Questions tagged [vortex]
The vortex tag has no usage guidance.
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Circulation theorem
The usual derivation of Kelvin circulation theorem start with the following steps:
$$\frac{D\Gamma}{Dt} = \frac{D}{Dt}\left (\oint_{C} \vec {V} \cdot d \vec{s}\right )= \oint_{C}\frac{D\vec{V}}{Dt}\...
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What is the topology of sine-Gordon equation?
In one pdf on solitons, I am finding the following written
For the sine-Gordon theory, it is much better to think of $\phi$ as a field modulo $2\pi$, i.e. as a function $\phi: R \rightarrow S_{1}$. ...
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Why does the 'vortex stretching term' not appear in Kelvin Circulation theorem?
The Kelvins circulation theorem states that "In a inviscid, barotropic fluid with conservative body forces, the circulation around a closed curve moving with the fluid remains constant with time; ...
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How to understand the Orbital angular momentum of a photon that is not an integer？
How to understand the topological charge that is not an integer, how would the signal OAM crosstalk if one were to model its transport in turbulence, for example, if the beam carries a topological ...
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Which are the incompressible flows around a sphere with no azimuthal vorticity?
Assume fluid velocity $\vec{u}(r, θ, φ)$
radial distance: r ≥ 0,
polar angle: 0° ≤ θ ≤ 180° (π rad),
azimuth : 0° ≤ φ < 360° (2π rad).
At r much larger than sphere radius the flow is $\vec{u}=u_0 * ...
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Measuring vortices in numerical $XY$-like models
I am simulating an $XY$ model, meaning that I have a $L\times L$ lattice with a unit vector $\vec s_i$ associated with each site. Each $\vec s_i$ is univocally specified by its angle $\theta \in [0,2\...
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Vortices in a Superconductor: triangular lattice VS other geometries
Why do vortices in a superconductor (i.e. magnetic flux-tubes) form triangular lattices? In one of the articles I found, I read that a square lattice would cause repulsion but a triangular lattice ...
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On Euler: the vorticity vector is not invariant, but vorticity over density is
I've been reading Frankel's Geometry of Physics but I'm struggling to understand a section devoted to "Additional problems on fluid flow" (Sec. 4.3c in my edition).
Consider a fluid flow in $...
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Are there any research mentioning the principle of tornados or maelstroms in plasma physics related to fusion?
There are many different ideas and concepts related to design of fusion reactors and handling plasma confinement, but what about designing one around the principles of a maelstrom or a tornado? Is ...
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Centripetal force in special case of fluid mechanics
If you put a ball on moving circular disc with angular velocity the ball moves outward but when we create a whirlpool (not so big) and put ball in it then why does it get sucked inward rather than ...
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Are closed streamlines necessary to have vortices?
I am studying fluid dynamics, and all the examples I have found so far about vortices show closed streamlines rotating around an axis.
All these examples suggest that having closed streamlines is a ...
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Unusual vortex actions along vehicle roof
Let me open by stating that I do understand the ethical implications of my failure to brush the snow off my roof.
After arriving at work I noticed an unusual snow erosion pattern on the roof of my car....
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Magnetic vortices in type 2 superconductors
Do I have magnetic vortices in the type-II superconducting phase without an external magnetic field and without an applied electric current?
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Topological classification of (classical, Abelian) vortices on a lattice
Consider the XY model on the square lattice. A field configuration $\theta$ is specified by an element of the Abelian group $\mathbb{R}/2\pi \simeq U(1)$ at each vertex of the lattice. The gradient of ...
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What happens with the tip vortices of two aircraft flying in the opposite direction?
Suppose that an aircraft flies with its wing through an tip vortex of another aircraft which flew in the opposite direction. Suppose that the shed wing tip vortex of both aircraft are exactly the same ...
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Guidance on the traits of whirlpools
My current understanding of whirlpools is that two opposing forces of water currents come into contact with each other and that somehow pushes the water down. I am under the assumption as well that ...
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What Continued Upwards Momentum Has to Do with Vortex in Bee Wings?
