Questions tagged [vortex]

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Kinetic energy of vortex rings

According to a standard textbook on fluid dynamics (Physical Hydrodynamics, Guyon et al., Oxford University Press, 2015), the order of magnitude of the velocity of a plane circular vortex ring of ...
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How to calculate strouhal number/vortex shedding frequency of the airfoil using mathematical approach?

As a part of my thesis, I am trying to find when the airfoil starts to flutter by changing pitch angles. I've computed the results in ANSYS Fluent. But now I've to calculate the same using a ...
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Curl of rotational fluid

If I consider a fluid which rotates as a rigid body, then the curl of the velocity field is $2\vec\omega$ where $\vec\omega$ is the angular velocity of the rigid body, but let us assume that we are ...
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How to calculate a single Abrikosov vortex's structure in superconductor through Ginzberg-Landau theory when $\kappa$ near $1/\sqrt{2}$?

As the title. We can find the approximate solution for large $\kappa$ in any textbook about superconductor.
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Assumptions in a Moving Fluid

I saw this paper recently "On Integrals of the Hydrodynamic Equations That Correspond to Vortex Motions" by Hermann Von Helmholtz. It can be found here. In this research paper he discovered ...
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Magnetic vortex in magnets

I was doing some physics problems and randomly came upon a seemingly very intelligent but very rude individual. His video in question was about magnetism and that there is a vortex and counter-vortex ...
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Vortex formation in an airfoil

How is a starting vortex formed when an airfoil (i.e cross-section of wings of a plane) starts to move?
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Vortex study using video analysis?

I would like to know if they can recommend books or works where vortices are studied through video analysis (for example with TRACKER). I am interested in this because in an undergraduate experimental ...
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Vacuum manifold of Glashow-Weinberg-Salam & lack of vortex solutions

Update: may have figured it out (below) I've been reading Preskill's notes on vortices, and he's included a couple of exercises at the end of section 1.3. In the first, you must look at the breaking ...
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When is it true that “for a given velocity field, the curl represents a vector equal to twice the angular velocity vector”?

On page 154 of Theoretical Physics, By: Georg Joos, Ira M. Freeman the following is stated: Thus for a given velocity field, $\text{curl} \mathfrak{v}$ represents a vector equal to twice the angular ...
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Is there a relationship between circulation and quantization?

The circulation ( https://en.wikipedia.org/wiki/Circulation_(fluid_dynamics) ) is defined as $$ \Gamma = \oint_\mathcal{C} \mathbf{v} \cdot d \mathbf{l}\tag{1} $$ where $\mathbf{v}$ is the velocity ...
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$\nabla \times \bf{u} \neq 0$ but $\oint_{c} \bf{u} \cdot \textit{d}r \textit{=0}$?

Consider the vector field $\vec{u}=(xy^2,x^2y,xyz^2)$ The curl of the vector field is $$\nabla \times\vec{u}=(xz^2,-yz^2,0)$$ Consider the line integral of $\vec{u}$ around the ellipse $C$ $x^2+4y^2=...
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Why does this ice cube rotate when it melts on a flat platform?

I had incidentally noticed this. An ice cube that fell on the kitchen granite platform started to melt and as it melted it also started to rotate. I tried to stop it by touching it, but it starts to ...
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Why are free vortices irrotational?

In free vortices (such as water draining in a sink) the molecules away from the center axis will be irrotational. Why is this the case in terms of how the forces on the individual molecules differ ...
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Are velocity fields in energy conserving systems necessarily irrotational?

