All Questions
1,855 questions with no upvoted or accepted answers
15
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1
answer
1k
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Kolmogorov/Energy spectrum for turbulent boundary layer
Previously, I have calculated energy spectrum for 3D isotropic turbulent flow data which is equally spaced in all three directions and then to compute the energy spectrum, one performs Fourier ...
- 259
10
votes
1
answer
3k
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Lagrangian for Perfect fluid Stress-Energy tensor
The wiki article on the Einstein-Hilbert action for General Relativity says that the stress-energy tensor $T_{\mu\nu}$ is related to the Lagrangian of matter, $\mathcal{L}_M$, by
$$T_{\mu\nu}=-2\frac{\...
- 5,991
10
votes
1
answer
232
views
What would be the optimal diameter of gold grains if you want to fill a pool with them and swim in it?
I was wondering, if I were to fill a pool with gold/gold dust, what would be the optimal diameter of the grains to minimalize the friction to a point at which you would be able to swim in it ((and if ...
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8
votes
0
answers
572
views
Is there a Lagrangian $L$ (equivalently an action functional $S$) which yields the Navier-Stokes equation?
The Navier-Stokes equation or the Euler equation are usually derived as the conservation laws.
However, I wonder if there exists a Lagrangian $L$ or equivalently, an action functional $S[\...
- 1,708
8
votes
0
answers
304
views
Why there is no chemical potential on this thermodynamic relation?
I was following the book by Landau and Lifshitz, Fluid Mechanics (2nd edition) and got stuck trying to understand one of their arguments. On the chapter about Relativistic Fluid Dynamics it is stated ...
- 542
7
votes
0
answers
111
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Can a "depressive soliton" wave exist? That is, can we have a trough without any crest? Why or why not?
I know that "soliton" waves can consist of a crest without a trough. One would expect the reverse to be true as well.
However, this Wikipedia excerpt says,
So for this nonlinear gravity ...
7
votes
1
answer
309
views
Extremum principle for gradient wind balance
Dear Physics StackExchange,
as is well known, analytic solutions of the Navier-Stokes equations are only available for very special flows. Therefore, in most fields concerned with fluid dynamics, a ...
- 663
6
votes
1
answer
133
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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 ...
- 12.6k
6
votes
0
answers
152
views
How to obtain hydrodynamics from many-body quantum mechanics?
Background: It is well known that the Schrodinger equation is equivalent to the Euler equation (with a "quantum potential" term) plus the probability conservation equation (which is formally ...
- 5,244
6
votes
0
answers
300
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Why is the Fokker-Planck equation only valid for the forward and backward velocities but not for the flux velocity?
I noticed that the Fokker-Planck equation is often only written for the forward velocity $\vec b$ and the backward velocity $\vec b^*$:
\begin{align}
\partial_t \rho + \nabla (\vec b \rho) &= D \...
- 10.3k
6
votes
0
answers
383
views
Is there a scale at which all solids can be treated as fluids?
I was answering an Earth Science SE question that involved the reasons why Earth has an equatorial bulge, and wanted to make an offhand comment such as "Real planetary constituents aren't this strong; ...
- 163
6
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0
answers
289
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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 ...
user242231
6
votes
1
answer
191
views
Hydrodynamic interaction between two spheres in $Re\ll 1$ flow
I am studying the interaction between two spherical particles of radius $a$ in a low Reynolds number flow. Because of linearity, I know that their respective velocities will be linear in the forces ...
- 1,813
6
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0
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115
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are alignment of star systems' orbital planes with ours better than random?
It obviously helps our observation of exoplanets if they transit their star from our point-of-view. I would guess that the chances of this alignment are better than if their orbital plane was randomly ...
- 161
6
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0
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456
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Minimum velocity required to "skip" a spacecraft across the atmosphere?
When, hopefully, Virgin Galactic spacecraft start regular operations in a few years, they will be simply travelling upwards, then achieving weightlessness for a short while, followed by a return ...
user108787
6
votes
1
answer
271
views
Do the Shallow Water Equations produce 2d vorticity/eddies? Why/Why not?
My understanding so far: given a small flow moving forward within a larger stationary body of water, the water ahead would pile up, creating hydrostatic pressure in all 2d directions (and thus ...
- 161
5
votes
0
answers
109
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Euler equations as the Euler-Lagrange equations in fluid dynamics
I am following Variational Principles of Mechanics by Lanczos, 4th edition, 1970 on the page 360 forward.
He is deriving the Euler equations of fluid flow.
He starts by defining the kinetic and ...
