[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