Related Experiment Video
Updated: May 14, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Nonlinear Rayleigh-Taylor instability of rotating inviscid fluids
1SKLTCS and CAPT, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China. jjtao@pku.edu.cn
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 16, 2013
Summary
Uniform rotation can slow down the nonlinear Rayleigh-Taylor instability in fluids. The Coriolis force acts as a restoring force, reducing the instability's amplitude across all wavelengths.
Area of Science:
- Fluid dynamics
- Plasma physics
- Astrophysical phenomena
Background:
- The Rayleigh-Taylor instability occurs at the interface of accelerated fluids with different densities.
- Understanding its nonlinear evolution is crucial for various physical systems, from inertial confinement fusion to astrophysical jets.
- Previous studies often focused on non-rotating or differently configured systems.
Purpose of the Study:
- To theoretically investigate the effect of uniform rotation on the nonlinear stage of the Rayleigh-Taylor instability.
- To determine if rotation can suppress or retard the development of this instability.
- To analyze the role of the Coriolis force in modifying the instability's saturation amplitude.
Main Methods:
- Theoretical analysis of fluid dynamics equations.
- Consideration of a rotating system with rotation axis normal to the acceleration.
- Mathematical modeling of the perturbed interface between two uniform inviscid fluids.
Main Results:
- The nonlinear stage of the Rayleigh-Taylor instability is theoretically shown to be retarded at any Atwood number in a rotating system.
- The Coriolis force arising from uniform rotation acts as an effective restoring force on the perturbed interface.
- Uniform rotation consistently decreases the nonlinear saturation amplitude of the interface, irrespective of the disturbance wavelength.
Conclusions:
- Rotation provides a stabilizing mechanism against the nonlinear Rayleigh-Taylor instability.
- The Coriolis force is key to suppressing the instability's growth and reducing its saturation amplitude.
- This finding has implications for controlling instabilities in rotating fluid systems and astrophysical contexts.
Related Concept Videos
01:28Irrotational Flow
Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
01:28Navier–Stokes Equations
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
01:28Euler's Equations of Motion
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
01:08Equation of Rotational Dynamics
Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic variables, it is seen that there is a mapping of the linear variables to the rotational ones. Linear displacement, velocity, and acceleration have their equivalents in rotational motion, which are angular displacement, angular velocity, and angular acceleration. Similar to the rotational variables, a mapping exists from Newton's second law of motion...
01:05Relating Angular And Linear Quantities - II
In the case of circular motion, the linear tangential speed of a particle at a radius from the axis of rotation is related to the angular velocity by the relation:
01:18Newtonian Fluid: Problem Solving
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...