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How do I find the absolute maximum and minimum values of the Lamb-Oseen Vortex?

For an angular velocity function derived by Navier-Stokes, $$ \omega \left(r,t\right)=\frac{\omega _0R_0^2}{R\left(t\right)^2}exp\left(-\frac{r^2}{R\left(t\right)^2}\right)$$ from which the azimuthal ...
Tayler Montgomery's user avatar
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What is the relationship between a fluid vortex's expansion rate and its kinematic viscosity?

I've read through research papers with very specific radius formulas pertaining to 2D fluid vortexes, such as confined rotation with variations in pressure and density ($\rho(r,t)$ and $p(r,t)$), ...
Tayler Montgomery's user avatar
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Is this assumption about a vortex's angular velocity reasonable?

I am deriving a velocity flow function $\psi(r,t)$ that could be derived by (1) establishing the relation between two vortex area functions, $a(t)$ and $A(r)$, using the disk method of integration, ...
Tayler Montgomery's user avatar
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What is the vortex pattern when the flow is passing an axis-symmetric vortex flowmeter?

It is wellknown that in 2D case, the vortices will be formed at the back of the bluff body and detached periodically from either side of the body in a pattern called Kármán vortex street. But what ...
MathArt's user avatar
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When pouring water into a water body, how does that form one or more vortices in the water body?

When pouring water into a water body, sometimes it forms one or more vortices and sometimes it doesn't. I know it has something to do with the conservation of angular momentum but what are the exact ...
Sunbeam's user avatar
6 votes
1 answer
127 views

Why do jet engine vortices go toward the ground?

This image was shown to us to illustrate how a tornado forms due to a low pressure region (also see Jet engine vortices). I find it odd that the tornado always ends up at the ground, where it is a ...
AlphaLife's user avatar
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How to derive the ODE from the EOM of vortex?

In the Lagrangian mode we have the equation of motion \begin{align} \partial_\mu F^{\mu\nu}&=j^\nu. \\ D_{\mu }D^{\mu}\phi +\mu^{2}\phi-\lambda(\phi^{*}\phi)\phi &=0. \end{align} Since we ...
Qian-Sheng's user avatar
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How to calculate the latitude/longitude by the RPM in the basin? [duplicate]

By seeing how the water swirls and whirlpools when going down the drain in a washbasin is it possible to tell something about the longitude or latitude where the individual is?
More Anonymous's user avatar
1 vote
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Hot dust contribution to whirlwinds forming

My father observed an event with a whirlwind and had an aha moment on its forming. What he saw was a weak wind blowing over a sun heated patch of dust, and when the dust rose up, all of suddenly a ...
Nemanja's user avatar
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Metric of a rotating Cosmic String

I searched on the internet superficially but I couldn't find it. Is there any reference that find the solution to Einstein's Field Equations for a rotating Cosmic String? Personally haven't got the ...
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Cosmic string in real space

I am considering $U(1)$ global cosmic string. In the case of wine-bottle potential with real field ($\phi$), it is known that there exists a static solution that corresponds to cosmic string (or ...
PhysicsStudy's user avatar
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2 answers
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What will happen if three equal tornadoes compressed together in one axis? [closed]

Imagine, 3 completely equal tornadoes with similar spin are compressing together by huge outer force in one axis and we can control the amount of outer force, what will happen as we gradually increase ...
QQQ's user avatar
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Best Shape for Creating a Liquid Vortex

I am trying to create a vortex in a closed tube, and I am wondering if there are any resources with research on what shape would be most effective for creating this vortex. Literally any shape, paddle,...
M.S.'s user avatar
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2 answers
50 views

How does a shear layer make vortices?

How does a shear layer make vortices? If you have 2 streams of air that are moving at different speeds or opposite directions right beside each other, how does that make a vortex? What causes the ...
Wyatt's user avatar
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Can vortices be formed in a non-viscous fluid?

As I understand vortices form when a part of a fluid is moving with greater velocity, than its neighbour parts, so its neighbour parts that are moving slower ''want to slow down its faster neighbour ...
Imagination's user avatar
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What is the physical significance of the cross product of curl of a vector field $v$ with another vector field $w$?

I think if curl of a vector field v corresponds to an applied rotation, it's cross product with a velocity vector field w (say) should give something analogous to the resulting torque. Am I close?
Benjamin Kurian's user avatar
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1 answer
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Physical significance of $\vec{w}$ $\times$ $($curl $\vec{v})$

I think if curl of a vector field $\vec{v}$ corresponds to an applied rotation, it's cross product with a velocity vector field $\vec{w}$ (say) should give something analogous to the resulting torque. ...
Benjamin Kurian's user avatar
2 votes
0 answers
36 views

Frequence vs speed of a moving object

Imagine swinging wood stick using hand (say it's a 1-meter long cylinder with 2 centimeter diameter, just for the sake of argument). When doing it fast (angular velocity = $\omega_1$), it will create ...
h218614's user avatar
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Vorticity in quantum field theory

Can you refer some good papers to read on quantum field vortices, and a comparison with classical field vortices?
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Would flux tubes be prevented from passing through a sufficiently thick superinsulating layer?

