Statistical Properties of Nonlinear Shell Models of Turbulence from Linear Advection Models: Rigorous Results

Details Statistical Properties of Nonlinear Shell Models of Turbulence from Linear Advection Models: Rigorous Results Statistical Properties of Nonlinear Shell Models of Turbulence from Linear Advection Models: Rigorous Results

2006-12-13

arxiv.org/abs/nlin/0612033v1

Nonlinear Sciences

Chaotic Dynamics

7 pages, 4 figures, submitted to Nonlinearity

Scientific paper

10.1088/0951-7715/20/6/006

In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and nonlinear fields coincide. The argument depended on an assumption of continuity of the solutions as a function of a parameter. The aim of this paper is to provide a rigorous proof for the validity of the assumption. In addition we clarify here when the swap of a nonlinear model by a linear one will not work.

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