Internal wave spectrum in shallow water: measurement and comparison with the Garrett-Munk model

The covariance matrix of sound-speed variations is determined from yo-yo CTD data collected during the SWARM 95 experiment at a fixed station. The data covered approximately 2 h and were collected during a period when nonlinear solitary internal waves were absent or negligible. The method of empirical orthogonal functions (EOF) is applied to the sound-speed covariance matrix assuming that the internal wave modes are uncorrelated. The first five eigenvectors are found to agree well with the theoretically modeled eigenfunctions based on the measured buoyancy frequency and the internal wave eigenmode equation. The mode amplitudes for the first five modes are estimated from the corresponding eigenvalues. They agree with the Garrett-Munk model if j*=1 is used instead of j*=3. A second method is used to deduce the mode amplitudes and mode frequency spectra by projecting the sound-speed variation (as a function of time) onto the theoretical mode depth functions. The mode amplitudes estimated with this method are in agreement with the EOF results. A modified Garrett-Munk model is proposed to fit the frequency spectrum of linear internal waves in shallow water.