Questions tagged [navier-stokes]

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

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Bernoulli principle (classic form) in irrotational viscous flow (a paradox?)

We derive the Euler equation for inviscid flow. Then, for irrotational flow, we use the Euler equation to get Bernoulli equation (classic form) and show it holds in the irrotational region (still ...
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How do I find the absolute maximum and minimum values of the Lamb-Oseen Vortex?

For an angular velocity function derived by Navier-Stokes, $$\omega \left(r,t\right)=\frac{\omega _0R_0^2}{R\left(t\right)^2}exp\left(-\frac{r^2}{R\left(t\right)^2}\right)$$ from which the azimuthal ...
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Favre Averaged Navier-Stokes equations

Consider the Navier-Stokes (NS) equation \frac{\partial (\rho u_i)}{\partial t} + \frac{\partial (\rho u_i u_j)}{\partial x_j} = - \frac{\partial p}{\partial x_i} + \frac{\partial}...
1 vote
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2D Stokeslet: a reference?

Consider the Stokes equation $$\begin{cases}\Delta u = \nabla p - F \\ \operatorname{div}(u)=0 \end{cases} \text{ in } \mathbb{R}^2,$$ with $u$ a velocity field, $p$ a pressure and $F$ a point force ...
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• 6,636
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How to mathematically derive the pressure contribution to drag force over a with viscous contribution determined?

I've looked in a lot of books on how it would be possible to derive the drag force over a sphere using PDEs. I've also learned in my fluid dynamics class how to derive the drag force of a rotating ...
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How to mathematically derive the pressure contribution to drag force over a sphere after the viscous stress is determined? [duplicate]

I've looked in a lot of books on how it would be possible to derive the drag force over a sphere using PDEs. I've also learned in my fluid dynamics class how to derive the drag force of a rotating ...
1 vote
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Finite Differencing with Incompressible Navier-Stokes Equations (Only Advection)

I'm trying to improve the advection method in a 2D-windfield. The Navier-Stokes Equations (NSE) are currently used for the influence of pressure, viscosity,... I am just focusing on the convective ...
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Where to find the article(s) saying that 3D Navier-Stokes solutions exist in case of a small initial velocity?

I've already been searching for here and on the internet, maybe not enough. PS: this result is stated in the Clay Mathematics Institute N-S problem definition, page 2: https://www.claymath.org/wp-...
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Cylindrical incompressible Navier-Stokes, are the derivatives commuative?

I am currently trying to understand a paper by Eckhardt et al. (https://doi.org/10.1017/S0022112007005629). In it, a transformation is performed on the cylindrical incompressible Navier-Stokes ...
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Can direction of frictional force be opposite to velocity?

The frictional force in incompressible Navier-Stokes equation is given by $$\vec F = \nu \nabla^2\vec v$$ Lets assume simple 1D-flow along $x$, where $v$ depends on $z$: $$v_x = v(z)$$ Then the ...
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What is the the Implication of Navier-Stokes Millenium Problem to Practice?

As a student of meteorology, I wonder why Navier-Stokes equations (NSE) are still not understood in terms of whether or not there are unique solutions. In atmospheric dynamics, NSE is used as a basic ...
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1 vote
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How does one calculate the viscous term in the integral form of navier stokes?

I learned about the integral form of the navier stokes equation and I am trying to find an explanation for this viscous term at the end but I've searched everywhere and I can't find anything. The ...
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Modeling fluid flow in extremely small pores (or channels) compared to the component

I want to model a non-wetting fluid flowing into tiny pores of a component using Navier-Stokes. Just for you to visualize, say I have a 2D rectangular component of dimensions $L*W$, and within that ...
102 views

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 ...
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1 vote
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Non-dimensionalisation of Navier-Stokes Equations [closed]

I am trying to numerically simulate a flow in which a fluid with kinematic viscosity $\nu=0.00001167$ m$^2$/s is injected into a cylindrical tube of diameter 0.00745m at a velocity of 45.9 m/s. Thus, ...
1 vote
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Derive Navier-Stokes equation from the action principle (Euler-Lagrange's equation) [duplicate]

Navier-Stokes equations are the most general equations in fluid dynamics: We ususlly derive it by the consevation laws and $F=ma$. But how to derive it from the Action principle or equivalently Euler-...
139 views

Is there specific form of Navier-Stokes equation for which mass can cross bounding surface?

In my textbook, we learned that Navier-Stokes (NS) equations can be derived from Reynolds transport theorem where the control volume is assumed to be fixed. But when the control volume is moving, can ...
28 views

Stress Tensor Normal Component (Newtonian Fluid) [duplicate]

I am trying to get an intuitive understanding of the normal components of the stress tensor for a Newtonian Fluid. The stress on the x face in the x direction is \sigma_{xx} = 2*\mu\frac{\partial u}{...
How to calculate pressure $p$ in the Navier-Stokes equation to simulate the time evolution of a fluid?
I wanted to simulate the motion of a fluid (continuously filling the entire space) in a given space, say $3$-dimensional Euclidean space. To calculate the dynamics of fluid motion, I used the Navier-...