标题： 旋转雷诺-贝纳德对流中的混沌转变和磁场生成 显示英文标题

标题： Transition to chaos and magnetic field generation in rotating Rayleigh-Bénard convection

摘要： 在三维旋转雷诺-贝纳德对流中，通过改变泰勒数和瑞利数作为控制参数，数值研究了流体动力学和磁流体动力学的对流吸引子。 首先，进行了流体动力学吸引子及其分岔的分析，识别了通过准周期性通往混沌的路径。 其次，通过引入一个初始磁场并测量其随泰勒数的变化（保持瑞利数不变）来研究磁流体动力学系统的特性。 对吸引子的分析表明，旋转对雷诺-贝纳德对流中的磁场生成有显著影响，临界磁普朗特数随旋转速率的变化呈非单调变化。 认为无滞后的爆裂分岔与开-关间歇性是导致发电机效应转变的原因。 显示英文摘要

摘要： Hydrodynamic and magnetohydrodynamic convective attractors in three-dimensional rotating Rayleigh-B\'enard convection are studied numerically by varying the Taylor and Rayleigh numbers as control parameters. First, an analysis of hydrodynamic attractors and their bifurcations is conducted, where routes to chaos via quasiperiodicity are identified. Second, the behaviour of the magnetohydrodynamic system is investigated by introducing a seed magnetic field and measuring its growth or decay as a function of the Taylor number, while keeping the Rayleigh number fixed. Analysis of the attractors shows that rotation has a significant impact on magnetic field generation in Rayleigh-B\'enard convection, with the critical magnetic Prandtl number changing nonmonotonically with the rotation rate. It is argued that a nonhysteretic blowout bifurcation with on-off intermittency is responsible for the transitions to dynamo.