The quantitative study of how fluids (gases and liquids) move.

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Physical Explanation for “Kolmogorov -5/3 spectrum” in Fluid Mechanics

According to Kolmogorov, the energy spectrum function of a turbulent fluid is given as, $E(k)=C\epsilon^{\frac{2}{3}}k^{\frac{-5}{3}}$ where $\epsilon$ is the energy flux and $k=\frac{2\pi}{r}$ ...
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How to estimate the Kolmogorov length scale

My understanding of Kolmogorov scales doesn't really go beyond this poem: Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity. ...
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Why does water flow out of an upside-down bottle? (Rayleigh Taylor Instability)

I am currently reading the excellent book An Indispensable Truth: How Fusion Power Can Save the Planet by Francis F. Chen and I came across this explanation. The Rayleigh–Taylor Instability ...
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Boundary layer theory in fluids learning resources

I'm trying to understand boundary layer theory in fluids. All I've found are dimensional arguments, order of magnitude arguments, etc... What I'm looking for is more mathematically sound arguments. ...
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189 views

How do subgrid-scale parametrisations in climate models work?

Global Circulation Models typically have grids of 100-300km on a side. There are obviously lots of atmospheric processes that happen at smaller scales than this. Convection, cloud formation, the ...
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How can I understand a Vortex Tube and its efficiency?

A Vortex Tube takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. Apparently, it has been described as a Maxwell's Demon. Both ...
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What can wavy patterned sand tell about the Fluid that formed it?

Sand on the bottom of the ocean as well as sand on the low-tide beach often forms wavy patterns. Do the parameters of these wavy patterns have any relation to the water and waves that formed them? If ...
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Zigzag flow of water along a vertical glass window

I've observed this behavior many times. When it rains, the rainwater will form vertical channels along a glass window. The flow of water is mostly confined within these vertical channels and the ...
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Fluid Mechanics with calculus on manifolds

Fluid Mechanics is a branch of physics that uses a lot of vector calculus in $\mathbb{R}^3$ to describe phenomena mathematically. Calculus on manifolds, however, is the straightforward generalization ...
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Branching lemon drop “smoke rings”

This might be hard to ask, but here goes nothing. I recently poured a cup of water into a black coffee cup. There was a light source--not very bright--above the cup. Anyways, I was squeezing a ...
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339 views

Are smaller soap bubbles more accelerated by wind?

If you blow a bunch of soap bubbles outside, and a gust of wind hits them, will the bigger ones be more or less accelerated by the wind than the smaller ones? Intuitively, and maybe from remembered ...
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Why can't helicopters reach mount everest?

Is there a reason why people can't just take the helicopter to mount Everest? Why is it that helicopters can't reach that high?
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Explanation that air drag is proportional to speed or square speed?

A falling object with no initial velocity with mass $m$ is influenced by a gravitational force $g$ and the drag (air resistance) which is proportional to the object's speed. By Newton´s laws this can ...
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How can rising bubbles shrink and disappear?

I was recently looking at a Wurlitzer juke box, and noticed something strange. It's decorated with liquid-filled tubes. Gas bubbles are injected at the bottoms of the tubes, and the bubbles naturally ...
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What equation of state is needed for liquid states?

I'm familiar with the ideal gas law $$PV=nRT$$ but I don't think it applies to liquids like water. If I'm wrong, please correct me! If I'm right, then what equation of state applies to liquids such ...
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A fly in an accelerating car

A fly is flying around in a car, the fly never touches any surface in the car only fly’s around in the air inside the car. The car accelerates. does the fly slam in to the rear window. or does the fly ...
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Conserved quantities and total derivatives?

I am having a bit of a crisis in understanding of the physical meanings of total derivatives. When a quantity $\rho$ (be it a vector or a scalar) is said to be conserved, then (mathematically) ...
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Why is there a space between the flame and the nozzle on the space shuttle?

Why is there some space between the flame and the nozzle on the space shuttle? (see above picture)
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Why do non-Newtonian fluids go hard when having a sudden force exerted on them?

You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else. What is it about a non-Newtonian fluid ...
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Why does the water level equalize in a series of tubes?

Say I have a series of tubes (not the internet) looking like this, where w represents water: ...
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How is viscosity described on the molecular level?

What is the 'molecular' origin of the viscosity? The molecular origin of elasticity is almost clear for me: at the very bottom the 'elasticity' comes from the attraction and repulsion between atoms ...
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How to make the bubbles in my soda drink last longer?

I would like to make the bubbles in my soda drink last longer. For example, one good thing to do is to keep the bottle shut when you don't drink. But what else I can do? Should I try to minimize the ...
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Fluid in a rotating cylinder

I have been wondering why a fluid in a rotating container has a parabola shape? Is it possible to prove this mathematically?
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Can air bubbles sink at extreme depths? [duplicate]

I was thinking earlier about air bubbles in water. if you had a bubble of air (say in a balloon) then as you take it down in water the bubble shrinks because of the pressure and because it is ...
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What is Relativistic Navier-Stokes Equation Through Einstein Notation?

Navier-Stokes equation is non-relativistic, what is relativistic Navier-Stokes equation through Einstein notation?
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Would a solution to the Navier-Stokes Millennium Problem have any practical consequences?

