# Kelvin-Helmholtz Shear Layer

Real-time 2D shear-layer instability simulation via the vorticity-streamfunction method, showing perturbation growth, vortex rollup, and pairing dynamics

> Canonical page: https://elysiatools.com/en/visualizations/navier-stokes-vortex-sheet

- **Category:** Physics

## Overview

Interactive 2D Navier-Stokes shear-layer simulation using the vorticity-streamfunction formulation. The model evolves a perturbed tanh vorticity sheet to show Kelvin-Helmholtz growth, vortex rollup, pairing, and increasingly complex mixing. Three visualization panels: (1) vorticity field with diverging blue-white-red contours for positive and negative rotation; (2) history plot tracking maximum vorticity and enstrophy against simulation time; (3) centerline vorticity power spectrum showing how dominant wavelengths shift during the rollup process. Numerical method: vorticity transport equation with first-order upwind advection, finite-difference diffusion, Poisson solve for streamfunction via SOR, and adaptive time stepping on a 256x128 grid. Adjustable parameters: Reynolds number Re (10-10000), flow speed U, perturbation amplitude A, perturbation frequency f. Four presets: Laminar Shear, Kelvin-Helmholtz, Vortex Rollup, Turbulent Transition. Real-time statistics: Reynolds number, simulation time, maximum vorticity, total kinetic energy, enstrophy, and grid size. Educational content explains free shear-layer instability, the vorticity-streamfunction method, vortex pairing, and engineering relevance to jet mixing, separation, combustion, and geophysical shear layers. Multi-language support (zh, en, es, fr, de, ru, pt).

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