World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

The Effect of Shear on the Generation of Gravity Waves : Volume 17, Issue 2 (12/04/2010)

By Humi, M.

Click here to view

Book Id: WPLBN0003980660
Format Type: PDF Article :
File Size: Pages 10
Reproduction Date: 2015

Title: The Effect of Shear on the Generation of Gravity Waves : Volume 17, Issue 2 (12/04/2010)  
Author: Humi, M.
Volume: Vol. 17, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


APA MLA Chicago

Humi, M. (2010). The Effect of Shear on the Generation of Gravity Waves : Volume 17, Issue 2 (12/04/2010). Retrieved from

Description: Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA. Previous research regarding the solutions of Long's equation always presumed that the flow far upstream is without shear. In this paper we derive the proper form of this equation when shear is present. We then apply a sequence of transformations to this equation which make it possible to linearize it while preserving its physical contents. We then derive conditions under which the solutions of this linear equation admit the existence (or creation) of gravity waves. We present also a solution of this model equation when the presence of shear in the overall flow is small.

The effect of shear on the generation of gravity waves

Baines, P. G.: Topographic effects in Stratified flows, Cambridge Univ. Press, New-York, 1995.; Nappo, C. J.: Atmospheric Gravity Waves, Academic Press, Boston, 2002.; 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(7), 939–942, 1998.; Doyle, J. D., Volkert, H., Dornbrac, A., Hoinka, K. P., and Hogan, T. F.: Aircraft measurements and numerical simulations of mountain waves over the central Alps: A pre-MAP test case, Q. J. Roy. Meteor. Soc., 128, 2175–2184, 2006.; 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 Moorem, D. W.: Steady two dimensional flow of fluid of variable density over an obstacle, J. Fluid. Mech., 28, 353–370, 1967.; Dubreil-Jacotin, M. L.: Sur la determination rigoureuse des ondes permanentes periodiques d'ampleur finie, J. Math. Pure. Appl., 13, 217–291, 1934.; Durran, D. R.: Two-Layer solutions to Long's equation for vertically propagating mountain waves, Q. J. Roy. Meteor. Soc., 118, 415–433, 1992.; Eckermann, S. D. and Preusse, P.: Global measurements of stratospheric mountain waves from space, Science, 286, 1534–1537, 1999.; 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. Ocean. Tech., 21, 495–500, 2004b.; Humi, M.: On the Solution of Long's Equation with Shear, Siam J. Appl. Math., 66(6), 1839–1852, 2006.; Humi, M.: Density representation of Long's equation, Nonlin. Processes Geophys., 14, 273–283, 2007.; Humi, M.: Long's equation in terrain following coordinates, Nonlin. Processes Geophys., 16, 533–541, 2009.; 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.; Miropol'sky, Yu. Z.: Propagation of internal waves in an ocean with horizontal density field non-uniformities, Izv. Atmos. Ocean. Phy+, 10, 312–318, 1974.; Miropol'sky, Yu. Z.: Dynamics of Internal Gravity waves in the Ocean, Kluwer, Boston, 2001.; Peltier, W. R. and Clark, T. L.: Nonlinear mountain waves in two and three spatial dimensions, Q. J. Roy. Meteor. Soc., 109, 527–548, 1983.; Picone, M.: Sui valori eccezionali di un parametro da cui dipende un'equazione differenziale lineare del secondo ordine, Ann. Scuola Norm. Sup. Pisa, 11, 1–141, 1909 (in Italian).; Shutts, G. J., Kitchen, M., and Hoare, P. H.: A large amplitude gravity wave in the lower stratosphere detected by radiosonde, Q. J. Roy. Meteor. Soc., 114, 579–594, 1988.; Shutts, G. J., Healey, P., and Mobbs, S. D.: A multiple sounding technique for the study of gravity waves, Q. J. Roy. Meteor. Soc., 120, 59–77, 1994.; Shutts, G. J.: Stationary gravity-wave structure in flows with directional wind shear, Q. J. Roy. Meteor. Soc., 124, 1421–1442, 1998.; 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.; Sturm, J. C. F.: Sur les equations differenielles lineares du second ordre, J. Math. Pure Appl., 1, 106–186, 1836 (


Click To View

Additional Books

  • Solar Wind Vs Magnetosheath Turbulence a... (by )
  • On the Character of Cosmic Ray Variation... (by )
  • Forecast Improvement in Lorenz 96 System... (by )
  • Isotropy Restoration Toward High-beta Sp... (by )
  • Analysis of the Geomagnetic Activity of ... (by )
  • Extreme Fluctuations of Vertical Velocit... (by )
  • Observing Spatio-temporal Clustering and... (by )
  • Finding Recurrence Networks' Threshold A... (by )
  • Frequency Distributions: from the Sun to... (by )
  • Phase Space Holes and Elementary Radiati... (by )
  • Role of the Hydrological Cycle in Regula... (by )
  • Emergent Behavior in a Coupled Economic ... (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.