Steady Solutions of Forced Burgers Equation

Makoto Okamura; Takuji Kawahara

doi:10.1143/JPSJ.52.3800

Steady Solutions of Forced Burgers Equation

Makoto Okamura, Takuji Kawahara

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

The Hopf-Cole transformation is used to obtain a steady solution of the forced Burgers equation when the driving force is a sinusoid. A reduced linear equation of damped Mathieu type is solved numerically by a Fourier expansion method. It is found that steady solutions exist for arbitrary values of the viscosity and the forcing. Whether the waveform is smooth or a shock appears depends on the relative magnitudes of the viscosity and the forcing. Comparisons are made with analytical solutions in some limiting cases and also with matched solutions.

Original language	English
Pages (from-to)	3800-3806
Number of pages	7
Journal	Journal of the Physical Society of Japan
Volume	52
Issue number	11
DOIs	https://doi.org/10.1143/JPSJ.52.3800
Publication status	Published - Jan 1 1983
Externally published	Yes

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

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10.1143/JPSJ.52.3800

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AB - The Hopf-Cole transformation is used to obtain a steady solution of the forced Burgers equation when the driving force is a sinusoid. A reduced linear equation of damped Mathieu type is solved numerically by a Fourier expansion method. It is found that steady solutions exist for arbitrary values of the viscosity and the forcing. Whether the waveform is smooth or a shock appears depends on the relative magnitudes of the viscosity and the forcing. Comparisons are made with analytical solutions in some limiting cases and also with matched solutions.

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Steady Solutions of Forced Burgers Equation

Abstract

All Science Journal Classification (ASJC) codes

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