[This space left intentionally blank]
Is a sum of random waves
a good model of the internal wave field?
or, an informal look at non-stationarity
Murray Levine
u   An cos(nt   n )
n
where
An  n
independent random variables
u
time
frequency
u-spectrum
Interesting information
in the modulations?
frequency
u-spectrum
Random phase
u
time
u
time
u-spectrum
High frequency Band
time
Random phase
u
time
u-spectrum
High frequency Band
time
So, look for the modulation
of spectral bands…
Are the modulations consistent
with the random wave model?
Use data from the Ocean Storms experiment
Moored Observations
NE Pacific Ocean
47deg 25’N, 139 deg 18’W
1987-88
10 month time series
2
10
1
u-spectrum
10
Ocean Storms
194 m
0
10
-2
-1
10
-2
10
-1
10
0.1
0
10
Frequency, cph
1
Spectrum as function of t, S(t)
0.1 cph
0.5 cph
1.2 cph
u-spectrum
Ocean Storms
194 m
0
time, days
300
Spectrum of S(t)
Ocean Storms
194 m
0.1 cph
0.5 cph
1.2 cph
1/(300 days)
frequency
1/(10 days)
Spectrum as function of t, S(t) Ocean Storms
2000 m
u-spectrum
0.1 cph
0.5 cph
0
time, days
300
Spectrum of S(t)
Ocean Storms
2000 m
u-spectrum
0.1 cph
0.5 cph
1/(300 days)
frequency
1/(10 days)
Spectrum as function of t, S(t)
u-spectrum
0.1 cph
0.5 cph
1.2 cph
Random
Model
0
time, days
300
Spectrum of S(t)
0.1 cph
0.5 cph
1.2 cph
1/(300 days)
frequency
Random
Model
1/(10 days)
frequency
u-spectrum
Another Random phase
u
time
So, is the internal wave field look like this random phase model?
Ie is each freq band treated this way
Or is there information in the modulations, ie the non-stationary part
To investigate this idea a bit further use data from Ocean Storms experiment
Open NE pacific, 1987-88, 47deg 25’N 139 deg 18’W
So, Look at time varying spectra and see if random phase works.
Ie, similar question: can we generate a realisitic iw field by random phase?
Or stated another way: is there information about the wave field in these modulations
Break up the spectrum into bins