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

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How does the dissolution of salt affect the solution density?

Suppose you have a container of water as a solvent and you a certain amount of salt as a solute sitting at the bottom of the container that has yet to start dissolving. Supposing temperature and ...
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Why is the solution to the Blasius boundary layer problem self-similar?

In every course or textbook that I encountered so far, the authors transform the Navier-Stokes equations of the Blasius boundary layer problem into the Blasius ODE. The problem with many of those ...
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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 ...
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Solve unsteady state Bernoulli equation for flow in a pipe

I am an engineer studying an unsteady-state flow through a pipe. The Pipeline has been cleanly cut into two halves, without deforming the cylindrical form of the pipe, exposing the contents to ...
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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 ...
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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 ...
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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} + ...
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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 ...
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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 ...
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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 ...
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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 ...
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Does a whirlpool(vortex in water) continue in air(vortex in air),and when does a vortex stop?

First part: The question is both about the continuity of the water vortex(whirlpool) to vortex in air in time and in space. About continuity in time,does the vortex of the water slowly produce a ...
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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 ...
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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 ...
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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 ...
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Value of Stokes constant for air-water vapour interaction

I wish to estimate the Stokes force between air and water vapour. Where can I find a reference for the corresponding "Stokes constant"? Assume we have a composition of water vapour with air. I ...
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Specific form of Stokes's differential equation

Coming from a chemical background, I have next to no knowledge of the (as it seems to me) complex field of fluid dynamics, so bear with me here. I'm reading a paper written by seismologist Norman ...
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Acoustic/Gravity waves subject to constant wind

I'm trying to model an acoustic/gravity wave (atmospehric gravity waves) propagation through an idealized atmosphere but I'm struggling understanding the results I'm suppose to get. The atmospheric ...
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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 ...
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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} + ...
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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 ...