Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T07:18:36.116Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantification of turbulent mixing in colliding gravity currents

Published online by Cambridge University Press:  19 July 2018

Qiang Zhong Open the ORCID record for Qiang Zhong [Opens in a new window] ,
Fazle Hussain Open the ORCID record for Fazle Hussain [Opens in a new window]  and
Harindra J. S. Fernando Open the ORCID record for Harindra J. S. Fernando [Opens in a new window]
Qiang Zhong
Affiliation:
Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China
Fazle Hussain
Affiliation:
Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
Harindra J. S. Fernando*
Affiliation:
Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA Department of Aerospace & Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Collision between two identical counterflowing gravity currents was studied in the laboratory with the goal of understanding the fundamental turbulent mixing physics of flow collisions in nature, for example katabatic flows and thunderstorm outflows. The ensuing turbulent mixing is a subgrid process in mesoscale forecasting models, and needs to be parameterized using eddy diffusivity. Laboratory gravity currents were generated by simultaneously removing two identical locks, located at both ends of a long rectangular tank, which separated dense and lighter water columns with free surfaces of the same depth $H$. The frontal velocity $u_{f}$ and the velocity and density fields of the gravity currents were monitored using time-resolved particle image velocimetry and planar laser-induced fluorescence imaging. Ensemble averaging of identical experimental realizations was used to compute turbulence statistics, after removing inherent jitter via phase alignment of successive data realizations by iteratively maximizing the cross-correlation of each realization with the ensemble average. Four stages of flow evolution were identified: initial (independent) propagation of gravity currents, their approach while influencing one another, collision and resulting updraughts, and postcollision slumping of collided fluid. The collision stage, in turn, involved three phases, and produced the strongest turbulent mixing as quantified by the rate of change of density. Phase I spanned $-0.2\leqslant tu_{f}/H<0.5$, where collision produced a rising density front (interface) with strong shear and intense turbulent kinetic energy production ($t$ is a suitably defined time coordinate such that gravity currents make the initial contact at $tu_{f}/H=-0.2$). In Phase II ($0.5\leqslant tu_{f}/H<1.2$), the interface was flat and calm with negligible vertical velocity. Phase III ($1.2\leqslant tu_{f}/H<2.8$) was characterized by slumping which led to hydraulic bores propagating away from the collision area. The measurements included root mean square turbulent velocities and their decay rates, interfacial velocity, rate of change of fluid-parcel density, and eddy diffusivity. These measures depended on the Reynolds number $Re$, but appeared to achieve Reynolds number similarity for $Re>3000$. The eddy diffusivity $K_{T}$, space–time averaged over the spatial extent ($H\times H$) and the lifetime ($t\approx 3H/u_{f}$) of collision, was $K_{T}/u_{f}H=0.0036$ for $Re>3000$, with the area $A$ of active mixing being $A/H^{2}=0.037$.

