References

ACP

Atmospheric Chemistry and Physics

ACP

1680-7324

Copernicus GmbH

Göttingen, Germany

10.5194/acp-11-9395-2011

Simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear

Riemer

¹ ³ Montgomery

M. T.

¹ ²

Department of Meteorology, Naval Postgraduate School, Monterey, CA, USA

NOAA's Hurricane Research Division, Miami, FL, USA

current address: Institut für Physik der Atmosphäre, Johannes Gutenberg-Universität, Mainz, Germany

12 09 2011

11 17 9395 9414

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/11/9395/2011/acp-11-9395-2011.html

The full text article is available as a PDF file from http://www.atmos-chem-phys.net/11/9395/2011/acp-11-9395-2011.pdf

A major impediment to the intensity forecast of tropical cyclones (TCs) is believed to be associated with the interaction of TCs with dry environmental air. However, the conditions under which pronounced TC-environment interaction takes place are not well understood. As a step towards improving our understanding of this problem, we analyze here the flow topology of a TC immersed in an environment of vertical wind shear in an idealized, three-dimensional, convection-permitting numerical experiment. A set of distinct streamlines, the so-called manifolds, can be identified under the assumptions of steady and layer-wise horizontal flow. The manifolds are shown to divide the flow around the TC into distinct regions. The manifold structure in our numerical experiment is more complex than the well-known manifold structure of a non-divergent point vortex in uniform background flow. In particular, one manifold spirals inwards and ends in a limit cycle, a meso-scale dividing streamline encompassing the eyewall above the layer of strong inflow associated with surface friction and below the outflow layer in the upper troposphere. From the perspective of a steady and layer-wise horizontal flow model, the eyewall is well protected from the intrusion of environmental air. In order for the environmental air to intrude into the inner-core convection, time-dependent and/or vertical motions, which are prevalent in the TC inner-core, are necessary. Air with the highest values of moist-entropy resides within the limit cycle. This "moist envelope" is distorted considerably by the imposed vertical wind shear, and the shape of the moist envelope is closely related to the shape of the limit cycle. In a first approximation, the distribution of high- and low-θe air around the TC at low to mid-levels is governed by the stirring of convectively modified air by the steady, horizontal flow. Motivated by the results from the idealized numerical experiment, an analogue model based on a weakly divergent point vortex in background flow is formulated. The simple kinematic model captures the essence of many salient features of the manifold structure in the numerical experiment. A regime diagram representing realistic values of TC intensity and vertical wind shear can be constructed for the point-vortex model. The results indicate distinct scenarios of environmental interaction depending on the ratio of storm intensity and vertical-shear magnitude. Further implications of the new results derived from the manifold analysis for TCs in the real atmosphere are discussed.

References 1

Barnes, G M., Zipser, E J., Jorgensen, D., and Marks, F.: Mesoscale and convective structure of a hurricane rainband, J. Atmos. Sci., 40, 2125–2137, 1983.

Bender, M A.: The effect of relative flow on the asymmetric structure in the interior of hurricanes, J. Atmos. Sci., 54, 703–724, 1997.

Black, M L., Gamache, J F., Marks, F D., Samsury, C E., and Willoughby, H E.: Eastern Pacific Hurricanes Jimena of 1991 and Olivia of 1994: The effect of vertical shear on structure and intensity, Mon. Weather Rev., 130, 2291–2312, 2002.

Bolton, D.: The computation of equivalent potential temperature, Mon. Weather Rev., 108, 1046–1053, 1980.

Bui, H. H., Smith, R. K., Montgomery, M T., and Peng, J.: Balanced and unbalanced aspects of tropical-cyclone intensification, Q. J. R. Meteorol. Soc., 135, 715–1731, 2009.

Carr, L E. and Williams, R T.: Barotropic vortex stability to perturbations from axisymmetry, J. Atmos. Sci., 46, 3177–3191, 1989.

Charney, J G.: A note on large-scale motions in the tropics, J. Atmos. Sci., 20, 607–609, 1963.

