Matematičko modeliranje u fizičkoj oceanografiji

U ovom radu modeliramo termohalinu cirkulaciju u morskim bazenima, odnosno cirkulaciju do koje dolazi zbog promjene u salinitetu i temperaturi mora, to jest njegovoj gustoći. Naime, fluid ponire u područjima veće gustoće, a izvire u područjima manje, pa faktori poput dotoka slatke vode ili promjene u temperaturi utječu na njegovo gibanje. Uslijed djelovanja stalne Coriolisove sile, u bazenu dolazi i do javljanja dužobalnog strujanja koje se ovisno o smjeru kretanja dijeli u dva tipa - ciklonalnu cirkulaciju i anticiklonalnu. Cirkulacija se pojavljuje u površinskim slojevima i slabi bliže dnu. Ovisno o koeficijentima lateralnog, vertikalnog i horizontalnog trenja, na dnu se može pojaviti cirkulacija u suprotnom smjeru od površinske. U ovom radu nastojimo predvidjeti opisana kretanja morskih struja, te proučavamo njihovu ovisnost o koeficijentima trenja. Rad je podijeljen u tri veće cjeline: počevši od diferencijalnih jednadžbi koje opisuju gibanje fluida, u prvom poglavlju opisani su fizički i matematički opravdani postupci kojima model pojednostavljujemo na oblik prihvatljiv za analitičko ili numeričko rješavanje. U drugom poglavlju iz dobivenih diferencijalnih jednadžbi računa se eksplicitno rješenje za komponente gibanja u vertikalnom presjeku, kao i komponentu dužobalnog strujanja. Također se numeričkim metodama računa visina vodenog stupca i tlak na dnu bazena. U trećem poglavlju prikazana su i fizikalno opisana grafička rješenja prethodno izračunatih funkcija, te je promatran utjecaj koeficijenata trenja na pojavu suprotnog tipa cirkulacije u pridnenom sloju.In this thesis a thermohalic circulation model is being introduced, modelling the flow of water in sea basins as a result of variations of salinity and sea temperature, which in turn lead to variations in water density. The fluid sinks in the areas of increased density and rises in the areas of decreased density, causing factors such as fresh water intake, or a change in temperature to affect its flow. As a result of the continuous action of the Coriolis force, alongshore current also develops in the basin. This current belongs to one of two possible types based on its direction - cyclonic or anticyclonic. The circulation appears in the surface layers closest to the surface and weakens as the bottom is approached. Depending on lateral, vertical and horizontal friction coefficients, a current opposite the one at the surface can emerge near the bottom of the basin. In this thesis an attempt is made to predict the described sea current flow, while also studying its dependence on various friction coefficients. The thesis is split into three major parts: starting from differential equations describing the fluid movement, in the first chapter various methods which enable the simplification of the model to a form suitable for analytic or numeric solving are introduced. Furthermore, the physical interpretation, as well as the mathematical justification for these methods is also presented. In the second chapter, an explicit solution is calculated from the obtained differential equations for the current components in the vertical cross section, as well as the alongshore current component. Also, the sea level and the bottom pressure were numerically calculated. In the third chapter, the calculated results are presented through various graphs and their physical interpretation is also given. Finally, the effect of friction coefficients on the appearance of the opposite type of circulation at the basin bottom was also discussed