Question 1

What is the Rayleigh-Taylor instability?

Accepted Answer

It is a hydrodynamic instability that occurs whenever a denser fluid is supported by, or accelerated into, a lighter fluid. Gravity pulls the heavy fluid down through the light fluid, so any small ripple on the interface grows over time into descending spikes and rising bubbles.

Question 2

Why do mushroom-shaped plumes form?

Accepted Answer

As a heavy spike sinks, the velocity difference between the falling spike and the surrounding light fluid creates a secondary Kelvin-Helmholtz shear instability along its flanks. This rolls the tip of the spike outward into the familiar mushroom cap with two curling vortices.

Question 3

What is the Atwood number?

Accepted Answer

The Atwood number A = (ρ_heavy − ρ_light)/(ρ_heavy + ρ_light) is the dimensionless density contrast. It ranges from 0 (equal densities, neutrally stable) to 1 (heavy fluid in vacuum). A larger Atwood number gives faster, more violent plume growth.

Question 4

How fast does the instability grow?

Accepted Answer

In the early linear stage a perturbation of wavenumber k grows exponentially as exp(n·t), with growth rate n = sqrt(A·g·k). Short wavelengths grow fastest in the inviscid case, while viscosity and surface tension suppress the smallest scales and select a dominant wavelength.

Question 5

Where does the Rayleigh-Taylor instability appear in nature?

Accepted Answer

It shapes supernova remnants such as the Crab Nebula, drives mixing in inertial-confinement-fusion targets, governs salt domes rising through rock, sculpts mushroom clouds, and appears any time you invert a glass of water sealed by a card.

Question 6

How is the fluid simulated here?

Accepted Answer

The simulation solves a 2D incompressible two-fluid flow on a grid. A density field is advected with the velocity using a semi-Lagrangian scheme, buoyancy forces are added from gravity acting on the density, and a Jacobi pressure projection makes the velocity field divergence-free each step.

Question 7

What does the projection step do?

Accepted Answer

Incompressible fluid cannot be compressed, so its velocity field must have zero divergence. The projection step solves a Poisson equation for pressure and subtracts the pressure gradient from the velocity, removing any compression introduced by advection and buoyancy.

Question 8

Why does increasing viscosity calm the flow?

Accepted Answer

Viscosity diffuses momentum and damps velocity gradients, especially at small scales. This slows the roll-up of mushroom caps, smooths fine filaments, and lowers the growth rate of short-wavelength perturbations, producing larger, smoother plumes.

Question 9

What is the difference from the Kelvin-Helmholtz instability?

Accepted Answer

Rayleigh-Taylor is driven by buoyancy when heavy fluid sits over light fluid, while Kelvin-Helmholtz is driven by velocity shear between two streams. The two are linked: the shear along the flanks of a Rayleigh-Taylor spike triggers a secondary Kelvin-Helmholtz roll-up that forms the mushroom cap.

Question 10

Can the configuration ever be stable?

Accepted Answer

If the light fluid sits on top of the heavy fluid the arrangement is stable and ripples merely oscillate. The classic instability requires heavy-over-light (or equivalently acceleration directed from the light fluid into the heavy fluid). Surface tension can also stabilise sufficiently short wavelengths.

💧 Rayleigh-Taylor Instability — Heavy Over Light

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