JFM classification

Geophysical and Geological Flows: Gravity currents Geophysical and Geological Flows: Stratified flows Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 851 , 25 September 2018 , pp. 125 - 147
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23, 261–304.Google Scholar
Barenblatt, G. I. 1996 Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics, vol. 14. Cambridge University Press.Google Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.Google Scholar
Bourgeois, J., Sattari, P. & Martinuzzi, R. 2011 Alternating half-loop shedding in the turbulent wake of a finite surface-mounted square cylinder with a thin boundary layer. Phys. Fluids 23, 095101.Google Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 1–24.Google Scholar
Cantero, M. I., Lee, J. R., Balachandar, S. & Garcia, M. H. 2007 On the front velocity of gravity currents. J. Fluid Mech. 586, 1–39.Google Scholar
Chen, Q., Zhong, Q., Wang, X. & Li, D. 2014 An improved swirling-strength criterion for identifying spanwise vortices in wall turbulence. J. Turbul. 15, 71–87.Google Scholar
Clarke, R., Smith, R. & Reid, D. 1981 The morning glory of the Gulf of Carpentaria: an atmospheric undular bore. Mon. Weath. Rev. 109, 1726–1750.Google Scholar
Droegemeier, K. K. & Wilhelmson, R. B. 1985 Three-dimensional numerical modeling of convection produced by interacting thunderstorm outflows. Part I: control simulation and low-level moisture variations. J. Atmos. Sci. 42, 2381–2403.Google Scholar
Fernando, H. J. S. & Pardyjak, E. R. 2013 Field studies delve into the intricacies of mountain weather. EOS Trans. AGU 94, 313–315.Google Scholar
Fernando, H. J. S., Pardyjak, E. R., Di Sabatino, S., Chow, F. K., De Wekker, S. F. J., Hoch, S. W., Hacker, J., Pace, J. C., Pratt, T., Pu, Z. et al. 2015 The MATERHORN: unraveling the intricacies of mountain weather. Bull. Am. Meteorol. Soc. 96, 1945–1967.Google Scholar
Geyer, W. R., Lavery, A. C., Scully, M. E. & Trowbridge, J. H. 2010 Mixing by shear instability at high Reynolds number. Geophys. Res. Lett. 37 (22), 507–514.Google Scholar
Hannoun, I. A., Fernando, H. J. & List, E. J. 1988 Turbulence structure near a sharp density interface. J. Fluid Mech. 189, 189–209.Google Scholar
Harrison, S. J., Mecikalski, J. R. & Knupp, K. R. 2009 Analysis of outflow boundary collisions in north-central Alabama. Weath. Forecasting 24, 1680–1690.Google Scholar
Härtel, C., Meiburg, E. & Necker, F. 2000 Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries. J. Fluid Mech. 418, 189–212.Google Scholar
Holman, J. P. 1978 Experimental Methods for Engineers, p. 65. McGraw-Hill.Google Scholar
Hopfinger, E. J. 1987 Turbulence in stratified fluids: a review. J. Geophys. Res. 92 (C5), 5287–5303.Google Scholar
Huppert, H. E. & Simpson, J. E. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785–799.Google Scholar
Hussain, A. & Hayakawa, M. 1987 Eduction of large-scale organized structures in a turbulent plane wake. J. Fluid Mech. 180, 193–229.Google Scholar
Hussain, A., Kleis, S. & Sokolov, M. 1980 A ‘turbulent spot’ in an axisymmetric free shear layer. Part 2. J. Fluid Mech. 98, 97–135.Google Scholar
Hussain, A. F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303–356.Google Scholar
Intrieri, J., Bedard, A. Jr. & Hardesty, R. 1990 Details of colliding thunderstorm outflows as observed by Doppler lidar. J. Atmos. Sci. 47, 1081–1099.Google Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.Google Scholar
Kähler, C. J., Astarita, T., Vlachos, P. P., Sakakibara, J., Hain, R., Discetti, S., Foy, R. & Cierpka, C. 2016 Main results of the 4th international PIV challenge. Exp. Fluids 57, 1–71.Google Scholar
Karan, H. & Knupp, K. 2009 Radar and profiler analysis of colliding boundaries: a case study. Mon. Weath. Rev. 137, 2203–2222.Google Scholar
Kingsmill, D. E. & Andrew, C. N. 2003 An observational study of atmospheric bore formation from colliding density currents. Mon. Weath. Rev. 131, 2985–3002.Google Scholar
