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Reading: An exact integral of complete spectral equations for unsteady one-dimensional flow

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Original Research Papers

An exact integral of complete spectral equations for unsteady one-dimensional flow

Author:

George W. Platzman

The University of Chicago, US
About George W.

This investigation was supported through funds provided by the National Science Foundation (Grant NSF-GP-471, Technical Report 16, March 1964). It was completed at the National Center for Atmospheric
Research, Boulder, Colorado, where the author was in residence during 1963-64.

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Abstract

Finite-amplitude, one-dimensional, isothermal flow of a perfect gas is considered. When the flow is organized initially as a “linear” sound wave, it is equivalent to the solution of an “advection equation”. The flow that evolves in this way from an initial state is analyzed by means of a Fourier series in space, with time-dependent coefficients. These coefficients can be determined exactly when the initial velocity is a pure sinusoid. The result is such that the Fourier series in space is a Kapteyn series in time. The series is valid up to the time of shock formation. Throughout this interval the lowest harmonics inferred from severely truncated spectral equations are in good agreement with the exact solution. However, the spectral representation becomes very inefficient as the discontinuous state is approached.

How to Cite: Platzman, G.W., 2012. An exact integral of complete spectral equations for unsteady one-dimensional flow. Tellus A: Dynamic Meteorology and Oceanography, 16(4), pp.422–431. DOI: http://doi.org/10.3402/tellusa.v16i4.8995
Published on 01 Jan 2012.
Peer Reviewed

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