Dynamics - Waves

Question 0

What is angular frequency?

Answer 0

w= 2pi/t

Question 1

What is natural wave number?

Answer 1

1/lambda

Question 2

What are the phase velocity and phase speed?

Answer 2

Speed: Cp= w/k And velocity: Cp= w/k^2

Question 3

What is the group velocity vector?

Answer 3

Cg= dw/dk î + dw/dl j + dw/dm k

Question 4

What is the difference between dispersive and non-dispersive waves?

Answer 4

Dispersive waves the phase and group vectors are different. Non-dispersive waves have the same C and Cg.

Question 5

What is the Euler’s (DeMoive’s) formula?

Answer 5

e^iø= cos(ø)+isin(ø)

Question 6

How do waves travel in dispersion relation?

Answer 6

U(x)= Ae^i(kx+ly+mz-wt)

Question 7

What is the difference between linear and non-linear waves?

Answer 7

Linear waves don’t exchange energy(independent) but non-linear waves do.

Question 8

What keys are good to know for linearization?

Answer 8

1) Derivatives of constants (dū) =0
2) Multiplying perturbations turns into 0 (d’*d’=0)
3) Look for hydrostatic balance and geostrophic balance in the end to simplify

Question 9

What is a shallow water wave?

Answer 9

Wavelength are longer than depth. Also are non-dispersive since different wavelengths all move at same speed.

Question 10

What is reduced gravity?

Answer 10

g’= g(p1-p2)/p1 where p= rho

Question 11

What is the baroclinic mode equation?

Answer 11

C= sqrt(g’h1h2/H)

Question 12

How do baroclinic and barotropic waves move? In phase and out of phase?

Answer 12

Baroclinic = out of phase (slower)
Barotropic = in phase (faster)

Question 13

What is equivalent depth?

Answer 13

He= (g’/g)(h1h2/H)

Question 14

Sound waves are adiabatic. What does adiabatic mean?

Answer 14

Without heat

Question 15

Are sound waves dispersive?

Answer 15

They are non-dispersive. Speed of sound is a fundamental property of a fluid.

Question 16

What is the speed of sound Cs formula?

Answer 16

Cs= sqrt( yR’T) where y= Cp/Cy

Question 17

What is the formula for Brunt-Vaisala frequency? What does it tell us about the atmosphere?

Answer 17

N^2= (g/ø)(dø/dz)
Tells us about the stability of the atmosphere.
N^2(+)= stable
N^2(-)=unstable

Question 18

Stationary waves (m^2) are affected how?

Answer 18

By topography, wave speed, and stability

Question 19

What does it mean when m^2 is positive and negative?

Answer 19

(+) equals vertically stacked waves on a slope

-) equals evanescent waves (decaying with height

Question 20

What are the characteristics of a shallow water gravity wave in a single layer fluid?

Answer 20

1) they are hydrostatic
2) they are barotropic
3) they are non-dispersive

Question 21

What are the characteristics of a linear shallow water gravity waves in a two layer fluid?

Answer 21

1) they are hydrostatic
2) they are non-dispersive
3) barotropic is the fastest mode

Question 22

How do waves travel for vertical propagation in dispersion relation?

Answer 22

¥’=A/sqrt(p)*e^i(kx+ly+mz-wt)

Question 24

What is the dispersion relation for stationary internal gravity waves?

Answer 24

m^2= (N^2/u^2)-k^2

Question 25

How can you tell whether the atmosphere is inertially stable or unstable?

Answer 25

w^2>0 is inertially stable (dm/dy>0) | w^2<0)

Question 26

How can you tell when an atmosphere is statically stable?

Answer 26

dø/dz>0 is stable dø/dz<0 is unstable Ø increases as you go up in atmosphere as well as south towards equator

Question 27

How do we get barotropic instability? What is the condition required?

Answer 27

d^2u/dy^2 -B=0 1) Linear shear CANNOT give instability 2) Need negatively tilted trough 3) Need horizontal shear*

Question 28

Where do we find baroclinic instability?

Answer 28

1)Depends on vertical shear (from Vt) | Look by fronts where there is sharp temp gradient

Question 29

When can rossby waves not propagate vertically?

Answer 29

When the mean zonal winds are easterly or if they are westerly and exceed a certain speed

Question 30

What is the phase speed for internal waves?

Answer 30

=KhN/k^2