Modeling turbulent flow from dam break using slow manifolds

Dian Georgiev, Anthony Roberts, Dmitry Strunin

Abstract


We present a novel approach based on centre manifold techniques to describe the large scale dynamics of the mean turbulent dam-break flow. We avoid empirical assumptions about the cross-stream profile of the velocity; instead a solution is obtained using free surface and bed boundary conditions that accommodate constant turbulent shear as an approximately neutral mode. We describe the turbulent dynamics across the flow, and identify important factors affecting the turbulent dissipation in the lateral direction. Available experimental data verify the results.

References
  • J. Carr. Applications of centre manifold theory, volume 35 of Applied Mathematical Sciences. Springer--Verlag, 1981.
  • D. J. Georgiev, A. J. Roberts, and D. V. Strunin. The dynamics of the vertical structure of turbulence in flood flows. ANZIAM Journal, 48(CTAC-2006):C573--C590, 2007. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/124.
  • D. J. Georgiev, A. J. Roberts, and D. V. Strunin. Nonlinear dynamics on centre manifolds describing turbulent floods: $k$-$\omega $ model. Discrete and Continuous Dynamical Systems Supplements, (Special):419--428, 2007. http://aimsciences.org/journals/pdfs.jsp?paperID=2848&mode=full.
  • A. J. Hogg and D. Pritchard. The effects of hydraulic resistance on dam-break and other shallow inertial flows. Journal of Fluid Mechanics, 501:179--212, 2004.
  • I. M. Janosi, D. Jan, K. G. Szabo, and T. Tel. Turbulent drag reduction in dam-break flows. Experiments in Fluids, 37:219--229, 2004.
  • P. Keast and P. H. Muir. {EPDCOL}: A more efficient {PDECOL} code. ACM Transactions on Mathematical Software, 17(2):153--166, 1991.
  • Y. A. Kuznetsov. Elements of applied bifurcation theory, volume 112 of Applied Mathematical Sciences. Springer--Verlag, 1995.
  • N. K. Madsen and R. F. Sincovec. {PDECOL}: General collocation software for partial differential equations. ACM Transactions on Mathematical Software, 5(3):326--351, 1979.
  • I. Nezu. Open-channel flow turbulence and its research prospects in the 21st century. Journal of Hydraulic Engineering, 131(4):229--246, April 2005.
  • T. M. Oezgoekmen, T. Iliescu, P. F. Fischer, A. Srinivasan, and J. Duan. Large eddy simulation of stratified mixing and two-dimensional dam-break problem in a rectagular enclosed domain. Ocean Modelling, 16:106--140, 2007.
  • A. J. Roberts. Low-dimensional modelling of dynamics via computer algebra. Computer Physics Communications, 100:215--230, 1997.
  • A. J. Roberts. Computer algebra describes flow of turbulent floods via the Smagorinsky large eddy closure. Technical report, University of Southern Queensland, 2008. http://eprints.usq.edu.au/4008/.
  • A. J. Roberts, D. J. Georgiev, and D. V. Strunin. Model turbulent floods with the Smagorinski large eddy closure. http://arxiv.org/abs/0805.3192/.
  • P. K. Stansby, A. Chegini, and T. C. D. Barnes. The initial stages of dam-break flow. Journal of Fluid Mechanics, 374:407--424, 1998.

Keywords


dynamical systems, turbulence, center manifold theory, turbulent transport, mixing

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DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1466



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