The Fractional Landau Model

摘要

Herein the Landau model of the transition from laminar to turbulent fluid flow is generalized to include the effect of memory.The original Landau model is quadratically nonlinear and memoryless,with turbulent fluctuations decaying exponentially.However,recent experiments show a dependence of the decay of fluctuations on memory,with the exponential being replaced by an inverse power law.This transition is explained herein as being due to critical slowing down.The fractional calculus is used to model this memory and to relate the index of the inverse power law decay to that of the fractional derivative in time.