Navier-Stokes Flashcards
How are the Navier-Stokes equations derived?
- Begin with Cauchy’s equation
- Demand the stress tensor is symmetric
- Use observations to align the stress tensor with Newtonian fluids
- Demand the fluid is incompressible
What are the Navier-Stokes equations, in vector & index notation?
What is the boundary condition for solid surfaces?
Fluids don’t penetrate them or slip past them (stationary relative to the boundary). Fluid particles stay at the boundary.
What satisfies as initial conditions?
Specifying the velocity. Pressure doesn’t need to be specified as there are no time differentials of pressure.
What is the (dynamic) kinematic boundary condition?
Fluid particles on a free surface tend to stay on the free surface (from experiment).
What is the (dynamic) stress/traction condition?
The stress across a free surface has to be continuous.
What are the equations of parallel flow?
Given parallel flow, what equations emerge with no body force?
What is Couette flow?
Plates are infinitely long.
Assume G(t) = 0, no changes in pressure.
What is Poiseuille flow?
Pressure drives parallel flow. Assume no u = u(z,t) or body forces.
How would you solve for a steady-state of fluid moving down an incline plane with a free surface?
Solve the free surface first.
How would you solve “Rayleigh’s 1st problem” of an oscillating plate?
Assume the fluid goes up to infinity, there’s no z-dependence and no body forces.
