# Questions tagged [navier-stokes]

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

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### What are the Lorenz Equations used for?

In fluid dynamics I have come across two sets of equations, the Navier-Stokes equation and the Lorenz equations. From what I have read the Navier-Stokes equations always holds. So why do we need the ...
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### 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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### 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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### What are the assumptions of the Navier-Stokes equations?

I wanted to model a real life problem using the Navier-Stokes equations and was wondering what the assumptions made by the same are so that I could better relate my entities with a 'fluid' and make or ...
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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### Divergence of Cauchy Stress Tensor [closed]

On the wikipedia page for the Cauchy Momementum Equation, it's stated that the equation can be written as $$\rho \frac{D\,\textbf{v}}{D\,t} = \nabla \cdot \sigma + \textbf{f}$$ Where $\sigma$ is ...
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### 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 ...
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### Instantaneity of Stokes Flow

Background Info: A steady-state incompressible newtonian Stokes fluid occupying a domain $\Omega \in \mathbb{R}^2$ has flow velocity $\textbf{u}$ and pressure $p$ given by the following system of ...
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### Incompressible Fluid Flow around sphere (Stokes)

Stokes solved this 1851. I have a question regarding the derivation. Following Batchelor the equations to be solved are \begin{align} \nabla \left( \frac{p - p_0}{\mu} \right) = \nabla^2 \vec{u} = -\...
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The incompressible Navier-Stokes equations widely used in hydrodynamics don't have the gravitational acceleration. \begin{align} \frac{\partial u_i}{\partial x_i} & = 0, \\ \frac{\partial u_i}{\... 0answers 45 views ### Friction between 2 fluids in Navier Stokes I have a system with 2 different fluids, and I want to write a friction/viscosity term between them in their Navier-Stokes equation. Should it be in the form M(v_{1}-v_{2}) with M a friction ... 1answer 97 views ### Complex solutions to the Navier-Stokes equation I had recently ended up with a case where on solving the Laplace equation (for a fluid under certain conditions), the radial dependence turned out to be complex (in general). In such cases, do we work ... 0answers 186 views ### How to prove that Navier-Stokes equations are Lorentz invariant? I've been hearing recently that the Navier-Stokes (NS) equations are invariant under a Lorentz transformation, so I tried to prove it just changing terms of transformed velocity instead of the ... 1answer 143 views ### Mass conservation equation We have a small drop spreading on a completely wetting solid substrate. The drop shape is h(s,t). The coordinate system is cylindrical (s,z). The velocity fields are: u(s,z) in the s direction and w(s,... 1answer 602 views ### Is there a nice way to write Navier-Stokes equations in exterior calculus I'm considering to study some high-dimensional Navier-Stokes equations. One problem is to do write the viscous equation for vorticity, helicity and other conserved quantities. I think it might be ... 1answer 311 views ### Physical intuition for Incompressible Navier Stokes second term I'm trying to get an intuitive understanding of the Incompressible Navier Stokes equation (as for me thats the only way I can use it effectively and avoid the rote learning method): \rho(\frac{\... 1answer 68 views ### Flow field generated by a sphere in fluid What is a flow field generated by a swimming sphere in the fluid? (in low reynolds regime)? What is the flow field generated by a swimming cylinder in this regime? It seems that the question is not ... 1answer 71 views ### Incompressible 2D Navier-Stokes equation I am trying to solve for and simulate the vorticity numerically (finite difference method), however there's one part I was hoping to get some help with. I need to find the fluid velocity \mathbf{u} ... 1answer 65 views ### 2D Uniform Flow Inclined Plane - Reynolds Averaging: Leads to no Turbulence? We're looking at a fully developed flow along an inclined plate, the x coordinate is along the plate and the z coordinate is perpendicular to it. In 2D, uniform flow I end up with the continuity ... 1answer 262 views ### Interpretation of the time scale L^2/\nu During the scaling of the Navier-Stokes equations it is often made use the viscous time scale L^2/\nu, where L is the characteristic length and \nu the kinematic viscosity. What is the physical ... 1answer 97 views ### Transverse and longitudinal random forces I am trying to read following article: http://arxiv.org/pdf/1410.1262v1.pdf According to the equation (2.10) and (2.11), the random force is defined as  \langle f_i(x) \ f_j(x) \rangle = \delta(t-t'... 0answers 59 views ### Cascade vs Inverse Cascade: Energy flow in 2D and 3D turbulence We know that vortices tend to coalesce in 2D(inverse cascade) as opposed to 3D where they 'break down' into smaller vortices(cascade) ie. energy flows fro larger to smaller scales in 3D and opposite ... 1answer 272 views ### Boundary Layer Physics and Bernoulli Principle I was taught that the relative velocity of all fluid particles directly in contact with the boundary in a fluid flow is zero. In other words, that the relative velocity of fluid particles in the ... 1answer 257 views ### Existence and uniqueness of solutions to \nabla_a T^{ab}=0 in general (or special) relativity The equation in the title of this question can be a relativistic analogue of the Navier-Stokes equation (in the sense that, in the low-velocity limit, it reduces to Euler's equation when T^{ab} is ... 1answer 93 views ### Navier-Stokes eqs. correspond to F=m*a I have the (typical) Navier--Stokes system for incompressible fluid:div(u)=0\rho(u_t+u\cdot\nabla u)=-\nabla p+div(\nu\nabla u)+\rho g$$In a paper that I'm reading says that the term$$u_t+...
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I have some questions about this paper: Lagrangian/Hamiltonian formalism for description of Navier-Stokes fluids. R. J. Becker. Phys. Rev. Lett. 58 no. 14 (1987), pp. 1419-1422. After reading the ...
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### momentum balance equation for low reynolds number flow

This is a flow in a 2-D microchannel (h/L<<1). Low Reynolds number flow. The mass - conservation equation states $$\frac{\partial (\rho u)}{\partial x}+\frac{\partial (\rho v)}{\partial y}=0$$ ...
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### Exact solution of micropolar fluid for Poiseuille flow

I am new here, so i wondered if you could help me with a sytem of ordinary equations with constant coefficients. This model of equations refer to the well known Navier Stokes equations of fluid ...
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### Viscosity and energy balance

When solving Navier Stokes equations for viscous fluid over rigid surface, the viscous term in the momentum equation accounts for the momentum transfer between the fluid and surface in the near wall ...
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### Fluid simulation - why gradient of pressure is the term $\delta q$ in the projection step?

I'm learning stable fluids by reading Stam's paper. In the paper, it says, according to Helmholtz-Hodge Decomposition, I vector field $w$ could be decomposed to a divergence-free field and a curl-...