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Landau–Hopf theory of turbulence

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In physics, the Landau–Hopf theory of turbulence, named for Lev Landau and Eberhard Hopf, was until the mid-1970s[clarification needed] the accepted theory of how a fluid flow becomes turbulent. The theory says that as a fluid flows faster, it develops more and more Fourier modes. At first a few modes dominate, but under stronger conditions, it forces the modes to become power-law distributed, as explained in Kolmogorov's theory of turbulence.


  • Landau, L. D. (1944). "К проблеме турбулентности" [On the problem of turbulence]. Doklady Akademii Nauk SSSR. 44: 339–342.
  • Hopf, E. (1948). "A mathematical example displaying the features of turbulence". Communications on Pure and Applied Mathematics. 1: 303–322. doi:10.1002/cpa.3160010401.