Cho Kenichiro, Miyano Takaya, Toriyama Toshiyuki
Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Noji-Higashi, Kusatsu, Shiga 525-8577, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Sep;86(3 Pt 2):036308. doi: 10.1103/PhysRevE.86.036308. Epub 2012 Sep 10.
Inspired by the chaotic waterwheel invented by Malkus and Howard about 40 years ago, we have developed a gas turbine that randomly switches the sense of rotation between clockwise and counterclockwise. The nondimensionalized expressions for the equations of motion of our turbine are represented as a starlike network of many Lorenz subsystems sharing the angular velocity of the turbine rotor as the central node, referred to as augmented Lorenz equations. We show qualitative similarities between the statistical properties of the angular velocity of the turbine rotor and the velocity field of large-scale wind in turbulent Rayleigh-Bénard convection reported by Sreenivasan et al. [Phys. Rev. E 65, 056306 (2002)]. Our equations of motion achieve the random reversal of the turbine rotor through the stochastic resonance of the angular velocity in a double-well potential and the force applied by rapidly oscillating fields. These results suggest that the augmented Lorenz model is applicable as a dynamical model for the random reversal of turbulent large-scale wind through cessation.
受大约40年前马尔库斯和霍华德发明的混沌水车启发，我们开发了一种燃气轮机，它能在顺时针和逆时针旋转方向之间随机切换。我们的燃气轮机运动方程的无量纲表达式表示为一个由许多洛伦兹子系统组成的星状网络，这些子系统以燃气轮机转子的角速度作为中心节点共享该角速度，称为增强洛伦兹方程。我们展示了燃气轮机转子角速度的统计特性与斯里尼瓦桑等人[《物理评论E》65, 056306 (2002)]报道的湍流瑞利 - 贝纳德对流中大规模风的速度场之间的定性相似性。我们的运动方程通过角速度在双阱势中的随机共振以及快速振荡场施加的力实现了燃气轮机转子的随机反转。这些结果表明，增强洛伦兹模型可作为通过停止实现湍流大规模风随机反转的动力学模型。
