Rayleigh-Taylor Instability Visualization Demo

Overview

This demonstration showcases XDL’s advanced scientific visualization capabilities through a simulation of the Rayleigh-Taylor instability - a classic fluid dynamics phenomenon where a dense fluid sits atop a lighter fluid, creating characteristic mushroom-shaped structures as they mix.

What is Rayleigh-Taylor Instability?

The Rayleigh-Taylor (RT) instability occurs when:

  • A heavier fluid is positioned above a lighter fluid
  • Small perturbations at the interface grow exponentially
  • The heavy fluid “falls” through the light fluid in finger-like plumes
  • Beautiful, turbulent mixing patterns emerge

This phenomenon is observed in:

  • Supernovae - when stellar material is accelerated outward
  • Inertial Confinement Fusion - affecting fuel compression
  • Oceanography - thermocline mixing
  • Atmospheric science - cloud formation
  • Industrial processes - mixing and separation

Features Demonstrated

This demo showcases:

1. Multiple Perceptually Uniform Colormaps

  • Viridis - Default, excellent for scientific data
  • Plasma - Purple to yellow gradient
  • Turbo - Improved rainbow colormap
  • Inferno - Black through orange to white

2. Density Field Visualization

  • High-resolution (200x200 grid) fluid simulation
  • Real-time evolution of mixing interface
  • Color-coded density values

3. Vector Field Visualization

  • Velocity field quiver plots (arrows)
  • Color-coded by velocity magnitude
  • Subsampled for clarity

4. Multi-Frame Time Series

  • 6 timesteps: 0, 50, 100, 200, 400, 800 steps
  • Shows instability growth over time
  • Captures transition from smooth interface to turbulent mixing

5. Side-by-Side Comparisons

  • 4-panel colormap comparison images
  • Demonstrates advantages of perceptually uniform colormaps
  • Shows same data with different color schemes

Generated Visualizations

The demo generates 30 images total:

Per Timestep (6 timesteps × 5 images = 30 images)

  1. rt_viridis_XXXX.png - Density field with Viridis colormap
  2. rt_plasma_XXXX.png - Density field with Plasma colormap
  3. rt_turbo_XXXX.png - Density field with Turbo colormap
  4. rt_velocity_XXXX.png - Velocity field quiver plot
  5. rt_comparison_XXXX.png - 4-panel colormap comparison

Plus:

  • rt_initial_comparison.png - Initial state comparison

Running the Demo

Prerequisites

Ensure you have Rust and the XDL dependencies installed:

cd /path/to/xdl
cargo build --release

Execute the Visualization 

# From the xdl root directory
cargo run --release --example rayleigh_taylor_viz

Expected Output 

Rayleigh-Taylor Instability Visualization Demo
================================================

Initializing simulation (200x200 grid)...
Initial density stats: (1.0, 2.0, 1.5)

Rendering initial state with multiple colormaps...
  ✓ Saved: rt_initial_comparison.png

Simulating 50 steps...
Density stats: (1.0123, 1.9877, 1.5)
Rendering frame 50 visualizations:
  ✓ Saved: rt_viridis_0050.png
  ✓ Saved: rt_plasma_0050.png
  ✓ Saved: rt_turbo_0050.png
  ✓ Saved: rt_velocity_0050.png
  ✓ Saved: rt_comparison_0050.png

[... continues for each timestep ...]

✅ Visualization complete!

Generated 30 images showcasing:
  • Density field evolution with Viridis, Plasma, Turbo, and Inferno colormaps
  • Velocity field quiver plots
  • Side-by-side colormap comparisons

The Rayleigh-Taylor instability demonstrates:
  • Heavy fluid (top) falling through light fluid (bottom)
  • Mushroom-shaped plumes forming
  • Complex fluid mixing dynamics
  • Perceptually uniform colormap advantages

Simulation Details

Physics

  • Grid: 200 × 200 cells
  • Time step: 0.01
  • Gravity: 0.1
  • Viscosity: 0.001
  • Atwood number: 0.5 (density contrast parameter)
  • Initial perturbation: 4-wavelength sinusoidal disturbance

Numerical Method

  • Advection: Semi-Lagrangian scheme with bilinear interpolation
  • Diffusion: Explicit finite difference (Laplacian)
  • Boundary conditions: No-slip walls
  • Buoyancy: Density-driven force proportional to local density gradient

Simplifications

This is a demonstrative simulation, not a full Navier-Stokes solver:

  • Simplified pressure solve (omitted for demo)
  • No vorticity confinement
  • Basic viscous diffusion
  • Sufficient to show RT instability growth and mixing