Let's assume that we consider a bunch of particles (e.g. water or air) and we describe their velocity using a vector field $\vec v(\vec x, t)$. Moreover, let's assume that there is no external ...
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Vortex bound state for chiral $p$-wave half quantum vortex (HQV)

I understand that in a chiral $p$-wave half quantum vortex (HQV) only one spin state winds around the vortex and the other spin has no winding number associate with it. However, would there be an ...
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Textbooks/papers on behavior of rigid body in funnel or liquid vortex

I´d like to learn more about the behaviour of a rigid body, e.g. a ball, in either a funnel or a vortex created in a liquid. Is there any textbook or paper you recommend for beginners? In particular, ...
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Question about several details in the theory of “Taylor column”

My question refers to a remerkable phenomenon in fluid mechanics, in which flow velocities in a rotating tank of fluid (flow velocity is measured relative to a frame of reference that is rotating ...
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1answer
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Vorticity and angular momentum

In Taylor-Couette flow, the interior fluid becomes fully turbulent if the relative angular velocity of the cylinders is high enough. The turbulent fluid has a vorticity distribution, and each of the (...
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Vortex solution of Laplace equation (XY model)

The hamiltonian of XY model, which is closely connected with BKT - transition is following: \begin{equation} H=\frac{J}{2} \int \text{d}^2 r \, \nabla \varphi \cdot \nabla \varphi, \quad \...
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Is there a connection between bathtub drains and tornados?

In the MIT fluid videos (link with timestamp), I heard that a tornado is essentially the same physics as a bathtub drain, but upside down. It doesn't look that way to me. It looks like both fluids ...
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Non-zero vorticity and pressure

I know vorticity and pressure fields are related, I am just wondering if there are any scenarios when non-zero vorticity will not affect the pressure field?
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Gross-Pitaevskii equation and healing length

I am given the following GPE: $$-\frac{\hbar^2}{2mr}\frac{d}{dr} \Big( r \frac{d\chi}{dr} \Big) + \frac{\hbar^2}{2mr^2} \chi + (U_0 \chi^2-\mu)\chi=0.$$ I am asked to derive the healing length (not ...
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Energy of vortex-antivortex pair

I am given the following field in 2d: $$\theta(\mathbf{x}) = \phi(\mathbf{x}-\mathbf{x}_1) - \phi(\mathbf{x}-\mathbf{x}_2),$$ where $\mathbf{x}_1,\mathbf{x}_2$ are the position of the vortex and ...
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Why does a fluid form a vortex when it comes out of a hole at the bottom of a tank? Would vorticity arise in an ideal fluid flow as well?

We see that when water flows out of a bathtub through the hole at the bottom then vorticity arises. Following are some questions in relation to it: What is the reason for this vorticity in the above ...
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Velocity and pressure in vortex

I would like to ask why is the velocity lower when further away from the vortex centre and also why does the pressure increase further away from the vortex centre. When I try to do some readings, the ...
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Why does my tea periodically alternate its rotational speed after stirring? (Link to video below)

I noticed that after stirring, a bubble in the centre of my mug of tea changed the speed it was rotating at periodically. Speeding up, then slowing down, then speeding up again, etc. Almost like when ...
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What causes vortices at the billiard ball particle level?

In a fluid/gas model consisting of billiard ball hard particle collisions what are the key behaviours that are needed to manifest the larger scale vortices? I can only seem to find descriptions of ...
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51 views

Rotational, Potential Flow

The short answer is "by definition, potential flow is irrotational", but please hear me out. I was working through "Fundamentals of Aerodynamics" by Anderson, and I noticed the following when he ...
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Velocity potential of an irrotational vortex

I would like to investigate the isolines of a two-dimensional velocity potential of an irrotational vortex defined using polar coordinates as $v=\frac{K}{r}$. I understand that the velocity ...
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An interesting observation: Ordered, up and down movement of vortex rings in water

I was watching a video on David Tong's research work when I stumbled upon a peculiar movement of vortex rings in water. Around the 1:20 time mark, Baths and Quarks: Solitons explained, David Tong uses ...
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Please help me to solve this question [duplicate]

Question on viscosity Help me clear my doubt
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1answer
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How do the vortices in vortex-induced vibrations (VIV) form?

I am currently doing a research project on the topic of the Vortex Bladeless technology in a technical college course. I have been researching VIV and the intuition behind this, but I am still ...
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Vortex chamber for maximum vacuum at given pressure difference?

Suppose we have a cylindrical vortex chamber with one exit pipe at the top. ( like here: https://ars.els-cdn.com/content/image/1-s2.0-S092188311830520X-gr2.jpg ) The air comes inside through the ...
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Why does the cold air coming down from an ice cream oscillate?

