  Transverse vibrations can induce the non-linear compression of a thin film of
air to levitate objects, via the squeeze film effect. This phenomenon is well
captured by the Reynolds' lubrication theory, however, the same theory fails to
describe this levitation when the fluid is incompressible. In this case, the
computation predicts no steady-state levitation, contradicting the documented
experimental evidence. In this letter, we uncover the main source of the
time-averaged pressure asymmetry in the incompressible fluid thin film, leading
the levitation phenomenon to exist. Furthermore, we reveal the physical law
governing the steady-state levitation height, which we confirm experimentally.