In this answer to how bumblebees fly, it says that
The wing motion has a sort of double lift feature. By twisting her wings over at the end of each down stroke, the upward momentum is never lost. ...
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Derivation of vorticity equation (incompressible flow)
In the following derivation of the vorticity equation, I do not understand how $\nabla \cdot v=0$ implies $\frac{1}{\rho^2}\nabla \rho \times \nabla p=0$.
We start with the Euler equation
$$\frac{\...
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Do hurricanes spin?
It is often said that the spin of a hurricane forms as a result of being in a rotating reference frame with the spin caused by the coriolis force. For example, if you’re on a merry-go-round and you ...
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Is there instanton event in $\rm O(2)$ model?
For $\rm O(3)$ model, the hedgehog (or Monopole) like instanton events in the euclidean evolution usually disorder the long range correlation in the Neel configuration (change the skyrmion number of ...
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Material derivative of circulation, Kelvin's theorem
i'm trying to work with the material derivative $$\frac{D}{Dt}=\frac{\partial}{\partial t}+(\vec{u}\cdot \vec{\nabla}) $$ of the circulation $\Gamma=\oint_{C=\partial S}\vec{u}\cdot d\vec{l}$, that ...
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Turbulence from a sphere spinning in an incompressible liquid
When I look online I can find plenty of simulations of Stokes flow: incompressible liquid flowing past a spherical object. What I'm interested in is the problem of a sphere (of given size) spinning (...
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Helicity vs vorticity in skyrmion lattice
I am interested in clarifying the difference between the helicity and vorticity of a skyrmion.
There has been interest in centrosymmetric skyrmion hosting materials due to centrosymmetry giving a ...
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What do Hawking/Ellis mean exactly by "non-rotating families of geodesics"?
In The Large Scale Structure of Space-Time, Hawking and Ellis refer twice (page 4, page 78) to non-rotating families of geodesics.
I don't know what that means. Is a rotating geodesic one that ...
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Vorticity in an irrotational flow
My understanding is that if vorticity is zero, then the flow is irrotational. Does that mean we can never have nonzero vorticity in an irrotational flow? If not, how can we have vorticity in an ...
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When two opposing vortexes combine to form a dipole vortex, why does it always move in the same direction?
AS you know, when two opposing vortexes combine to form a dipole vortex, it always move in the same direction as shown with red arrow in figure below. I wonder, why? is there a equation for this ...
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Estimating the Characteristic Time of Spinning Tea
Suppose I have a cup of tea and stir it so it gains some angular velocity $\omega_0$. Could you estimate the characteristic time $\tau$ it takes for the tea to stop rotating (or to lose half its ...
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Isentropic fluid: cross product of gradients is zero, why?
In the vorticity equation we have the baroclinic term of the form: $$\frac{ {\nabla}\rho}{\rho}\times\frac{ {\nabla}{P} }{\rho}.$$
Why does it go to zero for isentropic flow?
I understand that, if the ...
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Can someone give a picture to visualize and elucidate the celebrated rhyme of Richardson about turbulence? [closed]
Richardson's celebrated rhyme is below:
Big whorls have little whorls,
which feed on their velocity,
and little whorls have lesser whorls,
and so on to viscosity.
(Lewis F. Richardson, 1920)
I read ...
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Curl of a velocity [closed]
In classical mechanics, is the curl of $\vec{v}$ always zero? As $\nabla$ is in position space and not in velocity space ($\nabla_v$). What am I missing regarding $\nabla$ operator in different spaces?...
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How do the Navier-Stokes equations predict vortex creation in a vorticity free fluid?
For this question I was looking at the Navier-Stokes equations after you get the curl, this gives you the equation:
$$\frac{\partial \vec{\Omega}}{\partial t}-\nabla \times (\vec{v} \times \vec{\...
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Vortex line, tube, sheet, and filament
In my study of fluid dynamics I have across these terms quite often and I am so far unable to create a physical picture in my head. Suppose we have a 3D velocity field $u$, and its corresponding ...
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Do vortex rings have an intrinsic forward momentum? (Feynman lectures II.41)
I was going through Feynman's lecture vol.II, #41 about non-viscous fluid mechanics, and he makes a point that I do not understand.
