Dynamics of Rotating Stratified Fluids

有序与混沌的实验与数值研究 提出了旋转分层流体中的动力学。 数值 计算和实验室实验将进一步阐明 侧壁边界和边界层分离的作用 两层斜压混沌的观测。 直接检索 流体柱运动的庞加莱截面将允许比较 实验室中的拉格朗日混合与 模型 例如，混合波状态，或摇摆状态 可以产生局部的（在空间中）混沌粒子动力学， 可以通过将Melnikov的方法应用于治理来预测 包裹运动的哈密尔顿动力系统。 的影响 弱到中等的“季节性”强迫将在两个研究， 实验室和完全解析的两层模型，目标是 验证先前结果的稳健性， 在低序状态下的剧烈不稳定和可预测性的丧失 包括这种强迫的模型。 拟议研究的一个重点是应用 最近的想法从动力系统到实验和 斜压气流的数值资料。 这些技术包括 奇异值分解，线性和非线性预测， 主正交分解 我们希望能产生 更清晰的图片（例如庞加莱截面和返回图） 数据的确定性部分，沿着更好地估计 维数、李雅普诺夫指数和其他定性特征 非线性斜压流的一部分。 的低阶描述 高分辨率数值解中的分形动力学 的准地转偏微分方程将是 寻求。

Experimental and numerical studies of ordered and chaotic dynamics in rotating stratified fluids are proposed. Numerical computations and laboratory experiments will further clarify the role of sidewall boundaries and boundary layer separation in observations of two-layer baroclinic chaos. Direct retrieval of Poincare sections of fluid column motions will allow a comparison of LaGrangian mixing in the laboratory with that predicted by models. For example, mixed wave states, or vacillatory states may generate localized (in space) chaotic particle dynamics that can be predicted by applying Melnikov's method to the governing Hamiltonian dynamical system for parcel motion. The effects of weak to moderate "seasonal" forcing will be studied both in laboratory and in fully resolved two-layer models, with the goal of verifying the robustness of previous results which showed a dramatic destabilization and loss of predictability in low order models that include such forcing. A focus of the proposed research is the application of recent ideas from dynamical systems to both experimental and numerical data on baroclinic flows. These techniques include singular value decomposition, linear and nonlinear prediction, and principle orthogonal decomposition. We hope to generate cleaner pictures (e.g. Poincare sections and return maps) of the deterministic part of the data, along with better estimates of dimension, Lyapunov exponents, and other qualitative signatures of nonlinear baroclinic flow. Low-order descriptions of the fractal dynamics observed in high resolution numerical solutions of the quasi-geostrophic partial differential equations will be sought.