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Is a sum of random waves a good model of the internal wave field?

Murray Levine

cos( )n n nn

u A t

independent random variables

or, an informal look at non-stationarity

n nA where

time

u

frequency

u-sp

ectr

um

Interesting information in the modulations?

frequency

u-sp

ectr

um

Random phase

time

u

time

u

time

u-sp

ectr

umHigh frequency Band

time

u

Random phase

High frequency Bandu-

spec

trum

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 ObservationsNE Pacific Ocean 47deg 25’N, 139 deg 18’W1987-88

10-1

100

10-2

10-1

100

101

102

Frequency, cph0.1 1

Ocean Storms194 m

u-sp

ectr

um

-2

10 month time series

time, days

u-sp

ectr

um

0 300

Ocean Storms194 m

0.1 cph0.5 cph1.2 cph

Spectrum as function of t, S(t)

Ocean Storms194 m

0.1 cph0.5 cph1.2 cph

Spectrum of S(t)

frequency1/(300 days) 1/(10 days)

Ocean Storms2000 m

time, days 3000

u-sp

ectr

um0.1 cph0.5 cph

Spectrum as function of t, S(t)

Ocean Storms2000 m

u-sp

ectr

um0.1 cph0.5 cph

Spectrum of S(t)

frequency1/(300 days) 1/(10 days)

Spectrum as function of t, S(t)RandomModel

time, days 3000

u-sp

ectr

um0.1 cph0.5 cph1.2 cph

Spectrum of S(t)

frequency

RandomModel

1/(10 days)1/(300 days)

0.1 cph0.5 cph1.2 cph

frequency

u-sp

ectr

um

u

time

Another Random phase

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