Under real conditions in the immediate vicinity of a coastline, waves
run up and down the beach surface. Let us consider first the function of mean sea level elevation when the only parameter dependent on the external UK-371804 factors is the parameter γ=Hhbr. When α = − 1, from (20), we obtain the following approximate relationship: equation(22) Hx=Hhbrhx=γbrhx. In practice, the value of parameter γbr ≈ 0.7 − 0.8. By substituting (22) in formula (14) we obtain: equation(23) Sxx≈316ρgγbr2h+ζ¯2. In the general case, the elevation of the mean sea level set-up ζ¯x is not a linear function of x. Note that if instead of equation we assume relation (20), the solution of equation (13) results in a nonlinear (as a function of distance) variability of the mean sea level elevation ( Dally et al. 1985): equation(24) dζ¯xdx=−3161hx+ζ¯xdH2xdx2. Figure 3 compares the mean sea level elevation set-up using the linear approximation (relation 17) and the nonlinear approximation (24). During a controlled large-scale laboratory experiment carried out in the Large Wave Channel in Hannover, a data XL184 solubility dmso set was gathered which compares better with the nonlinear set-up (Massel et al. 2005). The distance shown on the horizontal axis is the distance in metres for coastal areas, reflected by the beach heaped up in the GWK laboratory in Hannover (Figure 4),
where initially, the bottom was flat. Re-profiling into the bottom at an angle β = 1/20 starts at the point of 150 [m] from the beginning of the channel laboratory, and 230 [m] is the point of intersection of the sea water level with the seabed. ‘0’ is beginning of the wave channel, the point where waves
are generated. This notation has been retained to maintain consistency with the work by Massel et al. (2004). Elevation of the mean sea level is dependent on the characteristics VAV2 of the wave arriving from the open sea. Let us consider, therefore, changes in the mean sea level elevation during during several hours of a storm. Let us assume that as storm waves approach the costal zone, their height H0(t) changes over deep water according to the following formula: equation(25) H0t=1+cos2πt24−12+H0t0, where the height H0(t0) = 0.3 [m]. Let the wave period T = 6 [s] and the bottom slope β = 1/20 the duration of the storm is 24 hours. Depending on the height of the wave approaching the shore, the width of the surf zone changes. Figure 5 shows the changes of H0(t) in time during a 24-hour storm. The narrow strip of sea, along the coast, between depth Hbr, where the wave begins to break, and the shoreline is the surf zone. The experiment of Singamsetti & Wind (1980) shows that the depth at the breaking point Hbr, the breaking wave height Hbr and the value γbrnoindent are expressed by the following formulas: equation(26) Hbr=0.575β0.031H0tL0t−0.254H0t, equation(27) Hhbr=0.937β0.155H0tL0t−0.130, equation(28) hbr=0.614β−0.124H0tL0t−0.