Abstract
In this work we present Lattice Boltzmann simulations of a decaying vortex array in a 2D rectangular domain, which is bounded by a random rough wall from one side. In order to separate the effects of the collisions with the rough wall, the opposite (smooth) rigid wall is placed at a larger distance from the center of the vortex array. Periodic boundary condition is imposed in the perpendicular direction. Well defined random roughness is generated by the widely studied Wolf–Villain surface growth algorithm. The main finding is that collisions with a rough wall generate excess vorticity compared with a smooth boundary, while the kinetic energy decreases monotonously. A proper measure is the integrated excess enstrophy, which exhibits an apparent maximum at an “optimal” roughness range. Numerical values of the excess enstrophy are very sensitive to a particular configuration (wall shape and vortex lattice randomization), however the “optimal” roughness exhibits surface features of similar characteristic sizes than that of the decaying vortices.
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References
Aidun, C.K., Clausen, J.R.: Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech. 42, 439–472 (2010)
Barabási, A.L., Stanley, H.E.: Fractal Concepts in Surface Growth. Cambridge University Press, Cambridge (1995)
Benzi, R., Succi, S., Vergassola, M.: The lattice Boltzmann equation: theory and applications. Phys. Rep. 222, 145–197 (1992)
Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94, 511–525 (1954)
Biswas, G., Eswaran, V. (eds.): Turbulent Flows: Fundamentals. Experiments and Modeling. Narosa Publishing, New Delhi, India (2002)
Bracco, A., McWilliams, J.C., Murante, G., Provenzale, A., Weiss, J.B.: Revisiting freely decaying two-dimensional turbulence at millennial resolution. Phys. Fluids 12, 2931–2941 (2000)
Boffetta, G., Ecke, R.E.: Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427–51 (2012)
Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364 (1998)
Chester, S., Meneveau, C., Parlange, M.B.: Modeling turbulent flow over fractal trees with renormalized numerical simulation. J. Comput. Phys. 225, 427–448 (2007)
Clercx, H.J.H., Maassen, S.R., van Heijst, G.J.F.: Spontaneous spin-up during the decay of 2D turbulence in a square container with rigid boundaries. Phys. Rev. Lett. 80, 5129–5132 (1998)
Clercx, H.J.H., Nielsen, A.H., Torres, D.J., Coutsias, E.A.: Two-dimensional turbulence in square and circular domains with no-slip walls. Eur. J. Mech. B - Fluids 20, 557–576 (2001)
Clercx, H.J.H., van Heijst, G.J.F.: Two-dimensional NavierStokes turbulence in bounded domains. Appl. Mech. Rev. 62, 020802 (2009)
Ding, L., Shi, W., Luo, H.: Numerical simulation of viscous flow over non-smooth surfaces. Comput. Math. Appl. 61, 3703–3710 (2011)
Filippova, O., Hänel, D.: Grid refinement for Lattice-BGK models. J. Comput. Phys. 147, 219–228 (1998)
Flack, K.A., Schultz, M.P.: Roughness effects on wall-bounded turbulent flows. Phys. Fluids 26, 101305 (2014)
Flór, J.-B. (Ed.): Fronts, Waves and Vortices in Geophysical Flows. In: Lecture Notes in Physics, vol. 805. Springer, Berlin (2010)
Házi, G., Tóth, G.: Lattice Boltzmann simulation of two-dimensional wall bounded turbulent flow. Int. J. Mod. Phys. C 21, 669–680 (2010)
Házi, G., Tóth, G.: Regional statistics in confined two-dimensional decaying turbulence. Phil. Trans. R. Soc. A 369, 2555–2564 (2011)
He, X., Luo, L.-S.: Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 56, 6811–6817 (1997)
Jiménez, J.: Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173–196 (2004)
Kraichnan, R.H., Montgomery, D.: Two-dimensional turbulence. Rep. Prog. Phys. 43, 547–619 (1980)
Marusic, I., McKeon, B.J., Monkewitz, P.A., Nagib, H.M., Smits, A.J., Sreenivasan, K.R.: Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103 (2010)
Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 1. Dover, Mineola, NY (2007)
Rohde, M., Kandhai, D., Derksen, J.J., van den Akker, H.E.A.: Improved bounce-back methods for no-slip walls in lattice-Boltzmann schemes: theory and simulations. Phys. Rev. E 67, 066703 (2003)
Schneider, K., Farge, M.: Decaying two-dimensional turbulence in a circular container. Phys. Rev. Lett. 95, 244502 (2005)
Šmilauer, P., Kotrla, M.: Crossover effects in the Wolf–Villain model of epitaxial growth in 1+1 and 2+1 dimensions. Phys. Rev. B 49, 5769–5772 (1994)
Tabeling, P.: Two-dimensional turbulence: a physicist approach. Phys. Reports 362, 1–62 (2002)
Taylor, J.B., Borchardt, M., Helander, P.: Interacting vortices and spin-up in two-dimensional turbulence. Phys. Rev. Lett. 102, 124505 (2009)
Toppaladoddi, S., Succi, S., Wettlaufer, J.S.: Turbulent transport processes at rough surfaces with geophysical applications. Proc. IUTAM 15, 34–40 (2015)
Toppaladoddi, S., Succi, S., Wettlaufer, J.S.: Tailoring boundary geometry to optimize heat transport in turbulent convection. arXiv:1410.1959v5 [physics.flu-dyn] (2015)
Tóth, G., Házi, G.: Merging of shielded Gaussian vortices and formation of a tripole at low Reynolds numbers. Phys. Fluids 22, 053101 (2010)
Tóth, G., Házi, G.: Two-dimensional decaying turbulence in confined geometries. Int. J. Model. Simul. Sci. Comput. 5, 1441008 (2014)
Valcke, S., Verron, J.: Interactions of baroclinic isolated vortices: the dominant effect of shielding. J. Phys. Oceanogr. 27, 524–541 (1997)
van Heijst, G.J.F., Clercx, H.J.H., Molenaar, D.: The effects of solid boundaries on confined two-dimensional turbulence. J. Fluid Mech. 554, 411–431 (2006)
von Larcher, Th, Williams, P.D. (eds.): Modeling Atmospheric and Oceanic Flows: Insights from Laboratory Experiments and Numerical Simulations. Wiley, Hoboken, NJ (2014)
Wang, C.Y.: Flow over a surface with parallel grooves. Phys. Fluids 15, 1114–1121 (2003)
Weiss, J.B., McWilliams, J.C.: Temporal scaling behavior of decaying two-dimensional turbulence. Phys. Fluids A 5, 608–621 (1993)
Wolf, D.E., Villain, J.: Growth with surface diffusion. Europhys. Lett. 13, 389–394 (1990)
Acknowledgments
The authors thank Tímea Haszpra for technical help. This work was partially supported by the Hungarian Science Foundation under Grant Number OTKA NK100296.
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Tóth, G., Jánosi, I.M. Vorticity Generation by Rough Walls in 2D Decaying Turbulence. J Stat Phys 161, 1508–1518 (2015). https://doi.org/10.1007/s10955-015-1375-x
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DOI: https://doi.org/10.1007/s10955-015-1375-x