# 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 ...
122 views

### Do whirlpools in water have the same rotation speed regardless of size?

I recently read that all flat disk galaxies have the same rotation speed regardless of mass and size, so I was wondering if this same feature was visible in any other similar rotation such as a ...
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### Can gravitational waves carry momentum, and if so what mass/energy produces it, and is space-time capable of vortex formation?

This question is about gravitational waves postulated by Einstein. Is gravitational radiation a form of mass/energy that can form momentum? If it causes ripples in space-time, would space-time be ...
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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 ...
837 views

### How do speed and density change in a turbulent flow?

Suppose a fluid passes from having laminar flow, to having a turbulent flow (like when passing after an object). How do fluid speed and fluid density change after that?
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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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### 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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Could anyone suggest a good introductory book or any online resource about vorticity? I just now started to learn physics but I have a good mathematical background.
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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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### 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 ...
178 views

### 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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### Why are superfluid vortex lattices stable?

Both (a) neutral superfluids that are externally rotated, and (b) type-II superconductors (i.e. charged superfluids) under applied magnetic fields between the critical fields $h_{c1}$ and $h_{c2}$, ...
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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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### 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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### 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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### How can we define $\Gamma$ (circulation) around a point vortex?

I'm having trouble understanding something in a book that I'm reading (Chorin & Marsden intro to fluid mechanics): Next we shall examine a model of incompressible, inviscid flow. We imagine the ...
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### Difference between vorticity and circulation

The definition of vorticity is $\boldsymbol{\omega} = \nabla \times \mathbf{v}$, where $\mathbf{v}$ is the velocity vector field. Now, if I look at a rotating flow in cylindrical coordinates I find ...
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### What is actually the characteristic length in fluid dynamics description?

In many fluid-dynamics models and quantities (Reynolds number, Strouhal number... generally various turbulent flow descriptions) there is a parameter (usually $L$ or $\ell$) descripted as ...
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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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### How many independent properties can a photon have?

Two recent papers about photon orbital angular momentum have set my head spinning as well. I'll try to define "property" as something you can change in one arm of a Mach-Zehnder interferometer, and "...
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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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### 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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### 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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### 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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### Vortex in liquid collects particles in center

At xmas, I had a cup of tea with some debris at the bottom from the leaves. With less than an inch of tea left, I'd shake the cup to get a little vortex going, then stop shaking and watch it spin. ...
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Question on viscosity Help me clear my doubt
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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 ...