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Matematica Aplicada e Computacional

Título
Burgers turbulence and the spurious $k^{-3}$ energy spectrum debunked
Expositor
Uriel Frisch

Laboratoire Lagrange, Observatoire and Universite Cote d'Azur Nice, France
Data
Quinta-feira, 17 de maio de 2018, 14:00
Local
Sala 333
Resumo

Formal manipulations of the one-dimensional inviscid and unforced Burgers equation suggest that the energy spectrum $E(k)$  might follow a $|k|^{-3}$ rather than the $|k|^{-2}$, generally associated with shocks. The use of the Fourier-Lagrangian solution, introduced by Fournier and Frisch (L'equation de Burgers deterministe et statistique. 1983. J. Mec. Theor. Appl, vol. 2, pp. 699-750.) shows that the spurious $|k|^{-3}$ solutions stem from an improper use of the multi-stream behaviour associated with the Burgers-Vlasov equation. This will be a blackboard lecture intended for advanced students and specialists in PDEs, field theory and/or catastrophy theory.