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3 questions
4
votes
1
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Nonlinear waves equations derivation from Navier-Stokes
In my professor's lecture notes, I came across the next approach of studying non-linear waves in fluids. So we have compressible Navier-Stokes and continuity equation in 1D and we assume adiabatic ...
- 1,169
2
votes
2
answers
597
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Burgers' equations and shock waves
Given Burgers' equation, $m_{\tau} + mm_x = 0,$ one expects to have discontinuities and thus shock waves in the case the initial conditions are smooth. For example, one may take $m_0(x) = \sin(x), x\...
- 173
1
vote
1
answer
278
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Solution of Burgers' equation in preshock region
According to Hamilton's & Blackstock's Nonlinear acoustics (Section 4.5.4) the solution of Burgers' equation of the form:
$$
\frac{\partial P}{\partial \sigma} - \frac{1}{\Gamma}\frac{\partial^2 ...
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