Dynamics - Waves Flashcards
What is angular frequency?
w= 2pi/t
What is natural wave number?
1/lambda
What are the phase velocity and phase speed?
Speed: Cp= w/k And velocity: Cp= w/k^2
What is the group velocity vector?
Cg= dw/dk î + dw/dl j + dw/dm k
What is the difference between dispersive and non-dispersive waves?
Dispersive waves the phase and group vectors are different. Non-dispersive waves have the same C and Cg.
What is the Euler’s (DeMoive’s) formula?
e^iø= cos(ø)+isin(ø)
How do waves travel in dispersion relation?
U(x)= Ae^i(kx+ly+mz-wt)
What is the difference between linear and non-linear waves?
Linear waves don’t exchange energy(independent) but non-linear waves do.
What keys are good to know for linearization?
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
What is a shallow water wave?
Wavelength are longer than depth. Also are non-dispersive since different wavelengths all move at same speed.
What is reduced gravity?
g’= g(p1-p2)/p1 where p= rho
What is the baroclinic mode equation?
C= sqrt(g’h1h2/H)
How do baroclinic and barotropic waves move? In phase and out of phase?
Baroclinic = out of phase (slower) Barotropic = in phase (faster)
What is equivalent depth?
He= (g’/g)(h1h2/H)
Sound waves are adiabatic. What does adiabatic mean?
Without heat
Are sound waves dispersive?
They are non-dispersive. Speed of sound is a fundamental property of a fluid.
What is the speed of sound Cs formula?
Cs= sqrt( yR’T) where y= Cp/Cy
What is the formula for Brunt-Vaisala frequency? What does it tell us about the atmosphere?
N^2= (g/ø)(dø/dz)
Tells us about the stability of the atmosphere.
N^2(+)= stable
N^2(-)=unstable
Stationary waves (m^2) are affected how?
By topography, wave speed, and stability
What does it mean when m^2 is positive and negative?
(+) equals vertically stacked waves on a slope
-) equals evanescent waves (decaying with height
What are the characteristics of a shallow water gravity wave in a single layer fluid?
1) they are hydrostatic
2) they are barotropic
3) they are non-dispersive
What are the characteristics of a linear shallow water gravity waves in a two layer fluid?
1) they are hydrostatic
2) they are non-dispersive
3) barotropic is the fastest mode
How do waves travel for vertical propagation in dispersion relation?
¥’=A/sqrt(p)*e^i(kx+ly+mz-wt)
What is the dispersion relation for stationary internal gravity waves?
m^2= (N^2/u^2)-k^2
How can you tell whether the atmosphere is inertially stable or unstable?
w^2>0 is inertially stable (dm/dy>0)
w^2<0)
How can you tell when an atmosphere is statically stable?
dø/dz>0 is stable
dø/dz<0 is unstable
Ø increases as you go up in atmosphere as well as south towards equator
How do we get barotropic instability? What is the condition required?
d^2u/dy^2 -B=0
1) Linear shear CANNOT give instability
2) Need negatively tilted trough
3) Need horizontal shear*
Where do we find baroclinic instability?
1)Depends on vertical shear (from Vt)
Look by fronts where there is sharp temp gradient
When can rossby waves not propagate vertically?
When the mean zonal winds are easterly or if they are westerly and exceed a certain speed
What is the phase speed for internal waves?
=KhN/k^2
