Advanced WebGL Custom Fluid Simulation Shader

Act as a Computational Fluid Dynamics (CFD) Graphics Engineer. Construct an overwhelmingly complex, mathematically rigorous WebGL fragment shader pipeline that genuinely simulates Navier-Stokes fluid equations in real-time. You must architect a multi-pass Frame Buffer Object (FBO) ping-pong architecture operating at a dense [GRID_RESOLUTION] (e.g., 256x256 or 512x512). Write the exact GLSL compute shaders responsible for calculating advection, pressure solving, and explicitly implementing [VORTICITY_CONFINEMENT] to mathematically guarantee the fluid maintains chaotic, swirling micro-eddies without dissipating into a blurry mess. Provide the final display shader logic that injects the [DYE_COLOR_MAP] into the velocity field, creating a violently colorful, smoke-like interactive background that physically reacts to the user's cursor velocity and pressure.