标题： 一维水动力学模型生成湍流级联 显示英文标题

标题： One-dimensional hydrodynamic model generating turbulent cascade

摘要： 作为生成类似于惯性范围中Navier-Stokes湍流级联的最小数学模型，我们提出一个一维偏微分方程模型，在无粘情况下保持平方涡度类似量（能量）的积分。 在大尺度驱动和小粘性条件下，我们数值发现该模型表现出能量级联，具有对维度分析预测有显著修正的宽广能量谱，动力系统结构中的特殊间歇性和自相似性。 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.