kh2d-solver：一个用于理想化二维不可压缩开尔文-亥姆霍兹不稳定性研究的Python库

摘要

我们推出了一款开源Python库，用于模拟分层剪切流中的二维不可压缩开尔文-亥姆霍兹不稳定性。该求解器采用分数步投影法，通过快速正弦变换实现谱泊松求解，达到了二阶空间精度。实现过程中充分利用了NumPy、SciPy及Numba的即时编译功能，以确保计算效率。通过四个经典测试案例，我们探索了雷诺数1000至5000及理查森数0.1至0.3范围内的流动特性：经典剪切层、双剪切配置、旋转流及受迫湍流。利用香农熵与复杂度指数的统计分析表明，尽管雷诺数较低，双剪切层的混合速率仍比受迫湍流高出2.8倍。该求解器在标准桌面硬件上运行高效，384×192网格的模拟约在31分钟内完成。研究结果表明，混合效率取决于不稳定性生成路径而非仅强度指标，这对基于理查森数的参数化方法提出了挑战，并为气候模型中的亚网格尺度表征提供了改进方向。

English

We present an open-source Python library for simulating two-dimensional incompressible Kelvin-Helmholtz instabilities in stratified shear flows. The solver employs a fractional-step projection method with spectral Poisson solution via Fast Sine Transform, achieving second-order spatial accuracy. Implementation leverages NumPy, SciPy, and Numba JIT compilation for efficient computation. Four canonical test cases explore Reynolds numbers 1000--5000 and Richardson numbers 0.1--0.3: classical shear layer, double shear configuration, rotating flow, and forced turbulence. Statistical analysis using Shannon entropy and complexity indices reveals that double shear layers achieve 2.8times higher mixing rates than forced turbulence despite lower Reynolds numbers. The solver runs efficiently on standard desktop hardware, with 384times192 grid simulations completing in approximately 31 minutes. Results demonstrate that mixing efficiency depends on instability generation pathways rather than intensity measures alone, challenging Richardson number-based parameterizations and suggesting refinements for subgrid-scale representation in climate models.

kh2d-solver：一个用于理想化二维不可压缩开尔文-亥姆霍兹不稳定性研究的Python库

kh2d-solver: A Python Library for Idealized Two-Dimensional Incompressible Kelvin-Helmholtz Instability

摘要

Support