论文标题
流体模型的随机分裂：阳性Lyapunov指数
Random Splitting of Fluid Models: Positive Lyapunov Exponents
论文作者
论文摘要
在本文中，我们提供了足够的条件，使随机分裂系统具有正面的Lyapunov指数。我们验证了两种流体模型的随机分裂的这些条件：圆环上2D Euler方程的保守洛伦兹-96方程和盖金近似值。在此过程中，我们强调了这些方程式中的特定结构，例如剪切。由于正面的lyapunov指数是混乱的指标，而这又是湍流的特征，因此我们的结果表明，这些随机分裂的流体模型具有湍流的重要特征。
In this paper we give sufficient conditions for random splitting systems to have a positive top Lyapunov exponent. We verify these conditions for random splittings of two fluid models: the conservative Lorenz-96 equations and Galerkin approximations of the 2D Euler equations on the torus. In doing so, we highlight particular structures in these equations such as shearing. Since a positive top Lyapunov exponent is an indicator of chaos which in turn is a feature of turbulence, our results show these randomly split fluid models have important characteristics of turbulent flow.
