Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Navier–Stokes Equations01:28

Navier–Stokes Equations

887
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...
887
Euler's Equations of Motion01:28

Euler's Equations of Motion

604
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...
604
Energy Conservation and Bernoulli's Equation01:16

Energy 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...
9.6K
Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

505
Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
505
Couette Flow01:22

Couette Flow

505
Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
505
Conservation of Mass in Finite Cotrol Volume01:16

Conservation of Mass in Finite Cotrol Volume

1.4K
The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
1.4K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Limiting Absorption Principles and Linear Inviscid Damping in the Euler-Boussinesq System in the Periodic Channel.

Communications in mathematical physics·2025
Same author

Efficient quantum algorithm for dissipative nonlinear differential equations.

Proceedings of the National Academy of Sciences of the United States of America·2021
Same author

Bacteria Floc, but Do They Flock? Insights from Population Interaction Models of Quorum Sensing.

mBio·2019
See all related articles

Related Experiment Video

Updated: Oct 2, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.7K

Invariant Measures for the Stochastic One-Dimensional Compressible Navier-Stokes Equations.

Michele Coti Zelati1, Nathan Glatt-Holtz2, Konstantina Trivisa3

  • 1Department of Mathematics, Imperial College London, London, SW7 2AZ UK.

Applied Mathematics and Optimization
|February 25, 2022
PubMed
Summary
This summary is machine-generated.

Researchers proved the existence of an invariant measure for a stochastically forced one-dimensional Navier-Stokes system, crucial for understanding fluid motion long-term behavior. This work advances the analysis of complex fluid dynamics models.

Keywords:
Compressible fluidInvariant measureNavier–Stokes systemStochastic perturbation

More Related Videos

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

12.4K
Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

8.8K

Related Experiment Videos

Last Updated: Oct 2, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

8.7K
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

12.4K
Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

8.8K

Area of Science:

  • Fluid Dynamics
  • Stochastic Analysis
  • Partial Differential Equations

Background:

  • The study focuses on the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system.
  • This system models the motion of a compressible viscous fluid with a linear pressure law.

Purpose of the Study:

  • To investigate the long-time behavior of solutions for the specified Navier-Stokes system.
  • To prove the existence of an invariant measure for the associated Markov process.

Main Methods:

  • Generalization of the classical Krylov-Bogoliubov method to handle non-Feller Markov semigroups on non-complete metric spaces.
  • Derivation of polynomial and exponential moment bounds for the solutions.
  • Utilization of pathwise estimates to analyze the system's behavior.

Main Results:

  • Existence of an invariant measure for the Markov process generated by strong solutions has been proven.
  • The study successfully overcomes analytical challenges associated with non-complete metric spaces and non-Feller semigroups.

Conclusions:

  • The findings provide a fundamental understanding of the long-term statistical properties of the stochastically forced fluid system.
  • This research contributes to the rigorous mathematical analysis of complex fluid dynamics models.