I know the problem is especially of interest to mathematicians, but I was wondering if a solution to the problem would have any practical consequences. Upon request: this is the official problem ...
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How much of the forces when entering water is related to surface tension?

When an object enters water with high velocity, (like in Why is jumping into water from high altitude fatal?), most of it's kinetic energy will be converted, eg to accelerate water, deform the object ...
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General procedure for solving fluid flow problems

Could someone help me devise a short series of steps for solving an arbitrary fluid flow problem? Often the most difficult part of these problems is just figuring out what path to take in solving ...
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Where can I check a solution to 3D Navier Stokes?

A few years ago I developed a solution to the Navier-Stokes equations and as of yet have not been able to locate a similar version of the solution. I would like to know if anyone has seen a solution ...
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Does the wind gust over the ocean?

It is easy to observe that on a windy day, the wind does not blow for several hours at constant speed, then gradually subside. Instead, on a time scale of seconds or tens of seconds, there are ...
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Pendulum with water dripping out

Consider a pendulum, consisting of a string of length $l$ tied to a ball of negligible mass and radius $r$. The bob is filled with water, which has density $d$, and the pendulum is given a small push ...
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How is the water meniscus at the edge of a capillary tube

Suppose we have a capillary tube in which water can rise to a height of x cm. If we dip the tube such that the height above the surface is less than x, then how will the water meniscus be at the edge ...
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Why water in the sink follow a curved path?

When you fill the sink with water and then allow the water to be drained, the water forms a vortex.. And then it starts to follow a curved path downwards by effects of gravity.. Why this phenomena ...
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What part of the fan blade actually does the noise generation?

I'm trying to identify the sources of noise in spinning fan blades and what causes them. Is the noise only generated by the lead edge of the blade 'cutting through' air? and different parts of it ...
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How can these fluid dynamical smoke-ring phenomena be explained?

The Navier-Stokes fluid dynamics equations, said that, as Sir William Thomson (or Lord Kelvin) predicted: When two smoke-rings are moving in the same direction, with the same speed, one behind the ...
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Is surface of a solid a streamline?

In fluid dynamics, streamlines are defined as line where at each point flow velocity is tangential to the line. Is it correct to say surface of a solid a streamline? On the surface the velocity vector ...
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Phase Space Flow

Phase space flow shares characteristics with fluid flow such as incompressibility by Liouville's theorem. Extending the similarities one might be curious, does phase space flow have a characteristic ...
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Could motives aid in the study of the Navier-Stokes equations?

Recently, mathematicians and theoretical physicists have been studying Quantum Field Theory (and renormalization in particular) by means of abstract geometrical objects called motives. Amongst these ...
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Riemann invariants…Any physical interpretation?

I am really new to the CFD simulation, and started some simple algorithms recently. I then got introduced to the Riemann Invariants. Can any one provide some physical interpretation? Also, why is ...
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How do I intuit viscosity in a rotating fluid?

Suppose I have two plates with a viscous fluid in between. I slide them in the same direction (a direction in their own plane), one at $5 \,\text{m/s}$ and the other at $6 \,\text{m/s}$. Due to the ...
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What's the most efficient strategy to shake a bottle to create a global flow?

Consider a bottle of orange juice with pieces of the fruit gathered at the bottom of the bottle. You need to shake the bottle to evenly distribute the pieces in the bottle. The first part of the ...
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Critical bathymetric profile to maximize surge and minimize breaking?

Reading about storm surge, I found it fascinating that the gradual slope of the Gulf Coast of Florida resulted in a much higher storm surge but much lower energy release in breaking waves. Is there ...
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Deriving shallow water equations from Euler's equations

I would like to derive the one-dimensional shallow water equations from Eulers's equations. This works perfectly for the conservation of mass. Especially the meaning of the longitudinal fluid ...
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Lagrangian Coordinates in Fluid Flow

I apologize if this is not the right place to ask this question: I am currently reading a paper by Y. Brenier, where for the fluid flow he introduces a Lagrangian label $a$ instead of the vertical ...
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At what velocity does sea water leave a pipe run into a fresh water lake (for equal surface levels)?

If I took a fresh water lake* whose surface is exactly as sea level, and connect it to the sea with a pipe filled with sea water, with both ends of the pipe at exactly the same depth from the surface, ...
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What keeps a gas giant from falling in on itself?

There is not enough gravity at the center to start nuclear fusion, but it seems that there would be plenty enough to collapse the planet.
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Why are Navier-Stokes equations needed?

Can't we picture air or water molecules individually? Then, why are Navier-Stokes equations needed, after all? Can't we just aggregate individual ones? Or is it computationally difficult, or ...
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Why do blades of windturbine propellers as comp. to propellers of ships cover very different areas?

This is a thought I asked myself often, but never did real efforts to get an answer. Barsmonsters question about number of fans of a wind turbine made me think of it again Why do blades of aircraft ...
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Why is the answer to this diffusion example unintuitive?

Imagine a linear decrease in concentration from left to right. Using Fick's first law, $J = -D \frac{d \psi}{d x}$ for all x, from left to right, we have the same flux amount because the decrease is ...
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Effect of water pressure on sinking objects

As I understand, water pressure increases as we go towards bottom of the ocean. So if an object* is thrown into water and it starts sinking with some speed, does the sinking object's acceleration ...