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

909
The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.
909
Plane Potential Flows01:23

Plane Potential Flows

452
Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform...
452
Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

204
Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
204
Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

425
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...
425
Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

1.1K
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:
1.1K
Pole and System Stability01:24

Pole and System Stability

419
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
419

You might also read

Related Articles

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

Sort by
Same journal

Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta.

Proceedings. Mathematical, physical, and engineering sciences·2025
Same journal

Inferring the shape of data: a probabilistic framework for analysing experiments in the natural sciences.

Proceedings. Mathematical, physical, and engineering sciences·2023
Same journal

The Elbert range of magnetostrophic convection. I. Linear theory.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Soft wetting with (a)symmetric Shuttleworth effect.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

The quantum theory of time: a calculus for q-numbers.

Proceedings. Mathematical, physical, and engineering sciences·2022
Same journal

Integrable nonlinear evolution equations in three spatial dimensions.

Proceedings. Mathematical, physical, and engineering sciences·2022
See all related articles

Related Experiment Video

Updated: Sep 8, 2025

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

Stability of two-dimensional potential flows using bicomplex numbers.

V G Kleine1,2, A Hanifi1,2, D S Henningson1

  • 1Department of Engineering Mechanics, KTH Royal Institute of Technology, FLOW, Stockholm, Sweden.

Proceedings. Mathematical, Physical, and Engineering Sciences
|June 15, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a novel bicomplex number framework to unify complex velocity potential and real vector velocity representations in fluid dynamics stability analysis, particularly for the von Kármán vortex street.

Keywords:
bicomplex numberslinear systemspotential flowstabilityvortex

More Related Videos

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

11.7K
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

Related Experiment Videos

Last Updated: Sep 8, 2025

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
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

11.7K
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

Area of Science:

  • Fluid dynamics
  • Theoretical aerodynamics
  • Mathematical physics

Background:

  • Complex velocity potential is standard in 2D incompressible potential flows.
  • Real vector velocity is preferred in linear stability studies for perturbation representation.
  • Previous attempts to use complex velocity potential in stability studies had formal errors.

Purpose of the Study:

  • To reconcile differing complex representations in fluid flow stability analysis.
  • To develop a unified framework using bicomplex numbers.
  • To apply this framework to the von Kármán vortex street stability.

Main Methods:

  • Utilizing bicomplex numbers to bridge complex velocity potential and real vector velocity representations.
  • Applying the developed framework to analyze the stability of the von Kármán vortex street.
  • Deriving a generalized formula for stability analysis.

Main Results:

  • A successful reconciliation of the two complex representations is achieved.
  • A generalized formula for the stability of the von Kármán vortex street is derived.
  • Classical symmetric and staggered vortex street results are shown as specific cases of the generalized bicomplex formulation.

Conclusions:

  • The bicomplex framework offers a unified approach to fluid flow stability.
  • This method resolves formal errors in prior complex potential stability studies.
  • The generalized formula provides new insights into von Kármán vortex street dynamics.