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The influence of wave groups on the dual-frequency Doppler spectrum: Experimental and theoretical approach


  • Svein Jacobsen,

  • Torbjørn Eltoft


Experimental output data from a multifrequency, continuous wave, C band system have been investigated and discussed with reference to physical principles involved in modulation of small-scale centimetric water waves by larger-scale wave trains. Attention payed at field and laboratory measurements described in the literature show that the propagation velocity of certain wave components below the spectral peak occasionally differs from predictions of conventional linear theory. A one-dimensional theoretical analysis of the dual-frequency microwave response, including Doppler features and modulational effects induced by modulated wave trains, has been developed to throw light on this phenomenon. The theoretical expressions derived predict that wave train modulation should manifest itself as two narrow, Doppler-shifted peaks in the cross-product power spectrum generated from two distinct microwave returns. The wave field involved in the modulational process, is modeled as not only consisting of independently propagating Fourier components obeying the linear dispersion relation but also being composed of wave groups of Stokeslike waves, forming independent wave packets. Furthermore, each isolated packet is constructed to be a perturbation solution of the wave equations representing the sea surface boundary conditions. Experimentally, pronounced spectral components were observed with variations in magnitude and Doppler behavior which are consistent with proposed theory, surface truth, and results presented earlier.

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