Related Experiment Video
Updated: May 27, 2025
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
9.5K
Quasi-irrotational approximation for the Rayleigh-Taylor instability in a solid bounded by a rigid wall.
S A Piriz1, A R Piriz2, N A Tahir3
1Universidad de Castilla-La Mancha, Instituto de Investigaciones Energéticas (INEI), E.I.I.A., and CYTEMA, 45071 Toledo, Spain.
Physical Review. E
|February 20, 2025
Summary
A new approximation models Rayleigh-Taylor instability in finite elastic solids. This method provides accurate growth rates and analyzes elastic-plastic transitions, even with viscous fluids present.
Area of Science:
- Solid Mechanics
- Fluid Dynamics
- Materials Science
Background:
- The Rayleigh-Taylor instability is crucial in various physical phenomena.
- Existing models for semi-infinite media have limitations for finite elastic solids.
- Understanding elastic-plastic transitions is vital for material behavior analysis.
Purpose of the Study:
- To develop a quasi-irrotational approximation for linear Rayleigh-Taylor instability in finite elastic solids.
- To derive accurate expressions for instability growth rates.
- To analyze the stability and elastic-plastic transition boundaries, considering viscous fluids.
Main Methods:
- Developed a quasi-irrotational approximation for finite elastic solids.
- Applied the approximation to analyze stability and elastic-plastic transition boundaries.
- Extended the model to include viscous fluids beneath the elastic-plastic slab.
Main Results:
- The approximation yields simple and accurate expressions for instability growth rates.
- Results are consistent with existing models for semi-infinite media and recover them in the limit of thick slabs.
- The model successfully analyzes the boundaries of stability and elastic-plastic transition.
Conclusions:
- The quasi-irrotational approximation is effective for studying Rayleigh-Taylor instability in finite elastic solids.
- This approach extends previous findings for ideal fluids to include viscous fluids.
- The developed model offers a valuable tool for analyzing complex material behaviors under instability conditions.
More Related Videos
Related Concept Videos
01:28Irrotational Flow
363
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:
363
01:23Steady, Laminar Flow in Circular Tubes
138
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...
138
01:15Thin-Walled Hollow Shafts
162
In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution...
162
01:18Boundary Layer Characteristics
28
When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...
28
01:20Velocity Potential
317
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:
317
01:17Steady, Laminar Flow Between Parallel Plates
121
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
121