Koch, S. E., Dorian, P. B., Ferrare, R., Melfi, S., Skillman, W. C. & Whiteman, D. 1991 Structure of an internal bore and dissipating gravity current as revealed by Raman lidar. Mon. Weath. Rev. 119, 857–887.Google Scholar
Lapworth, A. 2005 Collision of two sea-breeze fronts observed in Wales. Weather 60, 316–318.Google Scholar
Liu, X. & Katz, J. 2006 Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Exp. Fluids 41, 227–240.Google Scholar
Mahoney, W. P. III 1988 Gust front characteristics and the kinematics associated with interacting thunderstorm outflows. Mon. Weath. Rev. 116, 1474–1492.Google Scholar
Manasseh, R., Ching, C. Y. & Fernando, H. J. S. 1998 The transition from density-driven to wave-dominated isolated flows. J. Fluid Mech. 361, 253–274.Google Scholar
Marino, B., Thomas, L. & Linden, P. 2005 The front condition for gravity currents. J. Fluid Mech. 536, 49–78.Google Scholar
Mashayek, A., Caulfield, C. P. & Peltier, W. R. 2013 Time-dependent, non-monotonic mixing in stratified turbulent shear flows: implications for oceanographic estimates of buoyancy flux. J. Fluid Mech. 736, 570–593.Google Scholar
Mashayek, A., Caulfield, C. P. & Peltier, W. R. 2017 Role of overturns in optimal mixing in stratified mixing layers. J. Fluid Mech. 826, 522–552.Google Scholar
Mohamed, M. S. & Larue, J. C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195–214.Google Scholar
Orf, L. G., Anderson, J. R. & Straka, J. M. 1996 A three-dimensional numerical analysis of colliding microburst outflow dynamics. J. Atmos. Sci. 53, 2490–2511.Google Scholar
Princevac, M., Fernando, H. J. S. & Whiteman, C. D. 2005 Turbulent entrainment into natural gravity-driven flows. J. Fluid Mech. 533, 259–268.Google Scholar
Purdom, J. F. 1976 Some uses of high-resolution GOES imagery in the mesoscale forecasting of convection and its behavior. Mon. Weath. Rev. 104, 1474–1483.Google Scholar
Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95–110.Google Scholar
Scarano, F. 2002 Iterative image deformation methods in PIV. Meas. Sci. Technol. 13, R1.Google Scholar
Simpson, J. E. 1987 Gravity Currents: In the Environment and the Laboratory. Ellis Horwood Limited.Google Scholar
Shin, J. 2002 Colliding Gravity Currents. University of Cambridge.Google Scholar
Shin, J., Dalziel, S. & Linden, P. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.Google Scholar
Sokolov, M., Hussain, A., Kleis, S. & Husain, Z. 1980 A ‘turbulent spot’ in an axisymmetric free shear layer. Part 1. J. Fluid Mech. 98, 65–95.Google Scholar
Strang, E. & Fernando, H. 2001 Entrainment and mixing in stratified shear flows. J. Fluid Mech. 428, 349–386.Google Scholar
Wakimoto, R. M. & Kingsmill, D. E. 1995 Structure of an atmospheric undular bore generated from colliding boundaries during CaPE. Mon. Weath. Rev. 123, 1374–1393.Google Scholar
van der Wiel, K., Gille, S. T., Smith, S. G. L., Linden, P. F. & Cenedese, C. 2017 Characteristics of colliding sea breeze gravity current fronts: a laboratory study. Q. J. R. Meteorol. Soc. 143 (704), 1434–1441.Google Scholar
Wilson, J. W. & Schreiber, W. E. 1986 Initiation of convective storms at radar-observed boundary-layer convergence lines. Mon. Weath. Rev. 114, 2516–2536.Google Scholar
Xu, D. & Chen, J. 2012 Experimental study of stratified jet by simultaneous measurements of velocity and density fields. Exp. Fluids 53, 145–162.Google Scholar
Zhong, Q., Hussain, F. & Fernando, H. J. S. 2018 Application of phase averaging to investigate spasmodic mixing in environmental flows. J. Environ. Fluid Mech. (under review).Google Scholar
Zhong, Q., Li, D., Chen, Q. & Wang, X. 2015 Coherent structures and their interactions in smooth open channel flows. Environ. Fluid Mech. 15, 653–672.Google Scholar
Zilberman, M., Wygnanski, I. & Kaplan, R. 1977 Transitional boundary layer spot in a fully turbulent environment. Phys. Fluids 20, S258–S271.Google Scholar