If water had the "normal" thermal expansion properties ( l(T) = l(0) +aT, where "a" is the thermal expansion coefficient, typically in the range of 1/100000 to 1/1000000 and positive) of most materials though its liquid phase, colder water would be at the bottom (assuming the mantle does not emit heat, which in many part of the ocean it does). Ice would be heavier than the fluid phase (and at any pressure, the relationship would be maintained the same or even make ice denser, since water is not very compressible, it is less compressible than ice). Luckily, between 4 C and at least - 20 C a is negative (yes, under the "normal freezing point, in what is called "supercooled water", the homogeneous crystallization of water does not happen until about -40 C).
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