The stationary spatially periodic flows in Rayleigh-Taylor instability: solutions multitude and its dimension

For the first time the classical hydrodynamics problem of stationary solutions in Rayleigh-Taylor instability (RTI) has been studied for three-dimensional space periodical flow. The existence of RTI stationary solutions multitude is shown for the general case of flow symmetry. The multitude dimension in functional space is studied ab initio by analysing an initial perturbation symmetry in the instability linear stage. The relation between flow symmetry and solutions multitude is established. The description of the stationary solutions for flows with five symmorphic plane groups symmetry are given. The RTI stationary flow free boundaries problem is derived in the first and second orders of approximations. Velocity and Fourier-amplitudes dependencies as parameters functions are obtained. The symmetry violations are examined, the limiting transitions to well known cases of plane and "high" symmetry flows and their accuracy are outlined. The physical reasons of the obtained incorrectness for the free surface problem in Rayleigh-Taylor instability are discussed.