It occurred to me that when I held a choc-ice the other day (a wooden paddle with a chocolate ice-cream above it with two large smooth sides) that I could occasionally feel cold air falling down onto ...
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Superfluid Vortex Lines Bifurcation and Winding Numbers

Vortex lines in superfluids are characterized by their quantised circulation: $k = \frac{h}{m}\times n$, where $n$ is the winding number in the sense of a topological winding number. Now, most vortex ...
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Vortex ring formation

I think I undersand how a vortex ring is formed when we use a long tube: Vorticity is "created" by the velocity gradient caused by the viscosity and then, when the gaz goes out, the Kelvin theorem ...
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How does the $U(1)$ global symmetry break in the gauged $XY$ model?

I'm studying the particle vortex duality, and I'm confused how we're able to say that in the Coulomb phase, the "hidden" $U(1)$ global magnetic symmetry spontaneously breaks. gauged XY model: $\...
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Why does a vortex last so long?

Yesterday I saw vortex shed from a kayak paddle around 40 yards behind the person paddling so it had been rotating for over a minute. Why isn’t the energy in this vortex dissipated quickly, e.g. why ...
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Is a typhoon/hurricane also affected by Magnus Effect?

We all know that typhoons move as they rotate.
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Vorticity of Fourier Expanded Velocity

I have been reading some papers which find all three components of the vorticity vector for a Fourier expanded (perturbation) velocity field i.e $\mathbf{u'}(x,y,z,t)=\int\mathbf{\hat{u}}(x,y,t)e^{...
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What is irrotational flow? How to judge?

For example, when the wing moves horizontally, the direction of fluid flow changes first to upward at the leading edge of the wing and then to downward at the trailing edge. Does it rotate? If the ...
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Vorticity - Rankine vortex: how can we say that $\frac{\partial u_\phi}{\partial z} = 0$

\subsection{a} A Vortex formed in a bathtub, tornado or in other real world scenarios, exhibit nearly a solid body rotation in the core while far away from the center the flow is irrotational. This ...
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The Energy Spectrum of Bound states in the Vortex Core of Type II Superconductors

In the calculation of the so-called Caroli-de Gennes energy states in a type II superconductor the following Bogoliubov-de Gennes Hamiltonian is used: $$ H=- (\frac{1}{2m}(\nabla+ie\mathbf{A}\sigma_z)^...
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Does linearly accelerating a swirling liquid slow down its angular motion?

Say you pour some freshly brewed coffee in your favourite mug and give it a nice stir. As you depart for your desk, does the (approx) linear acceleration you apply to the mug slow the coffee's overall ...
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Charge-Vortex Duality for Bosons

Consider a (2+1)d continuum field theory with the Minkowski action $$\mathcal{L}=|\partial\phi|^2-r|\phi|^2-u|\phi|^4,$$ where $\phi$ is a complex field. The theory undergoes a quantum phase ...
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What's the origin of the vortex's ansatz $\phi\big(\vec{x}\big)=f\big(r\big)e^{-in\theta}$?

What's the origin of the vortex's ansatz $\phi\big(\vec{x}\big)=f\big(r\big)e^{-in\theta}$ in the de Vega and Schaposnik paper? In their article Classical vortex solution of the Abelian Higgs model,...
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Is a hole better for ceating a toroidal vortex than a pipe?

Does a hole work better for creating a toroidal vortex, where the fluid starts to turn as it exits, than a pipe, where the flow inside is more laminar. Some high power vortex guns have a cone shaped ...
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92 views

How to calculate vortex shed frequency curve, versus speed of the incident current

I have a current of air that hits a cylinder, and an hot-wire probe is measuring the velocity behind the cylinder. I have an array of measured velocity and a frequency. How do I get the vortex shed ...
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Red colour of the Great Red Spot

In Wikipedia it is mentioned: "It is not known exactly what causes the Great Red Spot's reddish color. Hypotheses supported by laboratory experiments suppose that the color may be caused by ...

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