Related Experiment Video
Updated: Sep 30, 2025
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
9.7K
Incompressible Rayleigh-Taylor mixing in circular and spherical geometries
1Department of Physics and INFN, University of Torino, via P. Giuria 1, 10125 Torino, Italy.
Physical Review. E
|March 16, 2022
Summary
Convergent geometries in fluid dynamics cause mixing layers to drift inward, unlike planar cases. This inward drift in turbulent Rayleigh-Taylor instability is explained by a simple geometrical relation.
Area of Science:
- Fluid Dynamics
- Plasma Physics
- Astrophysics
Background:
- Rayleigh-Taylor instability drives turbulent mixing in fluids.
- Understanding mixing layer evolution is crucial for various scientific fields.
Purpose of the Study:
- Investigate turbulent mixing layer evolution in convergent geometries.
- Compare convergent vs. planar geometries for Rayleigh-Taylor instability.
- Analyze density flux and radial profile changes.
Main Methods:
- Numerical simulations in circular (2D) and spherical (3D) geometries.
- Application of the Boussinesq approximation.
- Analysis of turbulent fluid evolution.
Main Results:
- Convergent geometries cause mixing layer centers to drift inward.
- Radial density flux profiles exhibit inward drift.
- A geometrical relation for inward drift based on mass conservation was derived.
- Late-stage evolution shows inward-outward asymmetry in radial profiles.
Conclusions:
- Geometry significantly impacts mixing layer dynamics in Rayleigh-Taylor instability.
- Inward drift is a key characteristic of convergent geometries.
- The derived geometrical relation provides a predictive tool for fluid mixing.
Related Concept Videos
01:23Steady, Laminar Flow in Circular Tubes
485
Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is...
485
01:28Irrotational Flow
599
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:
599
01:20Velocity Potential
466
In steady, incompressible flow through a long, straight pipe with a uniform cross-section, the flow in the central region (far from the pipe walls) is irrotational. This irrotational nature means that fluid particles do not rotate around their axes, and a scalar function called the velocity potential, represented by ϕ, can be used to describe their movement. In irrotational flows, the velocity field V is defined as the gradient of the velocity potential:
466
01:30Dynamics of Circular Motion
14.2K
An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...
14.2K
01:10Deformation in a Circular Shaft
481
One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
481
01:16Energy Conservation and Bernoulli's Equation
9.6K
Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
9.6K