Abstract
Large eddy simulation is applied to model a fountain in a density-stratified fluid. The fountain is formed, as a vertical turbulent jet penetrates through a pycnocline. The jet flow is initiated by the formulation of a boundary condition in the form of an upward neutral-buoyancy fluid flow with the Gaussian axisymmetric mean-velocity profile and a given fluctuation level. It is shown that at a Froude number Fr higher than a certain critical value the fountain executes self-oscillations accompanied by internal wave generation within the pycnocline. The predominant self-oscillation mode is axisymmetric, when the fountain top periodically breaks down generating internal wave packets traveling toward the periphery of the computation domain. The characteristic frequency of the internal waves coincides with that of the fountain top oscillations and monotonically decreases with increase in Fr. The Fr-dependence of the fountain top oscillation amplitude obtained in the numerical solution is in good agreement with the predictions of the theoretical Landau model for the instability mode in the soft self-excitation regime.
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References
J.S. Turner, “Jets and Plumes with Negative or Reversing Buoyancy,” J. Fluid Mech. 26, 779 (1966).
R.C.Y. Koh and N.H. Brooks, “Fluid Mechanics of Waste-Water Disposal in the Ocean,” Annu. Rev. Fluid Mech. 7, 187 (1975).
R. Keeler, V. Bondur, and C. Gibson, “Optical Satellite Imagery Detection of Internal Wave Effects from a Submerged Turbulent Outfall in the Stratified Ocean,” Geophys. Res. Letters 32, L12610 (2005).
V.G. Bondur, V.M. Zhurbas, and Yu.V. Grebenyuk, “Mathematical Modeling of Turbulent Jets of Depth Waste Water in Coastal Aquatoria,” Okeanologiya 46, 805 (2006).
N.B. Kaye and G.R. Hunt, “Weak Fountains,” J. Fluid Mech. 558, 319 (2006).
N. Williamson, M. Srinarayana, S.W. Armfield, C.D. McBain, and W. Lin, “Low Reynolds-Number Fountain Behaviour,” J. Fluid Mech. 608, 297 (2008).
W. Lin and S.W. Armfield, “Direct Simulation of Weak Axisymmetric Fountains in a Homogeneous Fluid,” J. Fluid Mech. 403, 67 (2000).
Yu.I. Troitskaya, D.A. Sergeev, E.V. Ezhova, I.A. Soustova, and V.I. Kazakov, “Internal Wave Self-Generation by Buoyant Jets in a Stratified Reservoir,” Dokl. Ross. Akad. Nauk 419, 691 (2008).
E.V. Ezhova, D.A. Sergeev, A.A. Kandaurov, and Yu.I. Troitskaya, “Unsteady Dynamics of Turbulent Axisymmetric Jets in a Stratified Fluid. 1. Experimental Investigation,” Izv. Ross. Akad. Nauk. Fizika Atmosfery Okeana 48, 461 (2012).
V.P. Karlikov and O.V. Trushina, “Self-Oscillations of Plane Submerged Fountains,” Dokl. Ross. Akad. Nauk 361, 340 (1998).
V.P. Karlikov, S.L. Tolokonnikov, and O.V. Trushina, “Possible Classification of the Self-Oscillatory Spouting Regimes of Plane Vertical Submerged Jets of a Heavy Fluid,” Fluid Dynamics 44(3), 351 (2009).
O.A. Druzhinin and O.V. Troitskaya, “Internal Wave Generation by a Fountain in a Stratified Fluid,” Fluid Dynamics 45(3), 474 (2010).
A.V. Glazunov, “Vortex-Resolving Turbulence Modeling Using Mixed Dynamic Localized Closure. I. Formulation of the Problem, Description of the Model, and Diagnostic Numerical Tests,” Izv. Ross. Akad. Nauk. Fizika Atmosfery Okeana 45, 7 (2009).
A. Yoshizawa and K. Horiuti, “A Statistically-Derived Subgrid-Scale KInetic Energy Model for the Large-Eddy Simulation of Turbulent Flows,” J. Phys. Soc. Jap. 54, 2834 (1985).
C. Furbey, G. Tabor, H.G. Weller, and A.D. Gosman, “A Comparative Study of Subgrid Scale Models in Homogeneous Isotropic Turbulence,” Phys. Fluids 9, 1416 (1997).
O.M. Belotserkovskii, Numerical Modeling in Continuum Mechanics [in Russian], Nauka, Moscow (1984).
K.A. Brucker and S. Sarkar, “A Comparative Study of Self-Propelled and Towed Wakes in a Stratified Fluid,” J. Fluid Mech. 652, 373 (2010).
G.N. Abramovich, T.A. Girshovich, S.Yu. Krasheninnikov, A.N. Sekundov, and I.P. Smirnova, Theory of Turbulent Jets [in Russian], Nauka, Moscow (1984).
L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Pergamon Press, London (1987).
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Original Russian Text © O.A. Druzhinin, Yu.I. Troitskaya, 2013, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2013, Vol. 48, No. 6, pp. 135–146.
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Druzhinin, O.A., Troitskaya, Y.I. Internal wave radiation by a turbulent fountain in a stratified fluid. Fluid Dyn 48, 827–836 (2013). https://doi.org/10.1134/S0015462813060136
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DOI: https://doi.org/10.1134/S0015462813060136