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Rayleigh-Taylor Instability Growth Rate Calculator

Rayleigh-Taylor (RT) instability occurs at the interface between two fluids of differing densities when the heavier, denser fluid is accelerated into the lighter fluid (or when dense fluid sits on top of light fluid in gravity).

Density of the upper heavy fluid (e.g. water = 1000).

Density of the lower light fluid (e.g. air = 1.2).

Spatial wavelength of the interface ripple perturbation.

Gravity or dynamic acceleration in multiples of standard g (9.81 m/s²).

Calculated Result
49.6 s⁻¹

Linear Growth Rate (γ)

Atwood Number (A)

0.998

e-Folding Characteristic Time (τ)

20.17 ms

Perturbation Wavenumber (k)

251.3 rad/m

Calculation Breakdown

  1. Atwood Number: A = (ρ₂ - ρ₁) / (ρ₂ + ρ₁)0.998
  2. Wavenumber: k = 2π / λ251.3 rad/m
  3. Growth Rate: γ = √(A·g·k)49.6 s⁻¹
  4. e-Folding Time: τ = 1 / γ20.17 ms

What Is the Rayleigh-Taylor Instability Growth Rate Calculator?

Rayleigh-Taylor instability leads to interpenetrating "fingers" or "spikes" of dense fluid falling down and "bubbles" of light fluid rising up.

It plays a crucial role in supernova explosions, inertial confinement fusion (ICF) capsule implosions, and atmospheric mixing.

How Does the Rayleigh-Taylor Instability Growth Rate Calculator Work?

Evaluates the dimensionless Atwood number A.

Converts spatial wavelength into wavenumber k = 2*pi / lambda.

Calculates linear instability growth rate gamma and e-folding time tau.

Rayleigh-Taylor Instability Growth Rate Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

A = \frac{\rho_2 - \rho_1}{\rho_2 + \rho_1}, \quad k = \frac{2\pi}{\lambda}, \quad \gamma = \sqrt{A \cdot g \cdot k}, \quad \tau = \frac{1}{\gamma}

Linear Rayleigh-Taylor inviscid dispersion relation relating Atwood number and wavenumber to exponential growth rate.

How to Use the Rayleigh-Taylor Instability Growth Rate Calculator

  1. Enter the densities of the upper (dense) and lower (light) fluids.
  2. Enter the perturbation wavelength in millimeters.
  3. Optionally specify acceleration in Gs (e.g. 1000 Gs in centrifuge or fusion implosions).

Step-by-Step Example Calculation

Water-Air Gravitational Interface Inversion

Input Values:

upperDenseFluidDensityKgM3:1000
lowerLightFluidDensityKgM3:1.2
perturbationWavelengthMm:25
effectiveAccelerationG:1
Worked Steps: Water inverted above air in a ceiling container under 1G gravity.

Understanding Your Result

Growth rate gamma in s^-1 indicates how rapidly the perturbation amplitude grows (h(t) = h0 * exp(gamma * t)).

e-folding time is the time required for ripple amplitude to expand by a factor of e (~2.718).

Factors That Affect the Result

  • Surface tension: High interfacial surface tension stabilizes and suppresses short wavelengths (cutoff wavelength).
  • Viscosity: Fluid dynamic viscosity slows down growth rates at high wavenumbers.

When Should You Use This Calculator?

  • Inertial confinement fusion (ICF) target shell stability modeling.
  • Astrophysical modeling of crab nebula filaments and supernova core collapse.
  • Explosive welding and shaped-charge jet dynamics.

Assumptions & Limitations

  • Valid for small initial perturbation amplitudes (h << lambda) in the linear regime.
  • Inviscid formulation without surface tension cutoff damping.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Classical Rayleigh (1883) and Taylor (1950) analytical dispersion relation.

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