- 904
5
votes
0
answers
119
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Long-range fluctuations induced forced (or the classical Casimir effect)
According to literature, the Casimir effect refers to attraction of two parallel neutral metal plates due to the wavelength cutoff of quantum fluctuations between the two plates.
I come from condensed ...
- 905
5
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0
answers
66
views
Does bernoulli's principle exert a downward pull on a moving ship?
If you hold a spoon with its convex side next to a column of running tap water, it will be drawn to it, but does this apply to moving ships, where the hull is rounded like the spoon, and the water is ...
- 51
5
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0
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323
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Are sound waves in fluids also Goldstone modes?
One usually says that sound waves in a crystal, ie. phonons, are Goldstone modes of the broken translation symmetries. However, fluids have sound waves and also translation invariance. In fact, it's ...
- 8,134
5
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0
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189
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Is this wire-melting phenomenon a manifestation of the Plateau–Rayleigh instability; have I done my maths right?
In LECTURE 5: Fluid jets from MIT's 1.63J/2.26J Advanced Fluid Dynamics equation 23 is
$$\omega^2 =\frac{\sigma}{\rho R_0^3} k R_0 \frac{I_1(k R_0)}{I_0(k R_0)}\left(1 - k^2 R_0^2 \right)$$
and is ...
- 6,111
5
votes
2
answers
4k
views
Inverted U manometer
I have some doubts on inverted U manometer.
In the picture there is one U inverted manometer, the space above the liquid in the manometer is filled with air which can be admitted or expelled through ...
- 2,637
5
votes
0
answers
257
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relation of vortex street structure to Stroudhal & Reynolds Numbers
While on an expedition to a lake, it was noticed that the wind speeds gusted violently in seemingly periodic wakes and the proposed explanation was Von Karman vortex shedding off of nearby mountains ...
- 327
5
votes
0
answers
178
views
Where else in physics does one encounter Reynolds averaging?
Reynolds-averaged Navier–Stokes equations (RANS) is one of the approaches to turbulence description. Physical quantities, like for example velocity $u_i$, are represented as a sum of a mean and a ...
- 2,619
4
votes
1
answer
95
views
How to determine the alpha value of artificial viscosity in smoothed particle hydrodynamics?
I am confused about how to choose an appropriate value of $\alpha$ in the artificial viscosity. The value that I deduced is far from the recommended value and led to great numerical instability.
...
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4
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0
answers
300
views
How to obtain the matter Lagrangian from the stress-energy-momentum tensor $T_{\mu\nu}$?
I have obtained the components of stress energy momentum tensor
\begin{align}
T_{tt}&=\frac{\Phi^2}{2\pi\mathcal{G}r^2 \left(1+2\Phi\right)^3}\\
T_{rr}&=-\frac{\Phi^2}{2\pi\mathcal{G}r^2 \...
4
votes
0
answers
104
views
Rain drop trails on a car window prefer certain paths. Why?
Why do the raindrops always flow down in the middle?
That's a question given to me by my seven year old son.
Some background:
We are sitting in a bus with two windscreen wiper blades.
I hope that ...
- 1,106
4
votes
0
answers
70
views
At what pressure will ice remain as ice at 1000° C?
I am in 9th grade. Please forgive me if I ask any dumb questions. So, I was studying about gas laws and I came across an equation
$$\frac{p_1V_1}{T_1} = \frac{p_2V_2}{T_2}.$$
I wondered if there is ...
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4
votes
1
answer
136
views
A question for expert in geometrical method and Riemannian metrics
I'm a physical oceanographer with great interest in Theoretical Geophysical Fluid Dynamics. I have some ideas on the possibility to derive the so-called: geostrophic equilibrium (i.e. on a rotating ...
4
votes
0
answers
153
views
How to calculate the Euler equation for fluids in the newtonian limit from the stress-energy tensor?
I have been working through the exercises of Schutz's a first course in general relativity. In chapter 7 of the book there is a question about the conservation of the spatial components of stress-...
- 51
4
votes
1
answer
88
views
What's the best way to orient the bathroom door to optimize fart fan efficiency?
When using a fart fan I often close the bathroom door to around a 10° angle. I have no real idea why except for this strange notion that limiting the fresh air intake might increase air pressure and ...
- 149
4
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0
answers
64
views
Splashing of Falling Sphere does not depend on Sphere Size
I am reading through a Nature article where the authors study whether a sphere dropped from height into a body of water has enough velocity to splash and form the classic effect where air is pulled in ...
- 1,433
4
votes
0
answers
114
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Is there a height limit to the 'inflatable dancer'?
From the Bernoulli equation
$$\frac{p}{\rho} + \frac{v^2}{2} + gh = \mathrm{const.}$$
along streamlines, it seems that there should be an ultimate limit to the height of an 'inflatable dancer' when ...
