Questions tagged [navier-stokes]
The Navier-Stokes equations describe fluid flows in continuum mechanics.
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Calculate water points positions from Navier-Stokes equations [closed]
I am writing a physics simulation of water using shaders and Unity3D, and I think Navier-Stokes equations are pretty good fit for that task. I have low math knowledge, so it's hard for me to ...
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0answers
37 views
What are the limitations of this form of the Navier-Stokes equation?
$$
\frac{∂u}{∂t}+u\frac{∂u}{∂x}+v\frac{∂u}{∂y}+w\frac{∂u}{∂z}=\frac{−1}{ρ}\frac{∂P}{∂x}+gx+ν(\frac{∂^2u}{∂x^2}+\frac{∂^2u}{∂y^2}+\frac{∂^2u}{∂z^2})
$$
Why would someone use a form of this equation ...
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1answer
30 views
Why shear stress is assumed constant in the inner layer
In the derivation of the log-law and the viscous sub-layer velocity profiles, it is customary to assume that the shear stress is constant and equal to the wall shear stress. Is there any physical or ...
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1answer
280 views
Inversion of a metric
I am currently reading a paper by Bredberg $et.al$ arXiv:1101.2451 titled "From Navier-Stokes to Einstein". In this paper, the authors have considered a metric of the form \begin{eqnarray}ds^2_{p+2} = ...
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2answers
63 views
Navier-Stokes : divergence or covariant derivative of a tensor : 1 vector result?
I don't understand very well the following definition concerning Navier-Stokes equation :
where
$\vec{u}\otimes\vec{v}$ is a tensor (2,0), isn't it ?
This is not scalar since $\vec{u}\,\vec{v}^{T}...
3
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0answers
75 views
Characteristics of the Navier-Stokes equations as a set of PDE's
I am not entirely sure if I should ask this question here or not, but here goes: can anyone suggest any reference (book, article, etc.) about the Navier-Stokes equations from a mathematical point view?...
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1answer
35 views
How do you interpret this symbol within the following Navier-Stokes equations?
I was reading this fluid simulation paper(http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/ns.pdf) by Jos Stam and encountered these Navier-Stokes equations.
1.
2.
Now, I know that
...
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2answers
138 views
How should energy loss in a hydraulic jump be calculated?
The energy loss in a hydraulic jump is still calculated with the old equation of Bresse from year 1860;
(I.e., equation 7 in this paper from 2017)
$$
\frac{\Delta E}{E_1} = \frac{(\sqrt{1+8Fr^2}-3)^3}...
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0answers
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Does the “O” in this google doodle for Olga Ladyzhenskaya have anything to do with her work, or is it completely fanciful? [closed]
Google Doodle celebrates mathematician Olga Ladyzhenskaya
She was famous for fluid dynamics and partial differential equations, both of which are beyond my pay grade. And she worked on the Navier-...
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1answer
113 views
Assumptions for 2d simplification of Navier-Stokes flow
There are many cases where Navier-Stokes flow is simplified to a two-dimensional problem to reduce the costs for a numerical simulation, e.g., flow around an airfoil, channel flow or pipe flow.
To ...
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1answer
62 views
Navier-Stokes - Reynolds decomposition of energy equation
I am trying to apply the Reynolds decomposition to the Navier-Stokes equations for incompressible flows. At the moment I am doing that for the energy equation following the book Viscous Fluid Flow by ...
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1answer
38 views
Variational Navier-Stokes: where to find study material “for dummies”?
I have worked with the Navier Stokes equations before but I'm a physicist. I was talking to a mathematician and they use a complete different notation and I am very lost.
First of all, I use the ...
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1answer
36 views
How to classify your fluid is a transitioning from a liquid to gas from numerical computation
I saw at one time that if the kinetic energy/potential energy of the gas was approaching 1 then the gas is becoming a liquid. I can't find the reference where I found that though (it was on stack ...
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1answer
56 views
First Order Approximation of the Navier-Stokes Equation: Order of Magnitude of the Gradients of First-Order Fields
I am currently working on a project in acoustics and I am studying first and second-order approximations to the Navier-Stokes equation. I have been reading the book 'Theoretical Microfluidics' by ...
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3answers
114 views
Some confusions about Navier-Stokes equations
I just started working on the Navier-Stokes equations. I consider the following paper Seibold A compact and fast Matlab code solving the incompressible
Navier-Stokes equations on rectangular domains (...
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1answer
61 views
By which physical mechanism does the continuity equation in fluid mechanics work?
The Navier-Stokes equations consist of the momentum equation and the continuity equation. Consider the incompressible versions for the purpose of this question.
Continuity is always talked about as a ...
