ar X iv : c ha o - dy n / 99 05 01 6 v 1 1 2 M ay 1 99 9 Pulses in the Zero - Spacing Limit of the GOY Model
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چکیده
We study the propagation of localised disturbances in a turbulent, but momentarily quiescent shell model (an approximation of the Navier-Stokes equations on a set of exponentially spaced momentum shells). These disturbances represent bursts of turbulence travelling down the inertial range, which is thought to be responsible for the intermittency observed in turbulence. Starting from the GOY shell model, we go to the limit where the distance between succeeding shells approaches zero (" the zero spacing limit ") and helicity conservation is retained. We obtain a discrete field theory which is numerically shown to have pulse solutions travelling with constant speed and with unchanged form. We give numerical evidence that the model might even be exactly integrable, although the continuum limit seems to be singular and the pulses show an unusual super exponential decay to zero as exp(−const σ n) when n → ∞, where σ is the golden mean. Finally we show that the maximal Lyapunov exponent of the GOY model approaches zero in this limit. Shell models of turbulence have increasingly been used as a laboratory for testing hypotheses about the statistical nature of Navier-Stokes turbulence. Even though they are derived by heuristic arguments they are surprisingly adept at reproducing the statistical properties of high Reynolds number turbulence. The reasons behind the apparent success of the shell models still remains unclear. In the present paper an attempt will be made to examine the detailed behaviour of one particular shell model – the so-called GOY model
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تاریخ انتشار 1999