All Questions
4 questions
6
votes
2
answers
5k
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What does $(\mathbf{u}\cdot\nabla)\mathbf{u}$ mean in the Navier-Stokes equation?
I am studying the Navier-Stokes equations and I have the equation in the form:
$$\rho \dfrac{\partial{\mathbf{u}}}{\partial{t}} + \rho (\mathbf{u}\cdot\nabla)\mathbf{u} - \mu\nabla^2\mathbf{u} + \...
2
votes
1
answer
355
views
$\nabla$, $\cdot \nabla$, $\nabla \cdot$, $\nabla^2$ - What do they do? [closed]
I'm trying to teach myself Smoothed Particle Hydrodynamics. Unfortunately, my background is in electronics, so the Navier Stokes equations are somewhat alien to me, as is vector calculus. The video I'...
- 114
3
votes
2
answers
5k
views
Feynman's subscript notation
Consider this vector calculus identity:
$$
\mathbf{A} \times \left( \nabla \times \mathbf{B} \right) = \nabla_\mathbf{B} \left( \mathbf{A \cdot B} \right) - \left( \mathbf{A} \cdot \nabla \right) \...
- 163
0
votes
1
answer
305
views
What does an "elementary value $\delta$ of a quantity" mean?
In page-11 of I.E irodov Fundamental laws of mechanics, some notation used in the book is introduced. There, it is said that $\delta$ denotes the elementary value of a quantity but what exactly does ...
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