NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-20-121-2013 Scaling for lobe and cleft patterns in particle-laden gravity currents Jackson A. 1 Turnbull B. 1 Munro R. 1 Process and Environmental Research Division, Faculty of Engineering, University of Nottingham, Nottingham, UK 18 02 2013 20 1 121 130 Copyright: © 2013 A. Jackson et al. 2013 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://npg.copernicus.org/articles/20/121/2013/npg-20-121-2013.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/20/121/2013/npg-20-121-2013.pdf

Lobe and cleft patterns are frequently observed at the leading edge of gravity currents, including non-Boussinesq particle-laden currents such as powder snow avalanches. Despite the importance of the instability in driving air entrainment, little is known about its origin or the mechanisms behind its development. In this paper we seek to gain a better understanding of these mechanisms from a laboratory scale model of powder snow avalanches using lightweight granular material. <br><br> The instability mechanisms in these flows appear to be a combination of those found in both homogeneous Boussinesq gravity currents and unsuspended granular flows, with the size of the granular particles playing a central role in determining the wavelength of the lobe and cleft pattern. When scaled by particle diameter a relationship between the Froude number and the wavelength of the lobe and cleft pattern is found, where the wavelength increases monotonically with the Froude number.

 References Bush, J., Thurber, B., and F., B.: Particle clouds in homogeneous and stratified environments, J. Fluid Mech., 489, 29–54, <a href="http://dx.doi.org/10.1017/S0022112003005160">https://doi.org/10.1017/S0022112003005160</a>, 2003. Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stabiltiy, Oxford University Press, Oxford, UK, 1961. Duff, R., Harlow, F., and Hirt, C.: Effects of diffusion on interface instability between gases, Phys. Fluids, 5, 417–425, 1962. H{ä}rtel, C., Carlsson, F., and Thunblom, M.: Analysis and direct numerical simulation of the flow at a gravity-current head. Part 2. The lobe-and-cleft instability, J. Fluid Mech., 418, 213–229, 2000. Huppert, H.: Flow and instability of a viscous current down a slope, Nature, 300, 427–9, 1982. Lord Rayleigh: Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, in: Scientific Papers, vol.&nbsp;II, p.&nbsp;200, Cambridge University Press, Cambridge, UK, 1900. Massey, B.: Mechanics Of Fluids, Taylor & Francis, Abingdon, UK, 8th Edn., 2006. McElwaine, J., Patterson, M., and Dalziel, S.: Lobe and cleft formation at the head of a gravity current, Proceedings of the XXI International Congress of Theoretical and Applied Mechanics, 15–21, 2004. Neufeld, J.: Lobe-cleft patterns in the leading edge of a gravity current, M.S. thesis, Department of Physics, University of Toronto, Canada, 2002. Nohguchi, Y. and Ozawa, H.: On the vortex formation at the moving front of lightweight granular particles, Physica D, 238, 20–26, <a href="http://dx.doi.org/10.1016/j.physd.2008.08.019">https://doi.org/10.1016/j.physd.2008.08.019</a>, 2008. Pouliquen, O., Delour, J., and Savage, S.: Fingering in granular flows, Nature, 386, 816–817, 1997. Sharp, D.: An overview of Rayleigh-Taylor instability, Physica D, 12, 3–18, 1984. Simpson, J.: Effects of the lower boundary on the head of a gravity current, J. Fluid Mech., 53, 759–768, 1972. Simpson, J. and Britter, R.: The dynamics of the head of a gravity current advancing over a horizontal surface, J. Fluid Mech., 94, 477–495, 1979. Taylor, G.: The instability of liquid surfaces when accelerated in a direction perpendicular to their planes, I, Proc. R. Soc. Lon. Ser.&nbsp;A, 201, 192–196, 1950. Turnbull, B. and McElwaine, J.: A comparison of powder-snow avalnches at Vallee de la Sionne, Switzerland, with plume theories, J. Glaciol., 53, 30–40, 2007. Turnbull, B. and McElwaine, J.: Experiments on the non-{B}oussineq Flow of Self-Igniting Suspension Currents on a Steep Open Slope, J. Geophys. Res., 113, F01003, <a href="http://dx.doi.org/10.1029/2007JF000753">https://doi.org/10.1029/2007JF000753</a>, 2008. Turnbull, B., McElwaine, J., and Ancey, C.: Kulikovskiy-Sveshnikova-Beghin model of powder snow avalanches: Development and application, J. Geophys. Res., 112, F01004, <a href="http://dx.doi.org/10.1029/2006JF000489">https://doi.org/10.1029/2006JF000489</a>, 2007. Turner, J.: Buoyancy Effects in Fluids, Cambridge University Press, Cambridge, UK, 1973. Youngs, D.: Numerical simulation of turbulent mixing by Rayleigh-Taylor instability, Physica D, 12, 32–34, 1984.