# Questions tagged [navier-stokes]

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

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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-...
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### Physical Meaning of Divergence of Convective Velocity Term

When taking the divergence of the convective velocity term, I get the following: \begin{align} \nabla\cdot\left[\mathbf u\cdot\nabla\mathbf u\right]&=\frac{\partial}{\partial x_i}\left[u_j\frac{\...
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### Second-order covariant derivative in index notation [closed]

So I'm having problems finding the second order covariant derivitive in index notation. My teacher said to just find the covariant derivative of a covariant derivative, so I first started with finding ...
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### Wall Shear Stress

I have the solution of a Navier-Stokes simulation with an incompressible, Newtonian fluid with laminar flow. Now I compute the wall shear stress (vector) as $$\tau_n = \mu (\nabla u) n,$$ where $\mu$ ...
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### Solution of Navier-Stokes in a triangular pipe

I was doing some reading about Navier-Stokes equations and stumbled upon this PDF from a course at Clarkson University: http://webspace.clarkson.edu/projects/crcd/me537/downloads/...
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### Life at low Reynolds number (E. M. Purcell)

I am reading the talk given by E. M. Purcell (Nobel Prize winning physicist) named "Life at low Reynolds number". There are two things that I cannot understand. Purcell tells that the Stokes-Equation ...
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### Near a hard-wall, in which direction does a rigid spherical particle move when a positive torque is exerted upon it?

Consider a small rigid spherical particle of radius $a$ immersed in a viscous incompressible Newtonian fluid of shear viscosity $\eta$ in close vicinity to a hard-wall with stick (no-slip) boundary ...
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### Non-dimensionalizing incompressible Navier-Stokes

I have a question about non-dimensionalization of the incompressible Navier-Stokes (NS) equations. My understanding is that the purpose of non-dimensionalization is to "collapse" solutions onto one ...
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### Is it possible to change Pressure without changing Density?

I am still trying to understand Navier-Stokes equations. I understand the equations in general, BUT there is one aspect I still cannot digest: The equations assume that density is constant (okay, I ...
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### Fluid Density Vs Pressure (incompressible fluid)?

I am trying to understand Navier-Stokes fluid equations and I have two questions (these are very primitive questions, I am still trying to understand basic concepts) 1) all books say "assume that ...