The Navier-Stokes equations describe fluid flows in continuum mechanics.

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What is the mystery of turbulence?

One of the great unsolved problems in physics is turbulence but I'm not too clear what the mystery is. Does it mean that the Navier-Stokes equations don't have any turbulent phenomena even if we solve ...
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Occurrence of turbulences in Fluid Dynamics from the equations of motion?

How can it be shown that turbulences occur in Fluid Dynamics? I think poeple imply that they develope because of the $\text{rot}$ terms in the equations of motion, i.e. the Navier-Stokes equations, ...
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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 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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What's the shear rate in a turbulent flow?

The explanation of shear rate in laminar flow is straightforward: We imagine small layers of fluid that glide on each other. Now, in turbulent flow, this does not work as there are no layers. I'm not ...
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54 views

Calculate Euler equations of fluid dynamics without division?

I'm working on the calculation of the Euler equations with the finite volume method. Unfortunately I'm not allowed to do a division. So I'm wondering if there's a form which does not need a division. ...
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1answer
158 views

Help with Modeling a Liquid Vortex. (Related to General Fusion)

I want to model liquid lead swirling in a sphere. This is connected to General Fusion’s fusion machine. A 55 million dollar, Jeff Bezos funded, 60 person company trying to change the world with ...
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585 views

How to calculate the upper limit on the number of days weather can be forecast reliably?

To put it bluntly, weather is described by the Navier-Stokes equation, which in turn exhibits turbulence, so eventually predictions will become unreliable. I am interested in a derivation of the ...
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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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1answer
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Why does a transformation to a rotating reference frame NOT break temporal scale invariance?

Naively, I thought that transforming a scale invariant equation (such as the Navier-Stokes equations for example) to a rotating reference frame (for example the rotating earth) would break the ...
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1answer
128 views

Explicit form of the entropy production in hydrodynamics

I'm trying to understand how hydrodynamics arise from a precise, mathematical formulation of thermodynamics, learning mostly from Landau's "Hydrodynamics". So Landau starts from formulating the ...
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232 views

Navier-Stokes system

I have to study this system which name is Navier-Stokes. Can you explain please what means that $p$, $u$ and $(u \cdot \nabla)u$. What represents in reality? Tell me please, how should I read the ...
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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 ...