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General Characteristics of Pipe Flow II

General Characteristics of Pipe Flow II

When fluid enters a pipe, it first passes through the entrance region, where the velocity profile adjusts due to viscous effects. In this region, a boundary layer forms along the pipe walls and grows until it fully occupies the pipe's cross-section. Once the boundary layer merges, the flow becomes fully developed, with a steady velocity profile that remains consistent along the pipe's length.
The distance to reach a fully developed flow is called the entrance length and depends on the...

Boundary Layer Characteristics

Boundary Layer Characteristics

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...

Divergence and Stokes' Theorems

Divergence and Stokes' Theorems

The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...

Steady, Laminar Flow Between Parallel Plates

Steady, Laminar Flow Between Parallel Plates

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.

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:

Turbulent Flow

Turbulent Flow

Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...

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Related Experiment Video

Updated: Jun 4, 2025

Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Competition between merging and bifurcation in the generalized Rayleigh-Taylor instability.

Q Cauvet¹, B Bernecker¹, B Canaud¹

¹<a href="https://ror.org/00kn4eb29">CEA, DAM</a>, DIF- 91297 Arpajon, France and <a href="https://ror.org/03xjwb503">Université Paris-Saclay</a>, CEA, Laboratoire Matière en Conditions Extrêmes (LMCE), 91680 Bruyères-le-Châtel, France.

Physical Review. E

|December 18, 2024

Summary

The generalized Rayleigh-Taylor instability exhibits two nonlinear regimes: inertial growth (h∝t²) and collisional growth (h∝t). The collisional regime, featuring frictional forces, maintains constant structure sizes and highlights the role of bifurcation processes.

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Last Updated: Jun 4, 2025

Magnetically Induced Rotating Rayleigh-Taylor Instability

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Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

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Area of Science:

Fluid dynamics
Plasma physics
Astrophysical phenomena

Background:

The Rayleigh-Taylor instability drives mixing in fluids with different densities under acceleration.
Understanding nonlinear evolution is crucial for astrophysical jets, inertial confinement fusion, and supernovae.

Purpose of the Study:

To investigate the nonlinear dynamics of generalized Rayleigh-Taylor instability with a frictional force.
To analyze the distinct growth regimes and structural evolution influenced by collisional effects.

Main Methods:

Numerical simulations of fluid interfaces.
Extension of Alon's statistical model incorporating asymptotic bubble velocity and merging.
Inclusion of a frictional force simulating interpenetrating fluid collisions.

Main Results:

Identified two nonlinear regimes: inertial (h∝t²) and collisional (h∝t).
The collisional regime, characterized by friction, leads to self-similar structures of constant size.
Demonstrated the significance of bifurcation (bubble breakup) in the collisional regime.

Conclusions:

Frictional forces fundamentally alter Rayleigh-Taylor instability evolution, creating a distinct collisional regime.
The collisional regime's self-similar structures and the importance of bifurcation offer new insights into fluid mixing processes.