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

Euler's Equations of Motion01:28

Euler's Equations of Motion

1.0K
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 uniform across...
1.0K
Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

5.0K
A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time....
5.0K
Equations of Wave Motion01:02

Equations of Wave Motion

8.8K
Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
8.8K
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

2.4K
Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations:...
2.4K
Navier–Stokes Equations01:28

Navier–Stokes Equations

2.6K
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...
2.6K
Velocity Potential01:20

Velocity Potential

803
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:
803

You might also read

Related Articles

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

Sort by
Same author

Canonical variables for steep planar water waves over nonuniform beds.

Physical review. E, Statistical, nonlinear, and soft matter physics·2010
Same author

Water wave collapses over quasi-one-dimensional nonuniformly periodic bed profiles.

Physical review. E, Statistical, nonlinear, and soft matter physics·2010
Same author

Two different kinds of rogue waves in weakly crossing sea states.

Physical review. E, Statistical, nonlinear, and soft matter physics·2009
Same author

Water-wave gap solitons: an approximate theory and numerical solutions of the exact equations of motion.

Physical review. E, Statistical, nonlinear, and soft matter physics·2009
Same author

Highly nonlinear Bragg quasisolitons in the dynamics of water waves.

Physical review. E, Statistical, nonlinear, and soft matter physics·2008
Same author

Nonlinear stage of the Benjamin-Feir instability: three-dimensional coherent structures and rogue waves.

Physical review letters·2007

Related Experiment Video

Updated: Mar 16, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
04:35

Preparation of Free-Surface Hyperbolic Water Vortices

Published on: July 28, 2023

3.9K

Explicit equations for two-dimensional water waves with constant vorticity.

V P Ruban1

  • 1Landau Institute for Theoretical Physics, Moscow, Russia. ruban@itp.ac.ru

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary

This study presents exact equations for 2D inviscid free-surface flows with constant vorticity over uneven bottoms. An efficient and accurate numerical method is developed for solving these complex fluid dynamics problems.

More Related Videos

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
09:37

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole

Published on: August 26, 2019

6.2K
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

12.0K

Related Experiment Videos

Last Updated: Mar 16, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
04:35

Preparation of Free-Surface Hyperbolic Water Vortices

Published on: July 28, 2023

3.9K
Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole
09:37

Visualization of Flow Field Around a Vibrating Pipeline Within an Equilibrium Scour Hole

Published on: August 26, 2019

6.2K
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

12.0K

Area of Science:

  • Fluid dynamics
  • Applied mathematics

Background:

  • Free-surface flows are fundamental in many scientific and engineering disciplines.
  • Understanding flow dynamics over complex geometries is crucial for accurate modeling.

Purpose of the Study:

  • To derive exact and compact governing equations for 2D inviscid free-surface flows.
  • To develop an efficient and accurate numerical method for solving these equations.

Main Methods:

  • Utilizing conformal variables to simplify the governing equations.
  • Developing a novel numerical approach for flow simulation.

Main Results:

  • Exact and compact mathematical formulation of the flow dynamics.
  • Demonstration of an efficient and highly accurate numerical solution.

Conclusions:

  • The developed method provides a powerful tool for analyzing free-surface flows.
  • The exact equations offer a foundation for further theoretical and numerical advancements.