The question does not ask about how far can the eye see on a curving surface. The asker stated 'a flat surface' Since when in mathematics do we mix up a flat surface with a curved surface. You have turned a very simple question in to a complicated question by introducing a curved plane.
As one would expect, the further you travel from the Equator, the colder the ocean waters generally become. Near the Equator, surface water temperatures can be as high as 80Â° Fahrenheit (27Â° Celsius). Near the poles, the temperature drops to a chilly 28Â° Fahrenheit (-2Â° Celsius). The western side of oceans are usually warmer than the eastern side. This is due to the way in which both the atmospheric and oceanic currents move water from the equator towards the poles on the western side of oceans, and from the poles towards the equator on the eastern side of oceans.
1 Below the Sea Surface: Waters warmer than 10Â°C dominate the sea surface but do not extend much below 500 m within the ocean; tropical and subtropical surface water provide is just a veneer of warmth over a cold ocean; typical deep ocean temperature vary from 1Â° to 3Â°C. Pacific deep water is derived from the lower salinity water column of the southern ocean. 2  Towards the sea floor, temperatures are near 0Â°C marking the presence of Antarctic Bottom Water (AABW) derived from the very cold (-1.9Â°C; 34.65), dense water along the shores of Antarctica.