5.6 Energy Dispersion – Group Velocity

Non-dispersive waves (movie)Wave 1: K1, C1

Wave 2: K2, C2

K2=1.4*k1

C2=C1

The phase shift between the two waves does not change, so the total wave group does NOT change with time. It propagates at the same speed as individual waves.Nondispersive waves

Dispersive waves-1 (movie)

Wave 1: K1, C1

Wave 2: K2, C2

K2=1.4*k1

C2=1.4*C1The phase shift between the two waves changes with time, so the total wave group changes with time.Dispersive

Dispersive waves (snapshots)

t=t0

t=t1

x

v’

v’

x

The waves spread in space and the wave height decreases in time (the wave group broadens in time and energy is dispersed).

Internal Gravity waves (movie)

The vertical phase velocity and the vertical group velocity have opposite directions.

Cg

Cp

Cg

Cp

1-D Rossby waves (movie)

Assume U=0, Cg>0: eastward (following the wave envelop) Cp<0: westward (following the red circle)

cp =U −βo

k2

cg =U +βo

k2

2-D Rossby Waves(t = Day -5)

(t = Day 0)

(t = Day +5)

Stationary Rossby Waves

Years: Nino 3.4 1958: 1.607 1966: 1.308 1973: 1.639 1983: 2.548 1987: 1.254 1992: 1.820 1995: 1.013 1998: 2.396 2003: 1.162