Abstract
The special case of entrainment in a stratified flow, relevant to many geophysical flows such as oceanic overflows, so far has not been studied experimentally in terms of small-scale aspects around the turbulent/non-turbulent interface. In view of the fact that existing engineering concepts perform unsatisfactorily in practice, a new gravity current facility was designed with the goal to gain understanding of how stratification affects interfacial physics. Here, we present the design of the new setup and give details on the turbulence enhancement in the inflow and the refractive index matching technique used. Validation measurements ensure that there is negligible backflow and an essentially irrotational flow outside the current. Measurements via particle image velocimetry of a flow with inflow Reynolds and Richardson numbers of \(Re_0\approx \hbox{4,000}\) and Ri 0 = 0.22 are reported. An analysis in a laboratory frame agrees well with flow features reported in the literature, i.e., a streamwise invariant top-hat velocity scale and a Reynolds stress distribution are matched closely by a mixing length model. In a second step, the instantaneous interface position is determined based on a threshold on the normal enstrophy component. An investigation in a frame of reference conditioned on the interface position reveals a strong interfacial shear layer that is much more pronounced than the one observed in jet flows. Its thickness is about two times the Taylor microscale. The data moreover suggest the existence of a fairly strong interfacial density jump across the shear layer. The entrainment parameter is estimated at \(E \approx 0.04\) congruently from the evaluations in laboratory and conditioned frame, respectively.
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Notes
This open source code is publicly available from http://www.jpiv.vennemann-online.de/.
Note that with otherwise similar dimensions Chen et al. (2007) report an integral length as high as \(L=8\,\hbox{cm}\) resulting in a higher estimate of R λ.
References
Anand R, Boersma B, Agrawal A (2009) Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: evaluation of known criteria and proposal of a new criterion. Exp Fluids 47:995–1007. doi:10.1007/s00348-009-0695-5
Arneborg L, Fiekas V, Umlauf L, Burchard H (2007) Gravity current dynamics and entrainment - a process study based on observations in the Arkona basin. J Phys Oceanogr 37:2094–2113. doi:10.1175/JPO3110.1
Bisset DK, Hunt JCR, Rogers MM (2002) The turbulent/non-turbulent interface bounding a far wake. J Fluid Mech 451:383–410. doi:10.1017/10.1017/S0022112001006759
Chen J, Odier P, Rivera M, Ecke R (2007) Laboratory measurement of entrainment and mixing in oceanic overflows. ASME Conf Proc 2007(42894):1283–1292. doi:10.1115/FEDSM2007-37673
Corrsin S, Kistler A (1954) The free-stream boundaries of turbulent flows. NACA TN-3133, TR-1244:1033–1064
Daviero GJ, Roberts PJW, Maile K (2001) Refractive index matching in large-scale stratified experiments. Exp Fluids 31:119–126. doi:10.1007/s003480000260
Ellison TH, Turner JS (1959) Turbulent entrainment in stratified flows. J Fluid Mech 6(03):423–448. doi:10.1017/S0022112059000738
Holzner M, Lüthi B (2011) Laminar Superlayer at the Turbulence Boundary. Phys Rev Lett 106(13):134503. doi:10.1103/PhysRevLett.106.134503
Holzner M, Liberzon A, Guala M, Tsinober A, Kinzelbach W (2006) Generalized detection of a turbulent front generated by an oscillating grid. Exp Fluids 41:711–719. doi:10.1007/s00348-006-0193-y
Legg S, Briegleb B, Chang Y, Chassignet EP, Danabasoglu G, Ezer T, Gordon AL, Griffies S, Hallberg R, Jackson L, Large W, Özgökmen TM, Peters H, Price J, Riemenschneider U, Wu W, Xu X, Yang J (2009) Improving oceanic overflow representation in climate models: the gravity current entrainment climate process team. B Am Meteorol Soc 90:657–670. doi:10.1175/2008BAMS2667.1
Mathew J, Basu AJ (2002) Some characteristics of entrainment at a cylindrical turbulence boundary. Phys Fluids 14(7):2065–2072. doi:10.1063/1.1480831
McDougall TJ (1979) On the elimination of refractive-index variations in turbulent density-stratified liquid flows. J Fluid Mech 93(1):83–96. doi:10.1017/S0022112079001798
Odier P, Chen J, Rivera MK, Ecke RE (2009) Fluid mixing in stratified gravity currents: The Prandtl mixing length. Phys Rev Lett 102:134504. doi:10.1103/PhysRevLett.102.134504
Odier P, Chen J, Ecke R (2012) Understanding and modeling turbulent fluxes and entrainment in a gravity current. Phys D 241(3):260–268. doi:10.1016/j.physd.2011.07.010
Philip J, Marusic I (2012) Large-scale eddies and their role in entrainment in turbulent jets and wakes. Phys Fluids 24(5):055108. doi:10.1063/1.4719156
Phillips OM (1955) The irrotational motion outside a free turbulent boundary. Math Proc Cambridge 51:220–229. doi:10.1017/S0305004100030073
Rahmstorf S (2002) Ocean circulation and climate during the past 120,000 years. Nature 419(6903):207–214
da Silva CB, Taveira RR (2010) The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer. Phys Fluids 22(12):121702. doi:10.1063/1.3527548
Simpson JE (1999) Gravity currents. Cambridge University Press, Cambridge
Smyth WD, Moum JN (2000) Length scales of turbulence in stably stratified mixing layers. Phys Fluids 12(6):1327–1342. doi:10.1063/1.870385
Turner JS (1986) Turbulent entrainment—the development of the entrainment assumption, and its application to geophysical flows. J Fluid Mech 173:431–471. doi:10.1017/S0022112086001222
Westerweel J, Hofmann T, Fukushima C, Hunt JCR (2002) The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet. Exp Fluids 33:873–878. doi:10.1007/s00348-002-0489-5
Westerweel J, Fukushima C, Pedersen JM, Hunt JCR (2009) Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J Fluid Mech 631:199–230. doi:10.1017/S0022112009006600
Wolf M, Lüthi B, Holzner M, Krug D, Kinzelbach W, Tsinober A (2012) Investigations on the local entrainment velocity in a turbulent jet. Phys Fluids 24(10):105110. doi:10.1063/1.4761837
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This work is sponsored by the Swiss National Science Foundation (SNF) under project number 200021/132567.
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Krug, D., Holzner, M., Lüthi, B. et al. Experimental study of entrainment and interface dynamics in a gravity current. Exp Fluids 54, 1530 (2013). https://doi.org/10.1007/s00348-013-1530-6
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DOI: https://doi.org/10.1007/s00348-013-1530-6