This paper develops a simple model of the inertial range of turbulent flow, based on a cascade of vortical filaments. A binary branching structure is proposed, involving the splitting of filaments at each step into pairs of daughter filaments with differing properties, in effect two distinct simultaneous cascades. Neither of these cascades has the Richardson-Kolmogorov exponent of 1/3. This bimodal structure is also different from bifractal models as vorticity volume is conserved. If cascades are assumed to be initiated continuously and throughout space we obtain a model of the inertial range of stationary turbulence. We impose the constraint associated with Kolmogorov's four-fifths law and then adjust the splitting to achieve good agreement with the observed structure exponents $\zeta_p$. The presence of two elements to the cascade is responsible for the nonlinear dependence of $\zeta_p$ upon $p$. A single cascade provides a model for the initial-value problem of the Navier--Stokes equations in the limit of vanishing viscosity. To simulate this limit we let the cascade continue indefinitely, energy removal occurring in the limit. We are thus able to compute the decay of energy in the model.

中文翻译：

---

惯性范围的丝状级联模型

本文基于一连串涡流细丝，开发了一个简单的湍流惯性范围模型。提出了一种二元分支结构，包括在每一步将细丝分裂成具有不同特性的成对子细丝，实际上是两个不同的同时级联。这些级联都没有 1/3 的 Richardson-Kolmogorov 指数。这种双峰结构也不同于双分形模型，因为涡量体积是守恒的。如果假设级联在整个空间中连续启动，我们将获得静止湍流惯性范围的模型。我们施加与 Kolmogorov 的五分之四定律相关的约束，然后调整分裂以与观察到的结构指数 $\zeta_p$ 达到良好的一致性。级联中存在两个元素是 $\zeta_p$ 对 $p$ 的非线性依赖的原因。单个级联为 Navier-Stokes 方程在粘度消失极限下的初值问题提供了一个模型。为了模拟这个极限，我们让级联无限期地继续，能量去除发生在极限中。因此，我们能够计算模型中的能量衰减。