A Question about Kelvin’s circulation theorem

  • A
  • Thread starter Thread starter Seyn
  • Start date Start date
  • Tags Tags
    Fluid dynamic
AI Thread Summary
Kelvin's circulation theorem states that in inviscid flow with constant density and conservative body forces, the circulation around a contour is conserved for fluid particles. This raises the question of whether vorticity is also preserved for each fluid particle under these conditions. Analyzing the vorticity equation, it can be shown that under the same assumptions as Kelvin's theorem, the equation reduces to \frac{D\omega}{Dt} = 0, indicating that vorticity is indeed conserved. Therefore, Kelvin's theorem not only preserves circulation but also ensures the preservation of vorticity for fluid particles. This relationship highlights the fundamental principles of fluid dynamics in inviscid flows.
Seyn
Messages
6
Reaction score
1
In Currie’s fluid mechanics textbook, there is a statement “the vorticity of each fluid particle will be preserved.” as the result of Kelvin’s circulation theorem.
Kelvin’s circulation theorem claims that
For inviscid flow, constant density or barotropic fluid, conservative body force,
the circulation around an arbitrary contour is conserved following same fluid particle.
Does Kelvin’s theorem also guarantee the vorticity on each fluid particles? Why?
 
Physics news on Phys.org
Take a look at the vorticity equation under the same conditions as Kelvin's circulation theorem. Does it reduce to \frac{D\omega}{Dt} = 0?
 
Thread 'Gauss' law seems to imply instantaneous electric field'

Thread 'Gauss' law seems to imply instantaneous electric field'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
View full post »

Similar threads

A Why are the Navier-Stokes equations inconsistent in this case?
Replies
18
Views
2K
I Work - Energy Principle Application to Fluid Flow
Replies
35
Views
4K
I Work - Energy Principle Application to Fluid Flow
Replies
48
Views
5K
A Conservation Laws from Continuity Equations in Fluid Flow
Replies
2
Views
2K
I Why is this closed line integral zero?
Replies
8
Views
2K
Irrotationality somewhere = irrotationality everywhere?
Replies
2
Views
1K
Circulation Around an Airfoil and Starting Vortex
Replies
2
Views
2K
Doublet flow in Fluid Dynamics between two spheres or cylinders
Replies
0
Views
1K
Aircraft wings - Kelvins Circulation Theorem and the conservation of vorticity
Replies
6
Views
8K
I Is something wrong with my understanding of Liouville's Theorem?
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top