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Density Representation of Long's Equation : Volume 14, Issue 3 (11/06/2007)

By Humi, M.

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Book Id: WPLBN0004019824
Format Type: PDF Article :
File Size: Pages 11
Reproduction Date: 2015

Title: Density Representation of Long's Equation : Volume 14, Issue 3 (11/06/2007)  
Author: Humi, M.
Volume: Vol. 14, Issue 3
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2007
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Humi, M. (2007). Density Representation of Long's Equation : Volume 14, Issue 3 (11/06/2007). Retrieved from http://hawaiilibrary.net/


Description
Description: Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA. Long's equation describes two dimensional stratified atmospheric flow over terrain. Its solutions using regular first order perturbations and linear approximation were investigated analytically and numerically by many authors. Special attention was paid to the properties of the gravity waves that have been predicted to be generated as a result. In this paper we derive a new representation of this equation in terms of the atmospheric density. This new equation is used then to study the steady state that results from some ideal upstream density profiles and the generation of gravity waves. Furthermore we compare the new formulation with the stream function formulation of Long equation and develop new criteria for the stability of the flow.

Summary
Density representation of Long's equation

Excerpt
Durran, D. R.: Two-Layer solutions to Long's equation for vertically propagating mountain waves, Quart. J. Roy. Meteorol. Soc., 118, 415–433, 1992.; Abramowitz, M. and Stegun, I. A.: Handbook of Mathematical Functions, Dover Publications, New-York, 1970.; Baines, P. G.: Topographic effects in Stratified flows, Cambridge Univ. Press, New York, 1995.; Davis, K. S.: Flow of Nonuniformly Stratified Fluid of Large Depth over Topography, M.Sc thesis in Mechanical Engineering, MIT, Cambridge, MA, 1999.; Dewan, E. M., Picard, R. H., O'Neil, R. R., Gardiner, H. A., Gibson, J., Mill, J. D., Richards, E., Kendra, M., and Gallery, W. O.: MSX satellite observations of thunderstorm-generated gravity waves in mid-wave infrared images of the upper stratosphere, Geophys. Res. Lett., 25, 939–942, 1998.; Drazin, P. G.: On the steady flow of a fluid of variable density past an obstacle, Tellus, 13, 239–251, 1961.; Drazin, P. G. and Moore, D. W.: Steady two dimensional flow of fluid of variable density over an obstacle, J. Fluid. Mech., 28, 353–370, 1967.; Dutton, J. A.: The Ceaseless Wind, Dover Publications, New York, 1986.; Eckermann, S. D. and Preusse, P.: Global measurements of stratospheric mountain waves from space, Science, 286, 1534–1537, 1999.; Haagenson, P. L., Dudhia, J., Grell, G. A., and Stauffer, D. R.: The Penn State/NCAR mesoscale model(MM5), 1994, Source code documentation, NCAR Technical Note, NCAR/TN-392+STR, 1994.; Humi, M.: On the Solution of Long's Equation Over Terrain, Il Nuovo Cimento C, 27, 219–229, 2004a.; Humi, M.: Estimation of Atmospheric Structure Constants from Airplane Data, J. Atmos. Oceanic Technol., 21, 495–500, 2004b.; Humi, M.: On the Solution of Long's Equation with Shear, Siam J. App. Math, 66(6), 1839–1852, 2006.; Jumper, G. Y., Murphy, E. A., Ratkowski, A. J., and Vernin, J.: Multisensor Campaign to correlate atmospheric optical turbulence to gravity waves, AIAA paper, AIAA-2004-1077, 2004.; Lily, D. K. and Klemp, J. B.: The effect of terrain shape on nonlinear hydrostatic mountain waves, J. Fluid Mech., 95, 241–261, 1979.; Long, R. R.: Some aspects of the flow of stratified fluids I. Theoretical investigation, Tellus, 5, 42–57, 1953.; Long, R. R.: Some aspects of the flow of stratified fluids II. Theoretical investigation, Tellus, 6, 97–115, 1954.; Long, R. R.: Some aspects of the flow of stratified fluids III. Continuous density gradients, Tellus, 7, 341–357, 1955.; Long, R. R.: The motion of fluids with density stratification, J. Geophys. Res., 64, 2151–2163, 1959.; Nappo, C. J.: Atmospheric Gravity Waves, Academic Press, Boston, 2002.; Peltier, W. R. and Clark, T. L.: Nonlinear mountain waves in two and three spatial dimensions, Quart. J. Roy. Meteorol. Soc., 109, 527–548, 1983.; Shutts, G. J., Kitchen, M., and Hoare, P. H.: A large amplitude gravity wave in the lower stratosphere detected by radiosonde, Quart. J. Roy. Meteorol. Soc., 114, 579–594, 1988.; Smith, R. B.: Linear theory of stratified hydrostatic flow past an isolated mountain, Tellus, 32, 348–364, 1980.; Smith, R. B.: Hydrostatic airflow over mountains, Adv. Geophys., 31, 1–41, 1989.; Yih, C.-S.: Equations governing steady two-dimensional large amplitude motion of a stratified fluid, J. Fluid Mech., 29, 539–544, 1967.; Yih, C.-S.: Stratified flows, Academic Press, New York, NY, 1980.

 

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