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1answer
83 views
Confused about Navier-Stokes equation
Just look at the L.H.S of the compressible navier-stokes equation from wiki
$$\rho(\partial_t \vec{u}+\vec{u}\cdot\nabla\vec{u})=...$$
How can I add a vector $\partial_t \vec{u}$ and a scalar $\vec{...
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0answers
31 views
Converting this navier stokes solution into a incompressible solution?
I have an equation for a non-viscous compressible fluid with density, pressure and velocity given by:
$$ \begin{align}
\rho(x, y, z) &= \frac{3B}{a^2 + x^2 + y^2 + z^2} \\
p(x, y, z) &= \frac{...
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0answers
20 views
How would you model a single point outputting fluid in all directions whilst enclosed in a sphere?
The idea is this:
There is a point at the center of a sphere.
This point is releasing a fluid (say water) in all directions towards the edges of the sphere.
The fluid can collide with the sphere's ...
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3answers
107 views
Is Stokes equation a reduction of Navier-Stokes equations?
The following Stokes problem:
$$\begin{cases}-\nu\Delta u+\nabla p=f&,\textrm{in }\Omega\\ \nabla\cdot u=0&, \textrm{in } \Omega\end{cases}$$
is a reduction of the Navier--Stokes equations?
...
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2answers
156 views
Combined Poiseuille-Couette flow
I stumbled upon this exercise in James Fay "Fluid Mechanics" book, which I'm using to learn fluid dynamics by my own, and I am struggling a bit with it, any help will be appreciated:
The figure ...
2
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1answer
110 views
Flow up an inclined plane (laminar flow)
While learning fluid-dynamics, I stumbled across this problem that requires me to calculate the volumetric flow rate Q of a thin layer of oil leaking from a small hole in a barge, as depicted in the ...
2
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1answer
91 views
What is the interpretation of $(\textbf{u} \cdot \nabla)\textbf{u}$ in Stokes flow?
In very low Reynolds number flows, the Navier-Stokes equations can be reduced to the Stokes equation which is given by
\begin{gather}
\mu \nabla^2 \textbf{u} = \nabla p
\end{gather}
I am looking at ...
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0answers
25 views
Is it possible to define background independent fluid dynamics equations?
Imagine a lake, and you measured the distance from each molecule to it's neighbours for molecules to within say 3 molecular radii.
Taking this data you could reconstruct the positions of the ...
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1answer
180 views
Energy dissipation for force-free, incompressible Navier-Stokes equation with tangent boundary conditions on bounded domains
I consider the Navier-Stokes equation for uniformly incompressible, force-free, Newtonian fluids with constant viscosity. The equations describing the situation are:
$\partial_tv-v\times \text{curl}(...
9
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3answers
286 views
Should non-relativistic Navier Stokes Equations be modified so that they become pseudo-Lorentz invariant?
Choking mass flow seems to reflect the fact that fluid momentum density has a maximum value (in stationary conditions) equal to $\rho_* c_*$ where $\rho_*$ is the critical mass density and $c_*$ is ...
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3answers
174 views
Are there any cases where Stokes law does not apply in viscous fluids?
A friend of mine and I are conducting an experiment to find the relationship between terminal velocity and radius of a sphere (i.e trying to confirm Stokes law). We are using spheres ranging from 1....
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2answers
99 views
Stressing Over Stress Tensor Symmetry in the Navier-Stokes Equations
How do we know that the stress tensor must be symmetric in the Navier-Stokes equation? Here are some papers that discuss this issue beyond the usual derivations:
Behavior of a Vorticity Influenced ...
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1answer
170 views
Derivation of Darcy's law from Stokes equation
On the Wikipedia entry of Darcy's law, a derivation of Darcy's law from Stokes equation is provided. The derivation starts at the Stokes equation, which reads:
$$ \mu \nabla^2 u_i + \rho g_i - \...
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1answer
42 views
Introducing stream function with given velocity equation
Bit information about the problem
We are dealing with the slide coating process - where basically a polymer is being put onto a slot, which is moving in the $x$-direction with velocity $v_0$. The ...
2
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1answer
95 views
(Fluid Dynamics) Euler's equation including gravity
In fluid dynamics, we can write down the Euler's equation as
$\dfrac{\partial \mathbf{v}}{\partial t} + ( \mathbf{v} \cdot \mathbf{\text{grad}} ) \mathbf{v} = - \dfrac{\mathbf{\text{grad}} \; p}{\rho}...
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navier stokes equation with no boundary condition
if we may consider the unsteady motion of flat plate in infinite fluid and make Navier stoke equation into one-dimensional heat equation can we use only initial condition and one derivative condition ...
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1answer
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Stokes flow between 2 spheres
The problem is given like this:
Given two rotating spheres with constant angular velocity $\Omega_1$ and $\Omega_2$ around the vertical axis and pressure on the borders of spheres is $p_1$ and $p_2$...
