Some results of the hydrodynamic theory of finite-amplitude waves

Standing waves can be interpreted as free waves between two vertical walls; for a standing wave in an unlimited container there is no transport of liquid mass in the horizontal direction. Standing waves of finite amplitude also possess the following properties not possessed by the waves of the linear theory: (1) there are no motionless points, (2) the points of maximum amplitude (crests and troughs) are fixed, and coincide with the antinodes of the original linear wave, (3) the ordinates of the wave crests are greater in absolute magnitude than the ordinates of the troughs; the wave is similar to a trochoid curve; (4) the wave profile never becomes straight; and (5) the frequency of the oscillations depends not only on the wave length but also on the amplitude.