In fluid dynamics governed by the one-dimensional inviscid Burgers equation ∂_tu + u∂_xu = 0, stirring is explained by using the sticky particle model. A Markov process $([Z_t^1,Z_t^2],t\ge 0)$ describes the motion of random turbulent intervals, which evolve inside another Markov process $([Z_t^3,Z_t^4],t\ge 0)$, describing the motion of random clusters concerned with the turbulence. Then, the four velocity processes $(u(Z_t^i,t),t\ge 0)$ are backward semi-martingales. If one of them is a martingale, then any turbulent interval is reduced to a single point.

中文翻译：

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向后半鞅变成汉堡湍流

在由一维无粘性 Burgers 方程∂ _t u + u∂ _x u = 0 控制的流体动力学中，搅拌是通过使用粘性粒子模型来解释的。马尔可夫过程$([Z_{吨}^1,Z_{吨}^2],吨\ge 0)$ 描述随机湍流区间的运动，它在另一个马尔可夫过程中演化 $([Z_{吨}^3,Z_{吨}^4],吨\ge 0)$，描述与湍流有关的随机簇的运动。那么，四个速度过程$(你(Z_{吨}^{\mathrm{一世}},吨),吨\ge 0)$是后向半鞅。如果其中一个是鞅，那么任何湍流间隔都会减少到一个点。