An invariant in shock clustering and Burgers turbulence

Details An invariant in shock clustering and Burgers turbulence An invariant in shock clustering and Burgers turbulence

2011-06-15

arxiv.org/abs/1106.2879v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, no figures; v2: corrections made

Scientific paper

1-D scalar conservation laws with convex flux and Markov initial data are now
known to yield a completely integrable Hamiltonian system. In this article, we
rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence
from the perspective of integrable systems. Other relevant physical notions
such as energy dissipation and spectrum are also discussed.

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