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 'The Effect of Linear and Rotational Motion on Measured Weight'

Consider an extremely long and perfectly calibrated scale. A car with a mass of 1000 kg is placed on it, and the scale registers this weight accurately. Now, suppose the car begins to move, reaching very high speeds. Neglecting air resistance and rolling friction, if the car attains, for example, a velocity of 500 km/h, will the scale still indicate a weight corresponding to 1000 kg, or will the measured value decrease as a result of the motion? In a second scenario, imagine a person with a...
View full post »

Thread 'Coulomb gauge implies instantaneous radial electric field?'

Scalar and vector potentials in Coulomb gauge Assume Coulomb gauge so that $$\nabla \cdot \mathbf{A}=0.\tag{1}$$ The scalar potential ##\phi## is described by Poisson's equation $$\nabla^2 \phi = -\frac{\rho}{\varepsilon_0}\tag{2}$$ which has the instantaneous general solution given by $$\phi(\mathbf{r},t)=\frac{1}{4\pi\varepsilon_0}\int \frac{\rho(\mathbf{r}',t)}{|\mathbf{r}-\mathbf{r}'|}d^3r'.\tag{3}$$ In Coulomb gauge the vector potential ##\mathbf{A}## is given by...
View full post »
Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (First part)'

Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (First part)'

I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8 and stuck at some statements. It's little bit confused. > Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin. Solution : The surface bound charge on the ##xy## plane is of opposite sign to ##q##, so the force will be...
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
3K
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