ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-10-6777-2010 Lagrangian mixing in an axisymmetric hurricane model Rutherford B. 1 Dangelmayr G. 1 Persing J. 1 Kirby M. 1 Montgomery M. T. 2 Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA Department of Meteorology, Naval Postgraduate School, Monterey, CA 93943-5114, USA 23 07 2010 10 14 6777 6791 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/10/6777/2010/acp-10-6777-2010.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/10/6777/2010/acp-10-6777-2010.pdf

This paper discusses the extension of established Lagrangian mixing measures to make them applicable to data extracted from a 2-D axisymmetric hurricane simulation. Because of the non-steady and unbounded characteristics of the simulation, the previous measures are extended to a moving frame approach to create time-dependent mixing rates that are dependent upon the initial time of particle integration, and are computed for nonlocal regions. The global measures of mixing derived from finite-time Lyapunov exponents, relative dispersion, and a measured mixing rate are applied to distinct regions representing different characteristic feautures within the model. It is shown that these time-dependent mixing rates exhibit correlations with maximal tangential winds during a quasi-steady state, establishing a connection between mixing and hurricane intensity.

 References Antonsen~Jr., T M., Zhencan~Fan, Ott, E., and Garcia-Lopez, E.: The role of chaotic orbits in the determination of power spectra of passive scalars, Phys. Fluids, 8, 3094–3104, 1996. Artale, V., Boffetta, G., Celani, A., Cencini, M., and Vulpiani, A.: Dispersion of passive tracers in closed basins: Beyond the diffusion coefficient, Phys. Fluids, 9, 3162–3171, 1997. Braun, S A.: A cloud-resolving simulation of Hurricane Bob (1991): Storm structure and eyewall buoyancy, Mon. Weather Rev., 130, 1573–1592, 2002. Cram, T A.,~Persing, J., Montgomery, M T., and Braun, S A.: A Lagrangian trajectory view on transport and mixing processes between the eye, eyewall, and environment using a high resolution simulation of hurricane Bonnie (1998), J. Atmos. Sci., 64, 1835–1856, 2007. d'Ovidio, F., Fernandez, V., and Hernandez-Garcia, E.: Mixing structures in the Mediterranean Sea from finite-size Lyapunov exponents, Geophy. Res. Lett., 31(17), L17203, doi:10.1029/2004GL020328, 2004. Dunkerton, T J., Montgomery, M T., and Wang, Z.: Tropical cyclogenesis in a tropical wave critical layer: easterly waves, Atmos. Chem. Phys., 9, 5587–5646, doi:10.5194/acp-9-5587-2009, 2009. Frank, W M. and Ritchie, E A.: Effects of environmental flow upon tropical cyclone structure, Mon. Weather Rev., 127, 2044–2061, 1999. Frank, W M. and Ritchie, E A.: Effects of vertical wind shear on the intensity and structure of numerically simulated hurricanes., Mon. Weather Rev., 129, 2249–2269, 2001. Green, M A., Rowley, C., and Haller, G.: Detection of Lagrangian coherent structures in 3D turbulence, J. Fluid Mech., 2006. Haller, G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows, Physica D, 149, 248–277, 2001. Haller, G.: Finding finite-time invariant manifolds in two-dimensioanl velocity fields, Chaos, 10, 99–108, 2000. Haller, G.: Lagrangian coherent structures from approximate velocity data, Phys. Fluid., 14, 1851–1861, 2002. Haller, G.: Exact theory of unsteady separation for two-dimensional flows, J. Fluid Mech., 512, 257–311, 2004. Haller, G. and Poje, A.: Finite time transport in aperiodic flows, Physica D, 119, 352–380, 1997. Haller, G. and Yuan, G.: Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147, 352–370, 2000. Huber, M., McWilliams, J C., and Ghil, M.: A climatology of turbulent dispersion in the troposphere, J. Atmos. Sci., 58, 2377–2394, 2001. Ide, K., Small, D., and Wiggins, S.: Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets, Nonlinear Processes in Geophysics, 9(3/4), 237–263, 2002. Koh, T Y. and Legras, B.: Hyperbolic lines and the stratospheric polar vortex, Chaos, 12(2), 382–394, 2002. Kossin, J. and Eastin, M D.: Two distinct regimes in the kinematic and thermodynamic structure of the hurricane eyewall, J. Atmos. Sci., 58, 1079–1090, 2001. Kossin, J. and Schubert, W H.: Mesovortices, polygonal flow patterns, and rapid pressure falls in hurricane-like vortices, J. Atmos. Sci., 58, 2196–2209, 2001. Malhotra, N. and Wiggins, S.: Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic time-dependence, with applications to Rossby wave flow, J. Nonlinear Sci., 8, 401–456, 1999. Montgomery, M T., Bell, M M., S A. and Black, M.: Hurricane Isabel (2003): New insights into the physics of intense storms. Part I: Mean vortex structure and maximum intensity estimates., B. Am. Meteorol. Soc., 87, 1349–1354, 2006. Ottino, J M.: The kinematics of mixing: stretching, chaos, and transport, Cambridge University Press, New York, USA, 1989. Persing, J. and Montgomery, M T.: Hurricane superintensity, J. Atmos. Sci., 60, 2349–2371, 2003. Smith, R K., Montgomery, M T., and Zhu, H.: Buoyancy in tropical cyclones and other rapidly rotating atmospheric vortices, Dynam. Atmos. Oceans, 40, 189–208, 2005. Roll, H.: Physics of the marine atmosphere, Academic Press, 426 pp., 1965. Rotunno, R. and Emanuel, K.: An air-sea interaction theory for tropical cyclones. Part II:evolutionary study using a nonhydrostatic axisymmetric numerical model, J. Atmos. Sci., 44, 542–561, 1987. Rutherford, B., Dangelmayr, G., Persing, J., Schubert, W. H., and Montgomery, M. T.: Advective mixing in a nondivergent barotropic hurricane model, Atmos. Chem. Phys., 10, 475–497, doi:10.5194/acp-10-475-2010, 2010. Salman, H., Ide, K., and Jones, C K R T.: Using flow geometry for drifter deployment in Lagrangian data assimilation, Tellus A., 60(2), 321–335, 2008. Schubert, W H., Montgomery, M T., Taft, R K., Guinn, T A, Fulton, S R., Kossin, J P., and Edwards, J P. : Polygonal eyewalls, asymmetric eye contraction, and potential vorticity mixing in hurricanes, J. Atmos. Sci., 56, 1197–1223, 1999. Shadden, S C., Lekein, F., and Marsden, J E.: Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows, Physica D, 212, 271–304, 2005. Smagorinsky, J.: General circulation experiments with the primitive equation. I: The basic experiment, Mon. Wea. Rev., 91, 99–164, 1963. Surana, A. and Haller, G.: Ghost manifolds in slow-fast systems, with applications to unsteady fluid flow separation, Physica D, 237 1507–1529, 2008. Voth, G A. and T.C Saint, G D., and Gollub, J.: Mixing rates and symmetry breaking in two-dimensional chaotic flow, Phys. Fluid., 15, 2560–2566, 2003. Willoughby, H E.: Tropical cyclone eye thermodynamics, Mon. Weather Rev., 126, 3053–3067, 2001. Zhang, D L., Y L. and Yau, M K.: A multiscale numerical study of Hurricane Andrew (1992). Part V: Inner core thermodynamics, Mon. Weather Rev., 130, 2745–2763, 2002.