Towards the end, he discusses vortex rings (he takes the youtube-...
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What causes the formation of vortices in a separated flow?
Consider flow over a cylinder. At a high enough Reynold's Number, the strength of the adverse pressure gradient becomes too large for the boundary layer to be able to remain attached to the cylinder. ...
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Vorticity: what is the difference between $\nabla \times f$ and $\nabla \wedge f$? [duplicate]
I have always thought that we may obtain information about the vorticity of a vector field $f$ by considering the cross product $\nabla \times f$. In higher level texts on fluid mechanics I see that ...
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Vortex generated as a result of Newton's third law
This books states this process as a result of Newton's third law. However I just can't find ways to graps how the "vortex" is generated, is it a fundamental law? (The question emerges on the ...
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Topological charge change in QFT
Is it possible for the topological charge to change in quantum field theory?
The proofs in the following paper: Quantum soliton operators for vortices and superselection rules
are all based on the ...
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Finding angular velocity in viscous flow on circular path
I do not know whether this problem is even correct or not (the problem constitutes a 'what if' thought), but nonetheless providing a description
Suppose the viscous flow of a liquid in circular path. ...
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Acceleration of fluid in a magnetohydrodynamics vortex
In the following video we see a mercury vortex done by magnetohydrodynamics:
https://youtu.be/au4hbUm4mMo
In the following manuscript they say that the fluid will accelerate according to (14) ${}^1$:
...
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Can I treat fluid a rigid body calculating Moment of inertia? If not, how would I calculate it?
I wanted to set out calculating how much moment of inertia a bottle of water had so as to see how fast a bottle had to spin to create a non-zero constant angular velocity in the water.
As I understand,...
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Will two rotating disks in a fluid be 'attracted' to each other?
Imagine two rotating disks in a fluid like this drawing here:
The rotating disks will create a rotating flow by friction in the fluid. The flow between the disks will be higher velocity than the ...
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How does gravity affect the formation of vortices?
Context: I understand the axis of vortices can form in any direction (like underwater used by fishes). However, in large vortices in water bodies, for example, in a closed water bottle, the centre of ...
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Why is the energy of a vortex in a superconductor finite?
I just had a glimpse of the Ginzburg-Landau theory of superconductivity. I am surprised that that the energy of a vortex is finite. This is surprising because as far as I know, in superfluids, the ...
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Why does my coffee spin the opposite way that I spin the cup?
I was just drinking a latte in a large cup, and when I spun the cup (doing that smooth one handed “mixing” thing that you usually see with a mixed drink or something) I noticed the design on and the ...
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What role do quantized vortices play from the Superfluid model in Superfluid Vacuum Theory?
When rotating a superfluid (such as $^{4}$He) below its critical temperature, sometimes quantized vortices pop up, depending how fast one rotates this superfluid. In the SVT model, they propose that ...
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Why do "quantum vortices" form in superfluids?
I've been reading up on Superfluids, and they've fascinated me. I understand why their superfluid component has zero viscosity, but there's one aspect that's bothering me, and that's the formation of ...
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Argument for flux quantization
I am reading P. Coleman's Introduction to many-body physics. Coleman claims that At large distances, energetics favor a reduction of the circulation to zero
$$\lim_{R\rightarrow \infty}\omega=0$$
...
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How can I compute the axis of rotation of a fluid vortex from the velocity field?
Let's say I have data on the velocity vector field of a fluid vortex such as e.g. a Hurricane available on a regular 2D grid. How can I compute the axis of rotation of the velocity vector field to ...
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How exactly do vortices generate sound and cause pressure fluctuations to produce sound waves?
I wish to understand qualitatively, how vortices generate sound by creating longitudinal sound waves? Vortices are often mentioned as the cause of sound production for things like corrugated whirly ...
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Is vortex physics key to understand the universe simulation hypothesis? [duplicate]
Seth Lloyd, US computer scientist and Professor of Mechanical Engineering and Physics at the renowned Massachusetts Institute of Technology (MIT) says that the universe itself is a giant quantum ...
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