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Derive mechanical pressure from strain energy density
Similarly to thermodynamic pressure, when we have:
$$P_{therm} = (\frac{\partial U}{\partial V})_{S}$$
Can we define the mechanical pressure for a fluid as:
$$P_{mech} = \frac{\partial \psi}{\...
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1answer
114 views
Navier stokes equation - two dimensional simplified [closed]
The general Navier Stokes Equation is
$\dfrac{D\vec{v}}{D t}= \dfrac{d\vec{v}}{d t}+ \vec{v} .\nabla \vec{v} = \vec{g} - \dfrac{1}{\rho} \nabla p + \nu \nabla^2 \vec{v}$
The above equation can be ...
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3answers
370 views
Is Navier stokes a turbulence model?
Is Navier stokes a turbulence model? If yes, what is the use of k-omega model.. if no, what does the Navier stokes equation got to do with the turbulence models ..? I am very new to fluid dynamics... ...
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1answer
411 views
How do speed and density change in a turbulent flow?
Suppose a fluid passes from having laminar flow, to having a turbulent flow (like when passing after an object). How do fluid speed and fluid density change after that?
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2answers
573 views
What is the meaning of pressure in the Navier-Stokes equation?
I have a hard time to wrap my head around pressure in the Navier-Stokes equation! It may sounds ridiculous but still I cannot understand the true meaning of pressure in the Navier-Stokes equation. Let'...
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1answer
165 views
Non-dimensionalization of Navier-Stokes equations multiphase flows
I am currently dealing with multiphase flows and have to use the non-dimensional form of the Navier-Stokes equations (NSE).
In the scientific literature I found various formulations (and almost no ...
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0answers
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Derive total energy balance equation from Chapman-Enskog analysis of lattice Boltzmann equation
I'm interested to derive the total energy balance from Chapman-Enskog analysis of lattice Boltzmann equation (LBE). I know, I should go to the second moment of LBE (zeroth moment gives mass ...
3
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1answer
74 views
Coupling Navier-Stokes and stochastic models for particle tracking in micro-scale free convection?
I have been using a commercially available software to simulate laminar free convection in a specific small domain (let's use channel w/ heated lower wall as an example). The scale is approx 50-100 ...
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2answers
673 views
Zero velocity divergence for incompressible flow is derived from conservation of energy equation or conservation of mass equation?
I'm a bit confused about incompressible flow definition. In many textbooks or scientific articles, they simply claim that the incompressibility condition for Navier-Stokes equation is:
$\nabla \cdot \...
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2answers
121 views
Why does Anderson ignore a derivative of a normal viscous stress?
I am reading "Fundamentals of Aerodynamics" 5th edition, J.D.Anderson. In part 15.6, he said:
Consider a steady two-dimensional, viscous, compressible flow. The
x-momentum equation for such a ...
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1answer
33 views
How can a system of hoses each defined in their own non-inertial reference frame transmit energy information?
Rotating pipes <- image
Since energy is frame dependent, I can't find a relationship that makes energy invariant at the hose connection points in respect to each local frame in the general case. ...
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1answer
63 views
a flow through a pipe submeged in a moving fluid
There is a classic problem by which a fluid having a uniform velocity profile enters a tube. The pressure at the outlet is atmospheric, and the dimensions of that tube (diameter and length) are known. ...
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0answers
85 views
Can someone explain the Navier Stokes equations? [duplicate]
I am doing a research work on the Navier stokes equations but I don't really understand them, as I am a high school student. Could someone explain them to me in an easy way but kind of specific? Thank ...
0
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1answer
212 views
Incompressible Navier-Stokes equation in Fourier Space
I'm trying to derive the incompressible Navier-Stokes equation in Fourier space, given in e.g. Kraichnan & Montgomery (1980), Rep. Prog. Phys. 43 547 (PDF) (but probably countless other places), ...
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1answer
138 views
Original Derivations of Euler Equations or Navier-Stokes Equations
I've seen the derivations for both viscous and inviscid momentum balance in fluid flow in courses, but I'm curious as to where the original derivation for the equations now referred to Euler equations ...
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2answers
131 views
Stokes's law proportionality to radius
Is there a logical explanation why Stokes's drag
$F_d=6\pi R \eta v$
is proportional to the radius, $R$ of the sphere?
Naively I would have expected that it is proportional to the cross section, i....
1
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1answer
54 views
Bulk viscosity in jump conditions for shock waves
One of the jump conditions for shock waves can be derived from the Navier-Stokes equation and it takes the form (see Shu, Gas dynamics, p.212)
$\dfrac{d}{dx}\left(\rho u^2 + P - \frac{4}{3}\mu \frac{...
