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PONAŠANJE BRODA NA TALASIMA____________________________Zavisnost brzine i perioda talasa odtalasne dužineNagib talasa∂ζα ( , ) nnxt = = Akn ncos( kxn− ωnt+εn)∂xAαnon= Akn n= 2π λnU okviru linearne teorije, nagib talasa je mali...odnosno An λnBrzina strujanjaλ n [m] c n [m/s] T n [s]1 1,25 0,8100 12,5 81000 40 25...filmski trikovi∂φnkz nvxn = = ωnAne sin( knx− ωnt+εn)∂x∂φnkz nv zn= =−ω nA ne cos( k nx− ω nt+εn)∂zPa je brzina strujanjav = v + v =ω A e2 2n nx nz n nkznPREDAVANJA 2009. 45
PONAŠANJE BRODA NA TALASIMA____________________________vcOdnos brzine strujanja i brzine talasa jen n nnkz nω A e= =n n=onωnk nkz nkz nkAe α e 1brzina strujanja je daleko manja odbrzine prostiranja talasa...Poremećajni pritisakLinearizovani Koši-Lagranžev integral...pxzt ( , , ) = p ρ at− gz−ρ ∂φ∂tp′∞p′ = ∑ pnBez dokaza:∂φnkz npn=− ρ =± ρgAe nsin( k nx± ω nt+ εn) =Putanje delića tečnosti na dubini h su∂tkružnice radijusakh nA e − kz n=± ρgeζ ( x, t)Delići rotiraju oko svojih ravnotežnihpoložaja po kružnim putanjama čiji seradijus eksponencijalno smanjuje sdubinom vode...I dok delići tečnosti ostaju u neposrednojblizini svojih ravnotežnih položaja,poremećaj – talas tokom vremenaprevaljuje velika rastojanja...nn=1Poremećaj pritiska je harmonijska funkcijakoja ima frekvenciju talasa.......stvara promenljivu pobudnu silu, koja istomfrekvencijom deluje na brod i izaziva njegovoprinudno oscilovanje na talasima.nPREDAVANJA 2009. 46
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