Abstract
The Method of Characteristics. The method of characteristics is only one means of solving hyperbolic differential equations or systems of differential equations with real characteristics. Problems of this kind are also solved by related methods, such as simple wave theory, the Riemann method of integration, and the marching method. In addition, in a nonlinear system, shocks or jumps occur which cannot be studied by means of systems of equations with real characteristics, but must be studied by other methods. Loosely speaking, all methods mentioned above can be grouped under the single heading—the method of characteristics. If this definition is used, the method of characteristics is not new to meteorology. Richardson used the marching method correctly in the initial example in his monumental work on numerical weather prediction [15, pp. 6–10]. Rossby [16] used the Riemann method of integration to discuss the effect of a line source of planetary waves in a barotropic atmosphere. In all of its phases, however, the method of characteristics has been applied most often and most thoroughly to problems in gas dynamics and the flow of a shallow layer of fluid with a free surface. Riemann devised his method of integration to solve the problem of one-dimensional unsteady flow of a gas in a pipe, and most other methods have been developed with such problems in mind. Courant and Friedrichs [5] give a bibliography of this work.
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References
Abdullah, A. J., “Cyclogenesis by a Purely Mechanical Process.” J. Meteor., 6:86–97 (1949).
Alpert, L., “Notes on the Weather and Climate of Sey mour Island, Galapagos Archipelago.” Bull. Amer. meteor. Soc., 27:200–209 (1946).
Berggren, R., Bolin, B., and Rossby, C.-G., “An Aero-logical Study of Zonal Motion, Its Perturbations and Break-Down.” Tellus, Vol. 1, No. 2, pp. 14–37 (1949).
Brunk, I. W., “The Pressure Pulsation of 11 April 1944.” J. Meteor., 6:181–187 (1949).
Courant, R., and Friedrichs, K. O., Supersonic Flow and Shock Waves. New York, Interscience, 1948.
Crocker, A. M., Godson, W. L., and Penner, C. M., “Frontal Contour Charts.” J. Meteor., 4:95–99 (1947).
Freeman, J. C., “An Analogy between the Equatorial Easterlies and Supersonic Gas Flows.” J. Meteor., 5:138–146 (1948).
Freeman, J. C., “Reply: The Usefulness of Incompressible Models.” J. Meteor., 6:287 (1949).
Freeman, J. C., “Map Analysis in the Vicinity of a Pressure Jump.” Bull. Amer. meteor. Soc., 31:324–325 (1950).
Freeman, J. C., “The Wind Field of the Equatorial East Pacific as a Prandtl-Meyer Expansion.” Bull. Amer. meteor. Soc., 31:303–304 (1950).
Harrison, H. T., and Orendorff, W. K., “Pre-cold-frontal Squall Lines.” United Air Lines Meteor. Dept. Circ. No. 16 (1941).
Isenberg, J. S., The Method of Characteristics in Compressible Flow, Part I. Tech. Rep. No. F-TR-1173A-ND, Hdqtrs. Air Materiel Command, Wright Field, Dayton, Ohio, 1947.
Maynard, R. H., “Radar and Weather.” J. Meteor., 2:214–226 (1945).
McGurrin, M., The Principle of Open Channel Flow Ap plied to the Formation of Tornadoes. Unpublished, available at the Library of the U. S. Weather Bureau, Washington, D. C., 1942.
Richardson, L. F., Weather Prediction by Numerical Process. Cambridge, University Press, 1922.
Rossby, C.-G., “On the Propagation of Frequencies and Energy in Certain Types of Oceanic and Atmospheric Waves.” J. Meteor., 2:187–204 (1945).
Rossby, C.-G., “On the Dynamics of Certain Types of Blocking Waves.” J. Chinese geophys. Soc., 2:1–13 (1950).
Sherman, L., “The Neglect of Compressibility in the Flow of Gas at Low Speeds.” J. Meteor., 6:286–287 (1949).
Tepper, M., “A Proposed Mechanism of Squall Lines—The Pressure Jump Line.” J. Meteor., 7:21–29 (1950).
Tepper, M., “On the Origin of Tornadoes.” Bull. Amer. meteor. Soc., 31:311–314 (1950).
Tepper, M., and Freeman, J. C., “Analogy between Equatorial [Easterlies] and Supersonic Flows.” J. Meteor., 6:226 (1949).
U. S. Weather Bureau, Atlas of Climatic Charts of the Oceans. W. B. Publ. No. 1247, Washington, D. C., 1938.
Williams, D. T., “A Surface Micro-Study of Squall-Line Thunderstorms.” Mon. Wea. Rev. Wash., 76:239–246 (1948).
Williams, N. R., “Development of Dust Whirls and Similar Small-Scale Vortices.” Bull. Amer. meteor. Soc., 29:106–117 (1948).
Wexler, H., “Structure of Hurricanes as Determined by Radar.” Ann. N. Y. Acad. Sci., 48:821–844 (1947)
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Freeman, J.C. (1951). The Solution of Nonlinear Meteorological Problems by the Method of Characteristics. In: Malone, T.F. (eds) Compendium of Meteorology. American Meteorological Society, Boston, MA. https://doi.org/10.1007/978-1-940033-70-9_36
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DOI: https://doi.org/10.1007/978-1-940033-70-9_36
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