Waves fetch

Wave components with frequencies smaller than <7 cannot be amplified by the wind blowing over the sea surface because their relative velocity to the wind is zero or negative. This process Emits the bandwidth of a wave spectrum toward low frequencies at a given wind speed. The frequency of the spectral peak of the frilly developed wave spectrum is given in a first order by o-y. It is quite obvious that the wave duration and the wave fetch of a fully developed sea grow with increasing wind velocity. 

Wave size is determined by wind speed and fetch, the distance over the oceans surface which the wind travels. Favorable wind energy sites are generally western coastlines facing the open ocean such as the Pacific Coast of North America and the Atlantic Coast of Northern Europe. Norway, Denmark, Japan, and the United Kingdom are the world leaders in wave energy technologies. 

These limiting factors of the wave growth in an enclosed sea with the dimensions as the Baltic cause the average wave height to be smaller in particular during high wind speeds compared with the ocean where the fetch is limited only by the dimension of the wind field and the wave motion does not come into contact with the ocean bottom. 

The characteristics of sea states, their formation and observation, as well as the wave-generating factors, are discussed. Computation of the fetch, an important parameter in empirical calculation formulas which is difficult to determine, is described in detail. The values given in hterature clearly are too high and fail to take into account the spectral nature of sea state. 

Wave Generating and Wave Modifying Factors (Wind, Fetch,... 

In sea areas similar to the Baltic Sea, the wind direction determines the fetch and thereby the wave growth. 

Fetch The fetch is the length of a wind field, in which the direction and speed of the wind are approximately constant (see Fig. 7.6). This is the part of the sea surface on which the wind transmits its energy and thus causes wave growth. 

The starting position for the determination of the fetch lies in aquatoria, surrounded by coasts, leeward of coasts (see Fig. 7.5), and on the open sea at the leeward boundary of a wind field with homogeneous direction and speed (see Fig. 7.6) and ends at the position where the wave elements are to be calculated or measured. 

If the development of the sea state starts during offshore winds leeward of the coasts, the wave heights will increase in the direction of the open sea (see Fig. 7.5), and the fetch is calculated from the distance to the coast. In this context, it should be noted that the dimensions of the wind field must be such that the width of the field must be at least equal to its length (Quandt, 1980). In the Baltic Sea, such conditions are found only for easterly winds off the coast of the Baltic states and for southerly winds off the Polish coast. 

The wave heights in the Atlas zur Ermittlung der Wellenhdhe in der siidlichen Ostsee (Schmager, 1979) were calculated on this basis. Quandt (1980) calculated effective fetches of the B altic Sea for numerous positions as afunction of the wind direction (see Fig. 7.8). 

Depending on wind speed and fetch, wave growth is limited by the water depth (Fig. 7.11, top right). In areas with decreasing water depth ingoing waves will be deformed, and their transformation starts at a depth lower than half the wavelength (see Fig. 7.2). The life cycles of waves are finally ended when they break. 

A quick overview of the sea state parameters in the Baltic Sea is provided by the wave diagram (see Fig. 7.11). If the fetch (see Section 7.1.3.4) is known, the use of the diagram does not present much difficulty. For a fetch of 80 km and a wind speed of 45 kn the following information about the sea state conditions can be found in Table 7.5. 

The wave number-frequency spectrum of wind waves was measured at low wind velocity, 2.5 m s 1, and at two different fetches. Dominant dm-cm-scale wind waves are steep enough and are characterized by asymmetric profile and parasitic ripples generation even at such a low wind velocity, so that we expect that nonlinear effects can be quite strong. Co-located measurements of wave height were conducted using a wave gauge. The... 

Fig. 3. Frequency spectra (a) and phase velocities (b) of wind waves at two fetches (1 - small fetch, 2 - large fetch). Clean water, wind velocity 2.5 m/s. Solid line in Fig. 3b - phase velocity for linear gravity-capillary waves (surface tension 72 rnN/m) accounting for wind drift...

Fig. 4. Contrasts (a) and phase velocities (b) for cm-mm-scale wind waves at large fetch. Fig. 4a 1 - MOSA, 2 - OSA. Fig. 4b 0- clean water, - film 1, solid lines - linear theory for surface tension 72 mN m 1 and drift velocity 4 cm s 1 (curvel) and for surface tension 32 mN m"1 and drift velocity 3 cm s 1 (curve 2)...

The estimated bound wave/total wave ratio R is shown in Figure 6 for clean and contaminated water at the large fetch and in Figure 7 for the small fetch. 

Fig. 6. Relative intensity of bound components in the spectmm of wind waves. Large fetch. 0 - clean water, - film 1...

The wind wave tank of the University of Hamburg is 26 m long and 1 m wide. It is filled with lfesh water with a mean water depth of 0.5 m. The wind-tunnel height is 1 m, and the effective (maximum) fetch is 19 m. All measurements reported herein were performed at a fetch of 14.5 m and at wind speeds between 2 and 10 m s"1 generated by a radial blower. In the measurement and rain area, the metallic plates of the tank s roof were removed and, on the leeward side, replaced by Styrofoam panels to ensure the unattenuated transmission of the microwaves (Figure 2). At the windward side of the rain area plates of microwave absorbing material were vertically mounted in the direction of the specular-reflected radar beams. 

Here V (m/sec) is the wind speed at a height of 9 m above the water surface, and F (km) is the effective fetch. (The effective fetch is the average fetch projected onto the wind direction over a 90° arc, which is centered on the wind arrow.) The maximum horizontal component of the water-particle velocity at the bottom is, according to first-order wave theory. 

Fig. 2. Maximum horizontal particle speed at the bottom in water of depth

---