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 | |
| Publication status | Published - Jan 1 1983 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Cite this
Steady Solutions of Forced Burgers Equation. / Okamura, Makoto; Kawahara, Takuji.
In: Journal of the Physical Society of Japan, Vol. 52, No. 11, 01.01.1983, p. 3800-3806.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Steady Solutions of Forced Burgers Equation
AU - Okamura, Makoto
AU - Kawahara, Takuji
PY - 1983/1/1
Y1 - 1983/1/1
N2 - 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.
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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UR - http://www.scopus.com/inward/citedby.url?scp=0020847807&partnerID=8YFLogxK
U2 - 10.1143/JPSJ.52.3800
DO - 10.1143/JPSJ.52.3800
M3 - Article
AN - SCOPUS:0020847807
VL - 52
SP - 3800
EP - 3806
JO - Journal of the Physical Society of Japan
JF - Journal of the Physical Society of Japan
SN - 0031-9015
IS - 11
ER -