Analyzing the Results

What to Look For

  1. Initial State (t=0)
    • Clear interface between heavy (top) and light (bottom) fluids
    • Small sinusoidal perturbation visible
  2. Early Growth (t=50-100)
    • Perturbations begin to grow
    • Fingers starting to form
    • Interface becomes wavy
  3. Linear Growth (t=100-200)
    • Clear finger/spike formation
    • Heavy fluid fingers penetrating downward
    • Light fluid bubbles rising upward
  4. Nonlinear Regime (t=200-400)
    • Mushroom-shaped structures
    • Secondary instabilities
    • Vortex roll-up at plume heads
  5. Turbulent Mixing (t=400-800)
    • Complex, chaotic patterns
    • Extensive mixing region
    • Multiple length scales present

Colormap Comparison

Viridis vs. Rainbow/Jet:

  • Viridis maintains perceptual uniformity
  • Features remain visible across full range
  • No artificial “bands” or “hot spots”
  • Better for quantitative analysis

Plasma:

  • Excellent contrast
  • Good for highlighting fine structures
  • Purple-yellow gradient intuitive for hot/cold

Turbo:

  • Improved rainbow
  • More perceptually uniform than classic jet
  • Good for presentations

Inferno:

  • Black-body radiation inspired
  • Excellent for high dynamic range
  • Good for printing

Technical Implementation

File Structure 

examples/
├── rayleigh_taylor_demo.rs      # Simulation engine (241 lines)
├── rayleigh_taylor_viz.rs       # Visualization driver (309 lines)
└── RAYLEIGH_TAYLOR_README.md    # This file

Key Components

Simulation (rayleigh_taylor_demo.rs):

  • RTSimulation struct with density and velocity fields
  • step() - Evolve one timestep
  • simulate(n) - Run n timesteps
  • density_stats() - Get min/max/average density

Visualization (rayleigh_taylor_viz.rs):

  • render_density_field() - Render with any colormap
  • render_velocity_field() - Quiver plot of velocities
  • render_comparison() - 4-panel comparison image
  • Colormap implementations: viridis, plasma, turbo, inferno

Educational Value

This demo illustrates:

  1. Fluid Dynamics Fundamentals
    • Instability growth
    • Buoyancy-driven flow
    • Turbulent mixing
  2. Scientific Visualization Best Practices
    • Importance of colormap choice
    • Perceptual uniformity
    • Multi-modal representation (density + velocity)
  3. Computational Methods
    • Finite difference methods
    • Semi-Lagrangian advection
    • Eulerian vs. Lagrangian frameworks
  4. XDL Capabilities
    • High-quality scientific visualization
    • Flexible colormap system
    • Vector field rendering
    • Animation frame generation

Extending the Demo

Modifications to Try

  1. Different Initial Conditions:

    // In RTSimulation::new(), modify:
let wavelength = width as f64 / 6.0;  // More wavelengths
let perturbation_amplitude = 10.0;     // Larger perturbation

  2. Different Parameters:

    viscosity: 0.01,      // More viscous fluid
gravity: 0.2,         // Stronger gravity
atwood_number: 0.8,   // Greater density contrast

  3. Higher Resolution:

    let mut sim = RTSimulation::new(400, 400);  // 4x more grid points

  4. More Timesteps:

    let timesteps = [0, 25, 50, 100, 200, 400, 600, 800, 1000, 1200];

  5. Additional Visualizations:

    • Add streamline plots
    • Add vorticity visualization
    • Create animated GIF
    • Export to HTML with slider control

Performance

On a typical modern laptop:

  • Initialization: < 0.1 seconds
  • Per timestep: ~10ms (200×200 grid)
  • Per visualization: ~0.5 seconds
  • Total runtime: ~20-30 seconds

Scaling:

  • Simulation: O(N²) per step
  • Visualization: O(N²) per frame
  • Memory: ~10 MB for 200×200 grid

Scientific Accuracy

What’s Accurate:

  • Qualitative RT instability behavior
  • Growth of perturbations
  • Mushroom structure formation
  • Velocity field patterns

What’s Simplified:

  • No incompressibility constraint (divergence-free velocity)
  • No pressure solve
  • Basic boundary conditions
  • 2D instead of 3D

For Research-Grade Simulations, Consider:

  • Full Navier-Stokes solver (e.g., using XDL’s Python integration with PyFR, Basilisk, or ATHENA)
  • Higher-order numerical schemes
  • Adaptive mesh refinement
  • 3D domains

References

  1. Rayleigh, Lord (1883). “Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density”
  2. Taylor, G.I. (1950). “The instability of liquid surfaces when accelerated”
  3. Chandrasekhar, S. (1961). “Hydrodynamic and Hydromagnetic Stability”
  4. Sharp, D.H. (1984). “An overview of Rayleigh-Taylor instability”

Support

For questions or issues:

  • Check XDL documentation: docs/SCIENTIFIC_VISUALIZATION_GUIDE.md
  • Review examples: examples/
  • Report bugs: XDL issue tracker

Enjoy exploring the beautiful physics of fluid instabilities with XDL! 🌊💫