Chen, Y. and Yau, M. K.: Spiral bands in a simulated hurricane. Part I: Vortex Rossby wave verification, J. Atmos. Sci., 58, 2128–2145, 2001.

Chen, Y., Brunet, G., and Yau, M. K.: Spiral bands in a simulated hurricane. Part II: Wave Activity Diagnostics, J. Atmos. Sci., 60, 1240–1256, 2003.

Cotton, W R., Pielke, R A., Walko, R L., Liston, G E., Tremback, C J., Jiang, H., McAnelly, R L., Harrington, J Y., Nicholls, M E., Carrio, G G., and McFadden, J P.: RAMS 2001: Current status and future directions, Meteorol. Atmos. Phys., 82, 5–29, 2003.

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.

Dunion, J P. and Velden, C S.: The impact of the Saharan air layer on Atlantic tropical cyclone activity, B. Am. Meteorol. Soc., 85, 353–365, 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, http://dx.doi.org/10.5194/acp-9-5587-2009doi:10.5194/acp-9-5587-2009, 2009.

Emanuel, K., DesAutels, C., Holloway, C., and Korty, R.: Environmental control of tropical cyclone intensity, J. Atmos. Sci., 61, 843–858, 2004.

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.

Haller, G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows, Physica D, 149, 248–277, 2001.

Holton, J.: An introduction to dynamic meteorology, AcademicPress, London, 4th edn., 387–389, 2004.

Houze, R A., Cetrone, J., Brodzik, S R., Chen, S S., Zhao, W., Lee, W.-C., Moore, J A., Stossmeister, G J., Bell, M M., and Rogers, R F.: The hurricane rainband and intensity change experiment: Observations and modeling of Hurricanes Katrina, Ophelia, and Rita, B. Am. Meteorol. Soc., 87, 1503–1521, 2006.

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 Proc. Geoph., 9, 237–263, 2002.

Jones, S C.: The evolution of vortices in vertical shear. I: Initially barotropic vortices, Q. J. R. Meteorol. Soc., 121, 821–851, 1995.

Kimball, S. K.: A modeling study of hurricane landfall in a dry environment, Mon. Weather Rev., 134, 1901–1918, 2006.

Lamb, H.: Hydrodynamics, Dover Publications, New York, 6th edn., 1945.

Mallen, K J., Montgomery, M T., and Wang, B.: Reexamining the near-core radial structure of the tropical cyclone primary circulation: implications for vortex resiliency, J. Atmos. Sci., 62, 408–425, 2005.

Marks, F D., Houze, R A., and Gamache, J F.: Dual-aircraft investigation of the inner core of Hurricane Norbert. Part I: Kinematic structure, J. Atmos. Sci., 49, 919–942, 1992.

Melander, M V., McWilliams, J C., and Zabusky, N J.: Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation, J. Fluid Mech., 178, 137–159, 1987.

Montgomery, M T. and Kallenbach, R J.: A theory for vortex Rossby-waves and its application to spiral bands and intensity changes in hurricanes, Q. J. R. Meteorol. Soc., 123, 435–465, 1997.

Nguyen, S V., Smith, R. K., and Montgomery, M T.: Tropical-cyclone intensification and predictability in three dimensions, Q. J. R. Meteorol. Soc., 134, 563–582, 2008.

Pielke, R A., Cotton, W R., Walko, R L., Tremback, C J., Lyons, W A., Grasso, L D., Nicholls, M E., Moran, M D., Wesley, D A., Lee, T J., and Copeland, J. H.: A comprehensive meteorological modeling system – RAMS, Meteorol. Atmos. Phys., 49, 69–91, 1992.

Powell, M D.: Boundary layer structure and dynamics in outer hurricane rainbands. Part II: Downdraft modification and mixed layer recovery, Mon. Weather. Rev., 118, 918–938, 1990.

