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

learn more… | top users | synonyms

10
votes
1answer
460 views

About turbulence modeling

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 ...
3
votes
1answer
393 views

Torque on a rotational cylinder in viscous fluid

I've been stuck on what I'm pretty sure is a simple part of a larger question. It's a cylinder (radius a) spinning in a viscous fluid. It's rotating at rate $\Omega$ .During this question we get that ...
2
votes
1answer
127 views

Stress Force - Understanding Cauchy Stress Tensor

I've been trying to understand the derivation for the Cauchy Momentum Equation for so long now, and there is one part that every derivation glides over very quickly with practically no explanation ...
4
votes
0answers
2k views

Difference between Eulerian and Lagrangian formulation of Fluid Dynamics

Difference between Eulerian and Lagrangian formulation of Fluid Dynamics. I am completely new to fluid mechanics. Until now definition $F = ma$ was sufficient for me to solve any rigid body problems ...
3
votes
0answers
36 views

Bulk and dynamic viscosity in the atmosphere

I'm studying the physics of the atmosphere but I'm struggling with the matter of viscosity (Navier-Stokes equation) for gravito-acoustic waves. From Landau-Lifschitz : $$ (T)_{ij} = -p\delta_{ij} + ...
3
votes
0answers
29 views

Existence and uniqueness of solutions to $\nabla^a T_{ab}$ 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 ...
3
votes
0answers
137 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 ...
2
votes
0answers
27 views

What is the relationship between the Boltzmann Transport Equation and the Navier-Stokes Equation?

What is the relationship between the Boltzmann transport equation and the Navier-Stokes equation? Can the Navier-Stokes equation be derived from a moment of the Boltzmann transport equation?
2
votes
0answers
302 views

Derivation of the equation of motion of a viscous fluid by Landau & Lifshitz

I am trying to follow Landau and Lifshitz, from the Volume 6 (Fluid Mechanics) of the Course of Theoretical Physics, on their derivation of the momentum equation for a newtonian viscous fluid, but I ...
2
votes
0answers
46 views

Has this boundary condition been used in fluid flow?

I would like to know whether anyone has seen a boundary condition used in a fluid flow problem, of the following type. Suppose viscous incompressible fluid is to the left of a plane $x_1=a$, so the ...
1
vote
0answers
5 views

Why hydrodynamic turbulence without heat terms matters?

A lot of research is made on turbulence in "pure" Navier-Stokes equations (NSE). There is a notion of energy cascade when energy comes from larger scales to lower scales and than dissipate. However ...
1
vote
0answers
29 views

Solving inhomogeneous Stokes equation

I want to solve the Stokes inhomogeneous equation, i.e. $$\nabla^2 \vec v -\nabla P = \vec f(r,\theta)$$ $$\nabla\cdot\vec v=0$$ where $\vec f$ is irrotational, i.e. $\partial_y f_x - \partial_x ...
1
vote
0answers
57 views

Difference between a “source dipole” and a “force dipole”

I know quite well what a dipole is and in general what multipole moments are (in the context of, for instance, electrodynamics). What I find myself confused by is something called a "force dipole" in ...
1
vote
0answers
64 views

Is sonoluminescence relevant to the behaviour of Navier-Stokes (or converse)?

More precisely, could Sonoluminescence be a singularity of Navier-Stokes(NS)? Is there some other connection that might be interesting, or is it completely irrelevant? Wiki page mentions NS, but says ...
1
vote
0answers
126 views

How to integrate twice of this viscous term?

I am reading a paper, and I do not understand why the author said the following term when integrated twice will become, $\int\limits_\Omega {{\rm{d}}\Omega {{\bf{\psi }}^{\bf{u}}}\cdot\nabla ...
0
votes
0answers
27 views

Need to differentiate Pressure from normal stress in Navier stokes equation

Can someone please explain why pressure term is differentiated from the normal stress term while deriving the Navier-Stokes equation? $$ \frac{d Fx}{dV} = -\frac{\partial P}{\partial x} + ...
0
votes
0answers
77 views

st. venant shallow water equations for pipe flow

As far as I know from the fluid dynamics class, St. Venant equations (the shallow water equations) are derived by depth-integrating the Navier-Stokes equations. This depth-integrating is done with the ...
0
votes
0answers
137 views

How can I model computationally or experimentally the flow in my aquarium tank?

I have a 60-gallon aquarium tank and I have always wondered about the flow of water in the tank. Let's represent the flow of water in terms of a direction field representing velocity, so if we see the ...