S. & Hussain, A. K. M. F. 1995 Experiments on subharmonic resonance in a shear layer. J. Fluid Mech. 304, 343–372.Google Scholar
Hwang, S. D., Lee, C. H. & Cho, H. H. 2001 Heat transfer and flow structures in axisymmetric impinging jet controlled by vortex pairing. Intl J. Heat Fluid Flow 22 (3), 293–300.Google Scholar
Ivey, G. N., Winters, K. B. & Koseff, J. R. 2008 Density stratification, turbulence, but how much mixing? Annu. Rev. Fluid Mech. 40, 169–184.Google Scholar
Kelly, R. E. 1967 On the stability of an inviscid shear layer which is periodic in space and time. J. Fluid Mech. 27 (4), 657–689.Google Scholar
Lansky, I. M., O’Neil, T. M. & Schecter, D. A. 1997 A theory of vortex merger. Phys. Rev. Lett. 79 (8), 1479–1482.Google Scholar
Mac Low, M.-M. & Ingersoll, A. P. 1986 Merging of vortices in the atmosphere of Jupiter: an analysis of Voyager images. Icarus 65 (2–3), 353–369.Google Scholar
Monkewitz, P. A. 1988 Subharmonic resonance, pairing and shredding in the mixing layer. J. Fluid Mech. 188, 223–252.Google Scholar
Nikitopoulos, D. E. & Liu, J. T. C. 1987 Nonlinear binary-mode interactions in a developing mixing layer. J. Fluid Mech. 179, 345–370.Google Scholar
Paschereit, C. O., Wygnanski, I. & Fiedler, H. E. 1995 Experimental investigation of subharmonic resonance in an axisymmetric jet. J. Fluid Mech. 283, 365–407.Google Scholar
Patnaik, P. C., Sherman, F. S. & Corcos, G. M. 1976 A numerical simulation of Kelvin–Helmholtz waves of finite amplitude. J. Fluid Mech. 73 (2), 215–240.Google Scholar
Popiel, C. O. & Trass, O. 1991 Visualization of a free and impinging round jet. Exp. Therm. Fluid Sci. 4 (3), 253–264.Google Scholar
Rahmani, M., Lawrence, G. A. & Seymour, B. R. 2014 The effect of Reynolds number on mixing in Kelvin–Helmholtz billows. J. Fluid Mech. 759, 612–641.Google Scholar
Rajagopalan, S. & Antonia, R. A. 2005 Flow around a circular cylinder structure of the near wake shear layer. Exp. Fluids 38 (4), 393–402.Google Scholar
Schram, C., Taubitz, S., Anthoine, J. & Hirschberg, A. 2005 Theoretical/empirical prediction and measurement of the sound produced by vortex pairing in a low Mach number jet. J. Sound Vib. 281 (1-2), 171–187.Google Scholar
Shaabani-Ardali, L., Sipp, D. & Lesshafft, L. 2019 Vortex pairing in jets as a global Floquet instability: modal and transient dynamics. J. Fluid Mech. 862, 951–989.Google Scholar
Smyth, W. D., Nash, J. D. & Moum, J. N. 2005 Differential diffusion in breaking Kelvin–Helmholtz billows. J. Phys. Oceanogr. 35, 1004–1022.Google Scholar
Unal, M. F. & Rockwell, D. 1988 On vortex formation from a cylinder. Part 2. Control by splitter-plate interference. J. Fluid Mech. 190, 513–529.Google Scholar
Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2 (4), 355–381.Google Scholar
Winters, K. B., MacKinnon, J. A. & Mills, B. 2004 A spectral model for process studies of rotating density-stratified flows. J. Atmos. Ocean. Technol. 21, 69–94.Google Scholar
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1980 Vortex pairing in a circular jet under controlled excitation. Part 1. General jet response. J. Fluid Mech. 101 (3), 449–491.Google Scholar