Suppose you have a type-2 superconducting cube with a thick superinsulating layer passing through the middle of the cube; visualized below with (grey superconducting mass, violet superinsulator in ...
Sidharth Ghoshal's user avatar
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Assuming vortex defect pinning is equal, and number of tubes are equal should longer flux tubes lead to stronger pinning?

Suppose you have two superconductors that resemble rectangular prisms with identical width and length. The first superconductor call it $A$ is shorter than $B$ visualized below: Now both $A$ and $B$ ...
Sidharth Ghoshal's user avatar
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2 answers
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What would happen if I swirl a bottle of water in the space station?

Right now I am swinging a bottle of water in a tight circular motion to form a vortex, the vortex will last quite a while after I stopped swinging it. The vortex will took the shape of a funnel in 1g ...
user6760's user avatar
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1 vote
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Has Biot–Savart law real physics in fluids?

In this video from 28:27-36:50 author talk how Bio Sawrt law dont have any physics in aerodynamics, he say it is just math concept and how vorticity cant induce velocity in fluid somewhere in the ...
22flower's user avatar
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2 answers
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How would we explain a whirlpool shape without using centrifugal forces?

How would we explain a whirlpool shape formed in a bucket without using fictitious forces like centrifugal force? I am in high school and my teacher always gave me the explanation for shape of ...
Shyam's user avatar
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How does a fluid element have vorticity if the stress tensor is symmetric

Considering incompressible, Newtonian fluid as an example. The stress tensor is dependent on the symmetric part of the strain rate tensor, which is also symmetric. What I don't understand is, with a ...
Ishan Tandon's user avatar
1 vote
0 answers
52 views

How to calculate vortex movement in fluid dynamics?

I'm going mad...I just want to understand: Given there are three vortices of type "Rankine" in an incompressible 2D-fluid, each having radius R and a given vorticity $\Omega$ inside r<R. ...
MichaelW's user avatar
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Coriolis effect in the bathroom? [duplicate]

I understand that the Coriolis effect is not responsible for the spin effect in the bathroom, but I have never seen a rigorous math prof of this. Where could I find a proof of this? What references ...
eraldcoil's user avatar
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What does vorticity and circulation physically signify?

When I see say a circulation value of 0, pi, 2pi or -12pi, what should this mean to me? I am a beginner in fm and have been trying to understand vorticity and circulation's physical significance and ...
SR...'s user avatar
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1 answer
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Can an ideal fluid undergoes a turbulent flow?

I have read before that the existence of viscosity is the main reason for the appearance of vortex. However, by definition, an ideal fluid has $\eta=0$. So, can an ideal fluid undergo a turbulent ...
Jack's user avatar
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How can the vortex be an elemental potential flow if there is a point of curl?

Aero is not my speciality at all so apologies if missed anything. But when looking at potential flows, i thought the whole point is for there to be no rotation at any point and its that reason the ...
George kirby's user avatar
2 votes
2 answers
514 views

What is the physical meaning of "flow" or "circulation" in fluid dynamics?

In fluid dynamics, the line integral of velocity field is called "flow," or "circulation" if the curve is closed. But does velocity times length correspond to any physically ...
ashpool's user avatar
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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}\...
franchino's user avatar
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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 $\phi: R \rightarrow S_{1}$. ...
Arkaprava Sil's user avatar
2 votes
1 answer
95 views

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; ...
AK1987's user avatar
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1 vote
1 answer
176 views

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 ...
Matthias's user avatar
1 vote
0 answers
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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 * ...
David Jonsson's user avatar
2 votes
1 answer
76 views

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\...
sonarventu's user avatar
4 votes
1 answer
182 views

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 ...
Anshul Sharma's user avatar
1 vote
1 answer
105 views

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 $...
Stuart M.'s user avatar
1 vote
1 answer
40 views

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 ...
Andreas Zita's user avatar
2 votes
6 answers
776 views

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 ...
Chaos's user avatar
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1 answer
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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....
Nic Der Hund's user avatar
2 votes
0 answers
52 views

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 ...
Kai's user avatar
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1 vote
3 answers
75 views

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 ...
lWindy's user avatar
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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. ...
MeltedStatementRecognizing's user avatar
3 votes
1 answer
388 views

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{\...
bhoutik's user avatar
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2 votes
2 answers
181 views

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 ...
user avatar
0 votes
1 answer
148 views

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 ...
martín canullán's user avatar
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0 answers
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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 (...
StanThePhysicsMan's user avatar
1 vote
1 answer
54 views

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 ...
John's user avatar
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