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

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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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Why don't we talk about angular momentum at all in fluid mechanics?

People usually talk about similar (or maybe not?) things like vorticity or enstrophy in fluid mechanics, but no one talks about angular momentum, why?
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Could some design of a propeller be used in both air and water?

Propellers in water are smaller in diameter. They also move more slowly. On the other hand, aircraft propellers are larger in diameter, have narrower blades and operate at very high speeds. An ...
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Why do ice cubes stick together or to the edges of a drinking glass?

I was drinking iced-water from a drinking glass (made of glass) at a restaurant yesterday when I was taking a drink, I noticed that there is very little ice water coming out and then suddenly, the ice ...
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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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Does irrotational imply inviscid?

Let us consider a 2D irrotational flow, such that $\nabla\times\boldsymbol u =\boldsymbol 0$. Defining the stream function such that $\boldsymbol u =\nabla\times\psi \boldsymbol n$ where $\boldsymbol ...
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Polar vs non-polar fluid

In the book "Vectors, Tensors, and the Basic Equations of Fluid Mechanics" by Rutherford Aris I read the following: If the fluid is such that the torques within it arise only as the moments of ...
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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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What are the limitations of Smoothed-Particle Hydrodynamics?

I've been excited by some of the possibilities of Smoothed-Particle Hydrodynamics (SPH). I have seen some very exciting demonstrations of their use in 3D graphics, but I am wondering how well the ...
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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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Why does pressure act as a source for the gravitational field?

I'm asking for a qualitative explanation if there is one. My own answer doesn't work. I would have guessed it's because when a gas has pressure the kinetic energy adds to the rest mass of a given ...
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How can a droplet of liquid float on the surface of the same liquid?

This can happen during the rain, or when pouring water. Sometimes small (1-2 mm) droplets of water float on the surface for some time (a few seconds) before coalescing with the big body of water. A ...
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Does Liquid Immersion protect against G forces?

I'm under the impression that if an object is immersed in water it can be protected from the effects of Gravity - or in other terms appear to be in a 0G enviroment. Typical examples of this include ...
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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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Atmospheric Circulation

What is the simplest simulatable model giving our rotating earth its 3 circulation cells (Hadley, Ferrel, Polar)? The model should also show 1 circulation cell if the earth's rotation were stopped (or ...
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Helicopter, Tricopter, Quadccopter - what's really happening here? Are there generalized advantages on a small scale?

There have been, it seems, a proliferation of quad-copters commercially available. Amazon seriously tried to use them for deliveries. (Search Drone on their website.) The NFL uses one for cameras. ...
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Why Are Normal Shock Waves Unstable in a Converging Channel?

While learning about shock waves in an introductory Gas Dynamics course, it was revealed that normal shocks are unstable if formed in a converging channel. Even if the local conditions ostensibly ...
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Sailing against the wind. Is this a fair model?

I was ruminating the explanations about how boats can sail against the wind (or "into the wind"), and wondered if one could devise a simple mechanical model without hydrodynamics involved. Imagine a ...
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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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Why pouring milk from a height makes a chain shape?

I have noticed a chain-like shape when milk is poured from a height into a cup. Actually the chain pattern repeats itself after some distance and again till it reaches the milk in the cup. Any ...
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Could the phenomenon of vortex bursting be exploited to reduce wake turbulence?

One of the classic stories in the annals of aerospace engineering is the development (and subsequent redesign) of the F-18 and its Leading Edge Extensions (LEX) due to fatigue problems, problems that ...
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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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Sound Propagation using Finite-Difference Time-Domain (FDTD) considering wind effects

I am trying to plot the propagation of sound from a fixed source in a 2D environment using Finite-Difference Time-Domain (FDTD) Method taking into account the effects of the wind velocity. I came ...
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Is a venturi pump feasible at very low pressure?

I need assistance (or experience feedback) in estimating if a Venturi pump would work at low pressure. A boiler under vacuum (10% atmosphere) will produce steam (at a given speed depending on the ...
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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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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 does the lake surface appear darker in some areas?

My question: What causes the surface of the lake to appear darker in some places? My take on the matter: Firstly, I don't dare to say it's fishe which cause it. Secondly, the dark surfaces move ...
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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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Why do liquids separate in space?

I've seen videos of people in space (on ISS) who squeeze a bottle or something and liquid comes out, it then separates into smaller balls. Why is this surely it should stay pretty much together ...
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Exact Solutions to the Navier-Stokes Equations

There are a number of exact solutions to the Navier-Stokes equations. How many exact solutions are currently known? Is it possible to enumerate all of the solutions to the Navier-Stokes equations?
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Is it possible for wind to break the sound barrier?

I understand that in nature wind would never get high enough, but I am just curious as to whether physics would allow this to occur or not.
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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 ...
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Why does bad smell follow people (assuming they are not the source)?

When you are sitting in a room where there is a source of bad smell, such as somebody smoking or some other source of bad smell, it is often a solution to simply move to another spot where bad smell ...
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How does one derive the equation for the speed of sound?

In my acoustics books I see $$c^2 = \frac{\mathrm{d}P}{\mathrm{d}\rho}$$ where $c$ is the speed of sound, $P$ is the pressure and $\rho$ is the density. Where does this equation come from? In my ...
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Is there an analytical solution for fluid flow in a square duct?

I couldn't find one but assumed it must exist. Tried to find it on the back of an envelope, but got to an ugly differential equation I can't solve. I'm assuming a square duct of infinite length, ...
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Viscosity/Entropy ratio and unitary evolution in quantum gravity

Calculations of the shear viscosity of the quark-gluon plasma (QGP), observed in heavy ions collisions, are performed via the AdS/CFT correspondence [ref1]. One finds that the shear viscosity of the ...
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Wavy stream of liquid

When pouring a liquid into a glass some streams have a wavy shape, like the one in the following photo: (Couldn't find a better picture, sorry.) What causes the stream to be of such a shape?
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What causes the 'tears' in yoghurt drinks?

Fluid dynamical instabilities are present in many different everyday things. The famous tears in wine for example are a classical example of a Marangoni effect, where surface tension gradients due to ...
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Physical interpretation of the Lorenz system

The Lorenz equations $$ \frac{dx}{dt} = \sigma(y-x);\\ \frac{dy}{dt} = x(\rho-z)-y;\\ \frac{dz}{dt} = xy - \beta z $$ were (I believe) the first set of nonlinear equations known to exhibit chaotic ...
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Hydrostatic pressure on a teapot spout

The phenomenon where water flows on the outside side of a teapot spout is named "The teapot effect", and occurs due to a difference in pressure between water and the atmosphere. Consider the image of ...
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Drag on a spinning ball in fluid

I am a physics newbie (high school level) and I am wondering what happens when a spherical object is spinning on the spot in a bunch of gas (no gravity here, just an imaginary physics sandbox). Am I ...
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Intuitive explanation of Poiseuille's law — why $r^4$?

According to Poiseuille's law, the effective resistance of a tube is inversely proportional to the fourth power of its radius (as given by the following equation). $$R = \frac{ 8 \eta \Delta x}{\pi ...