Skip to main content Accessibility help
×
Home

Erosion of a sharp density interface by a turbulent jet at moderate Froude and Reynolds numbers

  • J. Herault (a1) (a2), G. Facchini (a2) and M. Le Bars (a2)

Abstract

Using water–salt water laboratory experiments, we investigate the mechanism of erosion by a turbulent jet impinging onto a density interface, for moderate Reynolds and Froude numbers. The Froude number is defined by $Fr_{i}=u_{i}/\sqrt{b_{i}g^{\prime }}$ , with $u_{i}$ and $b_{i}$ , the typical velocity and width of the jet at the interface, and $g^{\prime }$ the reduced gravitational acceleration. The Froude number $Fr_{i}$ characterizes the competition between inertial forces against the restoring buoyancy force. Contrary to previous observations reporting baroclinic destabilization of the interface, we show that the entrainment, in the range of parameters explored here, is driven by interfacial gravity waves. The waves are generated by the barotropic excitation coming from the turbulent fluctuations of the jet; they are then amplified by a mechanism of wave-induced stress; and they finally break and induce entrainment and mixing. Based on those physical observations, we introduce a scaling model for the entrainment rate, which varies continuously from $Fr_{i}^{3}$ to an $Fr_{i}$ power law from small to large Froude numbers, in agreement with the present and some of the previous laboratory data.

Copyright

Corresponding author

Email address for correspondence: johann.herault@imt-atlantique.fr

References

Hide All
Alexakis, A. 2009 Stratified shear flow instabilities at large Richardson numbers. Phys. Fluids 21 (5), 054108.
Babanin, A. 2011 Breaking and Dissipation of Ocean Surface Waves. Cambridge University Press.
Baines, W. D. 1975 Entrainment by a plume or jet at a density interface. J. Fluid Mech. 68 (2), 309320.
Baines, W. D., Corriveau, A. F. & Reedman, T. J. 1993 Turbulent fountains in a closed chamber. J. Fluid Mech. 255, 621646.
Banner, M. L. & Song, J. B. 2002 On determining the onset and strength of breaking for deep water waves. Part II. Influence of wind forcing and surface shear. J. Phys. Oceanogr. 32 (9), 25592570.
Breidenthal, R. E. 1992 Entrainment at thin stratified interfaces: the effects of Schmidt, Richardson, and Reynolds numbers. Phys. Fluids 4 (10), 21412144.
Cardoso, S. S. S. & Woods, A. W. 1993 Mixing by a turbulent plume in a confined stratified region. J. Fluid Mech. 250, 277305.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover Publications.
Cotel, A. J. & Breidenthal, R. E. 1996 A model of stratified entrainment using vortex persistence. Appl. Sci. Res. 57 (3–4), 349366.
Cotel, A. J., Gjestvang, J. A., Ramkhelawan, N. N. & Breidenthal, R. E. 1997 Laboratory experiments of a jet impinging on a stratified interface. Exp. Fluids 23 (2), 155160.
Dimotakis, P. E. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 6998.
Drazin, P. G. & Reid, W. H. 2004 Hydrodynamic Stability. Cambridge University Press.
Ezhova, E., Cenedese, C. & Brandt, L. 2016 Interaction between a vertical turbulent jet and a thermocline. J. Phys. Oceanogr. 46 (11), 34153437.
Fernando, H. J. S. 1991 Turbulent mixing in stratified fluids. Annu. Rev. Fluid Mech. 23 (1), 455493.
Fernando, H. J. S. & Hunt, J. C. R. 1996 Some aspects of turbulence and mixing in stably stratified layers. Dyn. Atmos. Oceans 23 (1), 3562.
Fischer, H. B., List, J. E., Koh, C. R., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.
Holmboe, J. 1962 On the behavior of symmetric waves in stratified shear layers. Geophys. Publ. 24, 67113.
Hussein, H. J., Capp, S. P. & George, W. K. 1994 Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet. J. Fluid Mech. 258, 3175.
Janssen, P. 2004 The Interaction of Ocean Waves and Wind. Cambridge University Press.
Khattab, I. S., Bandarkar, F., Fakhree, M. A. A. & Jouyban, A. 2012 Density, viscosity, and surface tension of water + ethanol mixtures from 293 to 323 K. Korean J. Chem. Engng 29 (6), 812817.
Kumagai, M. 1984 Turbulent buoyant convection from a source in a confined two-layered region. J. Fluid Mech. 147, 105131.
Lecoanet, D., Le Bars, M., Burns, K. J., Vasil, G. M., Brown, B. P., Quataert, E. & Oishi, J. S. 2015 Numerical simulations of internal wave generation by convection in water. Phys. Rev. E 91 (6), 063016.
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind. J. Fluid Mech. 14 (3), 385398.
Lin, C. C. 1954 Some physical aspects of the stability of parallel flows. Proc. Natl Acad. Sci. USA 40 (8), 741747.
Lin, Y. J. P. & Linden, P. F. 2005 The entrainment due to a turbulent fountain at a density interface. J. Fluid Mech. 542, 2552.
Linden, P. F. 1973 The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60 (3), 467480.
List, E. J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14 (1), 189212.
Meunier, P. & Leweke, T. 2003 Analysis and treatment of errors due to high velocity gradients in particle image velocimetry. Exp. Fluids 35 (5), 408421.
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3 (2), 185204.
Miles, J. W. 1960 On the generation of surface waves by turbulent shear flows. J. Fluid Mech. 7 (3), 469478.
Miles, J. W. 1961 On the stability of heterogeneous shear flows. J. Fluid Mech. 10 (4), 496508.
Morland, L. C. & Saffman, P. G. 1993 Effect of wind profile on the instability of wind blowing over water. J. Fluid Mech. 252, 383398.
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2 (5), 417445.
Shrinivas, A. B. & Hunt, G. R. 2014 Unconfined turbulent entrainment across density interfaces. J. Fluid Mech. 757, 573598.
Shrinivas, A. B. & Hunt, G. R. 2015 Confined turbulent entrainment across density interfaces. J. Fluid Mech. 779, 116143.
Shy, S. S. 1995 Mixing dynamics of jet interaction with a sharp density interface. Exp. Therm. Fluid Sci. 10 (3), 355369.
Strang, E. J. & Fernando, H. J. S. 2001 Entrainment and mixing in stratified shear flows. J. Fluid Mech. 428, 349386.
Sutherland, B. 2010 Internal Gravity Waves. Cambridge University Press.
Woodward, P. R, Herwig, F. & Lin, P.-H. 2014 Hydrodynamic simulations of H entrainment at the top of He-shell flash convection. Astrophys. J. 798 (1), 49.
Young, W. R. & Wolfe, C. L. 2014 Generation of surface waves by shear-flow instability. J. Fluid Mech. 739, 276307.
Yule, A. J. 1978 Large-scale structure in the mixing layer of a round jet. J. Fluid Mech. 89 (3), 413432.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Type Description Title
VIDEO
Movie

Herault et al. supplementary movie
Mixing process in the vicinity of the interface (15 × 20cm2) The dense fluid has been dyed by rhodamine and corresponds to the bright region.

 Video (9.3 MB)
9.3 MB

Erosion of a sharp density interface by a turbulent jet at moderate Froude and Reynolds numbers

  • J. Herault (a1) (a2), G. Facchini (a2) and M. Le Bars (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed