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Related Concept Videos

Buoyancy01:12

Buoyancy

When an object is placed in a fluid, it either floats or sinks. All objects in a fluid experience a buoyant force. For example, a metal ball sinks, while a rubber ball floats. Similarly, a submarine can sink and float by adjusting its buoyancy.  The concept of buoyancy raises several interesting questions. For instance, where does this buoyant force come from? How much buoyant force is required to make an object sink or float? Do objects that sink get any support at all from the fluid? 
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Bernoulli's Principle

Bernoulli's equation incorporates how fluid pressure changes across a static, incompressible fluid by equating the kinetic energy contribution to zero. It is also helpful in analyzing horizontal flows in which the gravitational energy density is constant throughout. The latter equation is so useful that it is called Bernoulli's principle. According to Bernoulli's principle, the fluid pressure drops if the speed increases and vice versa.
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In fluid mechanics, buoyancy and stability are key concepts for understanding the behavior of submerged and floating bodies. When a stationary body is fully or partially submerged in a fluid, the fluid exerts a force on the body known as the buoyant force. This force acts vertically upward through a point called the center of buoyancy, which is the center of the displaced fluid volume. According to Archimedes' principle, the magnitude of the buoyant force is equal to the weight of the fluid...
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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:
Navier–Stokes Equations01:28

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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...
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Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Instabilities in buoyant flows under localized heating.

M C Navarro1, A M Mancho, H Herrero

  • 1Departamento de Matemáticas, Facultad de Ciencias Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain.

Chaos (Woodbury, N.Y.)
|July 7, 2007
PubMed
Summary
This summary is machine-generated.

This study numerically investigates fluid instabilities in a free-surface layer within a cylinder heated nonhomogeneously from below. Researchers identified target patterns and spiral waves, even at infinite Prandtl numbers, revealing complex fluid dynamics.

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Area of Science:

  • Fluid dynamics
  • Nonlinear dynamics
  • Computational physics

Background:

  • Free surface fluid layers are crucial in various natural and industrial processes.
  • Understanding instabilities in nonhomogeneously heated systems is key to predicting complex behaviors.
  • Previous studies often focused on simpler heating conditions.

Purpose of the Study:

  • To numerically investigate instabilities in a fluid layer with a free surface in a cylindrical container.
  • To analyze the impact of localized heating from below on fluid behavior.
  • To characterize different types of instabilities, including target patterns and spiral waves.

Main Methods:

  • Numerical simulations of fluid dynamics.
  • Analysis of axisymmetric basic states and bifurcations.
  • Parametric study of dimensionless variables influencing instability patterns.

Main Results:

  • An axisymmetric basic state forms with imposed horizontal temperature gradients.
  • Identified instabilities include extended patterns (targets) and spiral waves.
  • Spiral waves persist even at infinite Prandtl numbers.
  • Localized structures emerge via Hopf or stationary bifurcations.

Conclusions:

  • Localized heating in a free-surface fluid layer can lead to diverse instabilities.
  • The study provides a comprehensive overview of these instabilities as a function of system parameters.
  • Findings are relevant for understanding pattern formation in confined fluid systems.