Why is water surface smooth?

Liquids have more disorder than solids. Their atoms are much more jiggly than solids, at the same temperature. How then a puddle of water undisturbed by winds etc is able to have a smooth surface?

A molecule/atom of the liquid minimises its energy by being surrounded by other molecules/atoms of the liquid. At the surface this isn't possible so the surface has an excess energy, and this interfacial energy produces a force called surface tension that tries to reduce the area of the surface. There is a fuller discussion of this in my answer to Why is Sticking to Glass a Lower Energy State for Water?.

The tendancy to reduce the surface are is why liquid droplets are round, because spherical shape minimises the surface area for any given volume. It also means the surface will be smooth because any roughness increases the surface area and therefore increases the energy.

The surface will not be precisely smooth because we expect that thermal vibrations will produce deformations of the surface with energies of the order of $kT$ per surface molecule. At a macroscopic scale these deformations are too small to see, but at the atomic scale the surface will be fuzzy rather than sharply defined.

• To expand on what John said, the fluid viscosity works in conjunction with the surface tension to dissipate any wave energy, and dampen any oscillations on the macroscale. – Chet Miller Sep 26 '16 at 12:21
• "A molecule/atom of the liquid minimises its energy by being surrounded by other molecules/atoms of the liquid" --How is the energy minimised because of being surrounded? – Sidarth Sep 26 '16 at 15:29

Even at the microscopic level you would not see any motion at the surface, though if the water is unevenly heated there would be currents.