The Equations of Oceanic Motions
Depth contours , shoreline configurations, and interactions with other currents influence a current's direction and strength. Ocean currents are primarily horizontal water movements. More specifically, ocean currents influence the temperature of the regions through which they travel. For example, warm currents traveling along more temperate coasts increase the temperature of the area by warming the sea breezes that blow over them. Perhaps the most striking example is the Gulf Stream , which makes northwest Europe much more temperate than any other region at the same latitude.
Other example is Lima, Peru , where the climate is cooler, being sub-tropical, than the tropical latitudes in which the area is located, due to the effect of the Humboldt Current. Surface oceanic currents are sometimes wind driven and develop their typical clockwise spirals in the northern hemisphere and counter-clockwise rotation in the southern hemisphere due to imposed wind stresses. In these wind-driven currents, the Ekman spiral effect results in the currents flowing at an angle to the driving winds. In addition, the areas of surface ocean currents move somewhat with the seasons ; this is most notable in equatorial currents.
On the equations of the large-scale ocean
Deep ocean basins generally have a non-symmetric surface current, in that the eastern equatorward-flowing branch is broad and diffuse whereas the western poleward flowing branch is very narrow. These western boundary currents of which the Gulf Stream is an example are a consequence of the rotation of the Earth. Deep ocean currents are driven by density and temperature gradients. Thermohaline circulation is also known as the ocean's conveyor belt which refers to deep ocean density-driven ocean basin currents.
These currents, called submarine rivers, flow under the surface of the ocean and are hidden from immediate detection. Where significant vertical movement of ocean currents is observed, this is known as upwelling and downwelling. Deep ocean currents are currently being researched using a fleet of underwater robots called Argo. Because the movement of deep water in ocean basins is caused by density-driven forces and gravity, deep waters sink into deep ocean basins at high latitudes where the temperatures are cold enough to cause the density to increase.
Surface currents are found on the surface of an ocean, and are driven by large scale wind currents. They are directly affected by the wind—the Coriolis effect plays a role in their behaviours. The thermohaline circulation is a part of the large-scale ocean circulation that is driven by global density gradients created by surface heat and freshwater fluxes.
Wind -driven surface currents such as the Gulf Stream travel polewards from the equatorial Atlantic Ocean , cooling en route, and eventually sinking at high latitudes forming North Atlantic Deep Water. This dense water then flows into the ocean basins.
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While the bulk of it upwells in the Southern Ocean , the oldest waters with a transit time of around years  upwell in the North Pacific. On their journey, the water masses transport both energy in the form of heat and matter solids, dissolved substances and gases around the globe.
The Equations of Oceanic Motions - Peter Müller - Google книги
In these aims, it succeeds admirably and very usefully. The book will surely become a standard reference for the ocean dynamicist who wants to get the equations and usual approximations right. For me, the book is already worth the price just for its thorough treatment of the Boussinesq approximation.
A satisfactory explanation of the tides, however, awaited the theory of gravity, supplied by Newton. The gravitational forces exerted by the Moon at several points on Earth are illustrated in Figure 1. These forces differ slightly from one another because Earth is not a point, but has a certain size: all parts are not equally distant from the Moon, nor are they all in exactly the same direction from the Moon.
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Moreover, Earth is not perfectly rigid. The side of Earth nearest the Moon is attracted toward the Moon more strongly than is the center of Earth, which in turn is attracted more strongly than is the side opposite the Moon. Thus, the differential forces tend to stretch Earth slightly into a prolate spheroid a football shape , with its long diameter pointed toward the Moon.
Figure 1: Pull of the Moon. Note that the differences have been exaggerated for educational purposes.
Calculations show that in this case, Earth would distort from a sphere by amounts ranging up to nearly 1 meter. The tide-raising forces, acting over a number of hours, produce motions of the water that result in measurable tidal bulges in the oceans. Water on the side of Earth facing the Moon flows toward it, with the greatest depths roughly at the point below the Moon.
Differential and Integral Equations
On the side of Earth opposite the Moon, water also flows to produce a tidal bulge Figure 2. Differences in gravity cause tidal forces that push water in the direction of tidal bulges on Earth. Figure 3: High and Low Tides. This is a side-by-side comparison of the Bay of Fundy in Canada at high and low tides. In the idealized and, as we shall see, oversimplified model just described, the height of the tides would be only a few feet. The rotation of Earth would carry an observer at any given place alternately into regions of deeper and shallower water.