In (12), D e is called the eddy viscosity and generated by turbulence at wind&ndash$ift layer. Where m is a constant, u∗ is the wind friction velocity, δ is the threshold wind friction velocity, c is the wave phase speed, and α 1 and α 2 are the dissipation coefficients due to wave–drift interaction. The involved physics and arguments are given in section 7. How to obtain a reasonable estimate for the MSS in a wider range of wavenumber is the main subject from section 2 through section 6. An optical sensor can detect water wave slopes generated by arbitrarily short water waves up to the wavelength of reflected light, while microwave radar can only measure a part of the surface slopes up to the radar wavelength. Their derived values are much higher than the observations of Cox and Munk (1954a, b), and much higher than the values required in (8). The MSS has also been derived from the ocean surface spectra ( Donelan and Pierson 1987 Apel 1994). (1992) is equal to our MSS for k up to 100 rad m −1. The comparison shows (not included in this paper) that the derived MSS by Jackson (1991) and Jackson et al. In their papers, the MSS contributed by the shorter waves is regarded as small structure and their effect on radar backscatter is included in the effective reflection coefficient, due to their special mathematical approach. (1992) used their derived MSS to determine the Phillips constant in the equilibrium range. (1992) is the part contributed by gravity waves. The eddy viscosity is due to turbulence at the wind-drift layer, which suppresses the spectrum of high-frequency waves with wavelengths on the order of millimeters. The parasitic capillary wave dissipation due to molecular viscosity can be balanced by the energy supply from the underlying waves, hence it is removed from the model. It is suggested that the k p/ k dependence observed in the range of gravity waves should not be extended to the region of short waves. This effect can be denoted by c 2/ U 2 10 or c 2/ c 2 p dependence of short-wave spectrum. The short-wave dissipation due to wave–drift interactions has the effect of suppressing the spectral density at high wind condition, which further influences the directional spreading rate. The physics included in this model on gravity–capillary wave spectrum is also illustrated. Also, the RBCS, calculated using the C-band filtered MSS, is in keeping with the ERS-1/-2 scatterometer empirically based algorithms CMOD3 and CMOD4. The radar backscatter cross section (RBCS), calculated from specular reflection theory using the Ku-band filtered MSS, is in keeping with the empirically based Ku-band models by Brown for the GEOS-3 13.9-GHz altimeter, and by Witter and Chelton for the Geosat 13.5-GHz altimeter. The MSS integrated from the above two spectra over high-frequency dissipation length (1 mm) fits the optical observations very well. Square waves frequently endanger boats and ships further out, so stay in the shallows to keep safe.The mean-square slope (MSS) of the sea surface for upwind and crosswind is derived, based on Phillips’ equilibrium spectrum and the model herein on gravity–capillary wave spectrum. Swimming out too far in the first place is preferable, as is getting out of the water as soon as the waves become too large. When you’re in the water, you may not notice that the waves are arranged in a grid, but you will notice that the swells grow larger and you must swim against two opposing currents. What happens if you become entangled in a square wave? Then you can go swimming safely and without crowds. Instead, you may spend your time sunbathing on the sand or swimming in the shallow water until the weather improves. It can be difficult for boats and swimmers to navigate these cross-seas because they can create waves up to 10 feet high and shift the direction of the wind.Īgain, this is quite unusual, but if it does occur, do not go out on a boat or swim in the water because it may be rough. The Île de Ré on France’s western coast is a fantastic site to watch them from a safe distance. These square waves do not occur frequently, but when they do, they are usually near the coast. The European Space Agency stated in 2010 that “the conditions are quite common in the ocean and occur when a windsea and a swell, or two swell systems, coexist.”Īccording to a 2004 survey, “a large percentage of ship accidents occurred in crossing sea states.” However, it is also one of the most terrifying sights to see in the waterĪ square wave, also known as a “cross sea,” is formed when two waves collide to form a square shape that resembles a checkerboard Yes, this does happen, and it’s a stunning sight. You may be familiar with rip currents and fluctuating tides, but you may be unaware of the dangers of square waves. Keep an eye out for waves and never turn your back on the sea. If you want to enjoy the ocean, remember to keep safe in it.
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