Analysis of ship‐generated surface waves using a method based upon the local Fourier transform

Abstract

Laser wave slope meter data of the surface wake of the U.S. Navy tug, USS Quapaw, is analyzed using a method based upon the local Fourier transform (LFT). Three cases at ship speeds of 8.0, 7.82, and 7.85 m/s. are analyzed (JOWIP 8–2, 9–2, and 9–3). The results are compared with a simple kinematical surface wake model. The analysis reveals several physical phenomena, including the steady Kelvin wake, a region of unsteady ship‐generated waves, and the turbulent wake. The Kelvin wake includes the transverse waves, the diverging waves, and the cusp line, which appears at an angle of about 19.5° off the turbulent wake and serves as the outer boundary for the wake. Although most of the Kelvin waves are linear, there is an indication of nonlinearity, as evidenced by a bound second harmonic, just inside the cusp line. The unsteady waves appear within the region about ±7° off the turbulent wake and have wavelengths between a few centimeters and about 2 m. In the region of the short diverging Kelvin waves and the unsteady waves, the wave slope meter data sets in JOWIP 8–2, 9–2, and 9–3 are significantly different: JOWIP 9–2 data contains the largest amount of slope variance near locations predicted by Kelvin wave theory, JOWIP 9–3 contain the largest slope variance at locations predicted for unsteady waves, while JOWIP 8–2 contains low values of steady and unsteady waves. The differences could be due to intermittency in the sources for the waves or, in the case of JOWIP 8–2, to decay due to surfactants. The short diverging Kelvin waves and the unsteady waves can serve as Bragg waves for a range of radar wavelengths and orientations. At some locations in the JOWIP 9–2 and 9–3 data sets, the slope variance integrated over a range of L band Bragg waves attains peak values that are comparable to the same integrated slope variance in a wind wave spectrum at moderate wind speed. Also discussed is the general utility of the LFT method for the analysis of intermittent, broadband, oceanographic vector data.