- 228
4
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0
answers
583
views
Minimum speed for a mantis shrimp punch to create cavitation?
When a mantis shrimp punches it creates cavitation, because of the speed it creates sudden changes in the water.
I want to know how slow can a mantis shrimp punch and still make cavitation?
Notes:
...
user239759
4
votes
0
answers
45
views
Does laminar flow of a mixture tend to result in mass separation?
In a laminar flow regime, a fluid separates into streamlines with a parabolic flow profile. Do particles within such a flow tend to become aligned by mass (e.g. lighter molecules travelling together ...
- 41
4
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0
answers
260
views
Why do large eddies in turbulence break-up
This is probably a silly question. But, Why do large turbulent eddies break up into smaller ones?
A possible argument
Why can't they (large eddies) retain their size and gradually diffuse instead of ...
- 149
4
votes
0
answers
160
views
Vortex ring solutions in General Relativity
Vortex rings are captivating toroidal self-reinforcing fluid systems that can happen in turbulent fluids. I wonder if something similar can exist as a solution to Einstein's gravitational equations
- 14.7k
4
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0
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961
views
Number of collisions per second a water molecule is experiencing in the fluid phase at ambient conditions
I am teaching a DNA course for lay people and I want to give them an indication of the number of collision per second a water molecule experiences in pure water. Similarily, I would like to know the ...
- 41
4
votes
1
answer
2k
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Stress Tensor Sign Convention
I'm hoping someone can clear up this confusion I have with the stress tensor. So here is what a stress tensor looks like as described by many authors:
I understand that the shear stresses acting on ...
- 177
4
votes
1
answer
805
views
Why is the total force at a free surface zero?
I am looking into waves on a free surface for which their are two main conditions:
Kinematic condition: Particles on the surface remain on the surface.
Dynamic condition: Forces acting on the surface ...
4
votes
0
answers
2k
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What's the meaning of a pressure coefficient in fluid mechanics?
I have a jet of air leaving a contraction from a pressurized tank at a velocity of 28.8 m/s and it's being directed towards a small object equipped with static pressure holes on its surface that give ...
- 1,158
4
votes
1
answer
73
views
How fast do the aerodynamic forces on a surface build up?
I`m currently working on my thesis in the field of active car aerodynamics. In order to design a controller to move parts of the cars body I need to know how fast the drag and downforce acting on this ...
F.Prior
4
votes
1
answer
627
views
Fluid dynamics tsunami
I have been given a energy head (pressure) in meters for a given tsunami on land.
If the tsunami hits a wall 1 meter by 1 meter, is it possible to calculate the height it will reach.
I am thinking it ...
- 49
3
votes
0
answers
71
views
When I make a whirlpool in the water, where does the other end of the vortex go?
A lot of the time when I'm at the pool I like to make whirlpools with my hand, like this:
From my limited understanding of fluid mechanics, vortices/vortex filaments/vorticity tubes cannot end within ...
- 649
3
votes
0
answers
87
views
Why is it legal to throw out the potential energy in the fluid approximation in GR?
Here's something that's confusing me:
In the fluid approximation in General relativity we only have kinematic terms. We do not have the potential energy of each term. This is not a realistic ...
- 1,349
3
votes
0
answers
84
views
Why are swimmers slower in shallow pools?
When I heard that swimming pools in the Olympics were slow due to shallowness ($\approx 2 \,\text{m}$ instead of $3 \,\text{m}$ deep), I thought it was due to the no-slipping condition, as for example ...
- 5,831
3
votes
0
answers
92
views
Why do water surfaces have persistent "average wavelength" patches?
Have you ever stood above a river or lake and noticed that the surface has visible "patches"? It looks like the surface has different average wavelengths in some areas, leading to the light ...
- 131
3
votes
0
answers
87
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Air resistance due to Helium vs Air
I was reading this technical note by NASA on windage power loss in alternators. In the paper, the power loss due to fluid shear between two concentric cylinders (a rotor and a stator) is derived.
The ...
- 31
3
votes
0
answers
45
views
Why is windspeed proportional to inflated area in windsock?
I have come across this image on Twitter on how to measure wind speed with a windsocket. I noticed that the rings look equally long in the photograph (and others) and measure a speed increase of 3 ...
- 227
3
votes
0
answers
121
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Questions regarding the derivation procedure of the Karman-Howarth-Monin relation
I was reading the book "Turbulence" written by Uriel Frisch (1995) and got stuck in following the proof of the Karman-Howarth-Monin relation. Although there is already a thread about it, I ...
- 147