Waves, Instabilities and Turbulence

Question 1

What extra information is needed for a general compressible flow - alongside the Navier-Stokes equation?

Answer 1

A relationship between ρ and p

+ the continuity equation

Question 2

What can be concluded if the initial vorticity of an irrotational flow is zero

Answer 2

it will remain so (irrotational)

Question 3

Define velocity potential,Φ

Answer 3

u = ∇Φ

where u is the velocity vector and Φ is a scalar function

Question 4

The names of the 2 characteristic boundary conditions/equations for free surface gravity waves

Answer 4

Kinematic
and Dynamic
BCs

Question 5

The dispersion relation for surface gravity waves tells you…

Answer 5

This tells us about the time dependence – the frequency – for a given wave vector

Question 6

Are shallow water waves dispersive or non-dispersive?

Answer 6

Non-dispersive

Don’t depend on k

Question 7

What type of waves move the fastest?

Answer 7

Waves with
- small k,
- long wavelength L = 2π/k
move fastest.

Question 8

How to extract the actual solution from the complex wave solutions?

Answer 8

Take the real part

Question 9

Conditions on Amplitude A

Answer 9

Must be small

Question 10

Difference between phase and group velocity?

Answer 10

The wave crests move with the phase velocity
but
the envelope moves with the group velocity

Question 11

What is the restoring force of Inertial waves?

Answer 11

Coriolis term

Question 12

In 2D/3D cases, is the phase or group velocity a vector?

Answer 12

Group velocity

Question 13

For inertial waves, the group velocity is ** to the wave vector and the envelope propagates
** to the wave crests

Answer 13

For inertial waves, the group velocity is perpendicular to the wave vector and the envelope propagates
parallel to the wave crests