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

The Buckingham Pi Theorem01:09

The Buckingham Pi Theorem

990
The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.
990
Euler's Equations of Motion01:28

Euler's Equations of Motion

590
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...
590
Newtonian Fluid: Problem Solving01:18

Newtonian Fluid: Problem Solving

419
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
419
Laminar Flow: Problem Solving01:24

Laminar Flow: Problem Solving

267
Laminar flow occurs when a fluid moves smoothly in parallel layers with minimal mixing and turbulence. In fluid mechanics, ensuring laminar flow within a pipe is essential for precise control of flow characteristics, especially in engineering applications. The key factor in determining whether flow remains laminar is the Reynolds number, a dimensionless quantity that depends on the fluid's velocity, density, viscosity, and the pipe's diameter. A Reynolds number of 2100 or lower...
267
Navier–Stokes Equations01:28

Navier–Stokes Equations

813
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...
813
Dimensional Analysis01:27

Dimensional Analysis

422
Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
In fluid mechanics, dimensional...
422

You might also read

Related Articles

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

Sort by
Same author

Open-flow mixing and transfer operators.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2022
Same author

Editorial: Mathematical problems in physical fluid dynamics: part I.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2022
Same author

Systematic search for extreme and singular behaviour in some fundamental models of fluid mechanics.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2022
Same author

Minimum wave speeds in monostable reaction-diffusion equations: sharp bounds by polynomial optimization.

Proceedings. Mathematical, physical, and engineering sciences·2020
Same journal

Correction to: 'Stokes settling and particle-laden plumes: implications for deep-sea mining and volcanic eruption plumes' (2020), by Mingotti et al.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

A stable hothouse triggered by a tipping mechanism.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Beyond distance: quantifying point cloud dynamics with persistent homology and dynamic optimal transport.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Global stability of the Atlantic overturning circulation: edge state, long transients and boundary crisis under CO2 forcing.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Morse index classification and landscape of Kuramoto system for Hebbian-based binary pattern recognition.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Interpretable and equation-free response theory for complex systems.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
See all related articles

Related Experiment Video

Updated: Sep 24, 2025

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
13:07

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Published on: January 15, 2022

4.1K

Editorial: Mathematical problems in physical fluid dynamics: part II.

D Goluskin1, B Protas2, J-L Thiffeault3

  • 1Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|May 9, 2022
PubMed
Summary
This summary is machine-generated.

Mathematical fluid dynamics research addresses unanswered questions in physics and applied mathematics. Recent advances combine modeling, computation, and analysis to tackle problems in fluid dynamical stability, transport, and vortex dynamics.

Keywords:
a priori boundsconvectionmixingtransportturbulencevortex dynamics

More Related Videos

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids
10:28

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

Published on: January 3, 2014

13.8K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.6K

Related Experiment Videos

Last Updated: Sep 24, 2025

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
13:07

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Published on: January 15, 2022

4.1K
Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids
10:28

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

Published on: January 3, 2014

13.8K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.6K

Area of Science:

  • Fluid dynamics research at the intersection of physics and applied mathematics.
  • Investigates fundamental questions in fluid dynamics with broad applications.

Background:

  • Many open questions in fluid dynamics relate to the validity of mathematical models, particularly partial differential equations.
  • Decades of research have yet to resolve core issues concerning these models and their physical interpretations.

Discussion:

  • Recent progress in fluid dynamics utilizes interdisciplinary approaches, merging modern modeling, computation, and mathematical analysis.
  • Focuses on mathematical problems with significant implications for physical phenomena.

Key Insights:

  • Explores fluid dynamical stability, transport, mixing, dissipation, and vortex dynamics.
  • Highlights the importance of mathematical rigor in understanding physical fluid behavior.

Outlook:

  • The theme issue showcases diverse approaches to complex mathematical problems in physical fluid dynamics.
  • Encourages continued integration of mathematical methods for advancing fluid dynamics understanding.