kh2d-solver: A Python Library for Idealized Two-Dimensional
  Incompressible Kelvin-Helmholtz Instability
Authors: name: Sandy H. S. Herho; name: Nurjanna J. Trilaksono; name: Faiz R. Fajary; name: Gandhi Napitupulu; name: Iwan P. Anwar; name: Faruq Khadami; name: Dasapta E. Irawan
Published: 2025-09-19 15:26:37

Abstract: 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.