Reasor, P D., Montgomery, M T., and Grasso, L D.: A new look at the problem of tropical cyclones in vertical shear flow: Vortex resiliency, J. Atmos. Sci., 61, 3–22, 2004.

Riemer, M., Montgomery, M. T., and Nicholls, M. E.: A new paradigm for intensity modification of tropical cyclones: thermodynamic impact of vertical wind shear on the inflow layer, Atmos. Chem. Phys., 10, 3163–3188, http://dx.doi.org/10.5194/acp-10-3163-2010doi:10.5194/acp-10-3163-2010, 2010.

Ritchie, E A. and Frank, W M.: Interactions between simulated tropical cyclones and an environment with a variable Coriolis parameter, Mon. Weather Rev., 135, 1889–1905, 2007.

Roy, R. and Olver, F. W J.: Lambert W function, in: NIST Handbook of Mathematical Functions, edited by Olver, F. W J., Lozier, D M., Boisvert, R F., and Clark, C W., Cambridge University Press, 2010.

Rutherford, B., Dangelmayr, G., and Montgomery, M T.: Lagrangian Coherent Structures in tropical cyclone intensification, Atmos. Chem. Phys. Disc., accepted, 2010.

Sapsis, T. and Haller, G.: Inertial particle dynamics in a hurricane, J. Atmos. Sci., 66, 2481–2492, 2009.

Shelton, K L. and Molinari, J.: Life of a six-hour hurricane, Mon. Weather Rev., 137, 51–67, 2009.

Simpson, R H. and Riehl, H.: Mid-tropospheric ventilation as a constraint on hurricane development and maintenance, in: Proc. Tech. Conf. on Hurricanes, D4.1–-D4.10, Amer. Meteorol. Soc., Miami, FL, 1958.

Smith, R. K., Ulrich, W., and Sneddon, G.: On the dynamics of hurricane-like vortices in vertical-shear flows, Q. J. R. Meteorol. Soc., 126, 2653–2670, 2000.

Tang, B. and Emanuel, K A.: Midlevel ventilation's constraint on tropical cyclone intensity, J. Atmos. Sci., 67, 1817–1830, 2010a.

Tang, B. and Emanuel, K A.: Entropy ventilation in an axisymmetric tropical cyclone model, in: 29th Conference on Hurricanes and Tropical Meteorology, 7C.2, Amer. Meteorol. Soc., Tucson, AZ, 2010b.

Wang, Y.: Vortex Rossby waves in a numerically simulated tropical cyclone. Part I: Overall structure, potential vorticity, and kinetic energy budgets, J. Atmos. Sci., 59, 1213–1238, 2002.

Weatherford, C L. and Gray, W M.: Typhoon structure as revealed by aircraft reconnaissance. Part II: Structural variability, Mon. Weather Rev., 116, 1044–1056, 1988.

Willoughby, H E., Marks, F D., and Feinberg, R J.: Stationary and moving convective bands in hurricanes, J. Atmos. Sci., 41, 3189–3211, 1984.

Zehr, R M.: Environmental vertical wind shear with Hurricane Bertha (1996), Weather Forecast., 18, 345–356, 2003.

Zhang, D.-L. and Kieu, C Q.: Potential vorticity diagnosis of a simulated hurricane. Part II: Quasi-balanced contributions to forced secondary circulations, J. Atmos. Sci., 63, 2898–2914, 2006.

Zipser, E J., Twohy, C. H., Tsay, S.-C., Thornhill, K L., Tanelli, S., Ross, R., Krishnamurti, T N., Ji, Q., Jenkins, G., Ismail, S., Hsu, N C., Hood, R., Heymsfield, G M., Heymsfield, A., Halverson,~J.,~Goodman, H M., Ferrare,~R.,~Dunion,~J P.,~Douglas,~M., Cifelli, R., Chen, G., Browell, E V., and Anderson, B.: The Saharan air layer and the fate of African easterly waves: NASA's AMMA field study of tropical cyclogenesis, B. Am. Meteorol. Soc., 90, 1137–1156, 2009.