标题： 产生湍流级串的一维流体力学模型 显示英文标题

标题： One-dimensional hydrodynamic model generating a turbulent cascade

摘要： 作为类似于 Navier-Stokes 湍流在惯性范围内的级联生成的最小数学模型，我们提出了一种一维偏微分方程模型，在无粘情况下保守平方涡度类似物（能量耗散）的积分。通过大尺度强迫和小粘性，我们在数值上发现该模型表现出能量耗散级联、具有与维数分析预测相当大校正的能量谱、动力系统结构中独特的间歇性和自相似性。 显示英文摘要

摘要： As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analogue (enstrophy) in the inviscid case. With a large-scale forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency and self-similarity in the dynamical system structure.