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 |
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
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Okamura, M., & Kawahara, T. (1983). Steady Solutions of Forced Burgers Equation. Journal of the Physical Society of Japan, 52(11), 3800-3806. https://doi.org/10.1143/JPSJ.52.3800