Frequency prediction from exact or self-consistent mean flows

A number of approximations have been proposed to estimate basic hydrodynamic quantities, in particular the frequency a limit cycle. One these, RZIF (for Real Zero Imaginary Frequency), calls for linearizing governing equations about mean flow and estimating as imaginary part leading eigenvalue. further reduction, SCM Self-Consistent Model), approximates well, resulting only from nonlinear interaction eigenmode with itself. Both proven dramatically successful archetypal case wake circular cylinder. Here, is applied thermosolutal convection, which supercritical Hopf bifurcation gives rise branches standing waves traveling waves. The solved by means full Newton method coupling approximate eigenmode. Although property verified waves, reproduces very near onset another isolated parameter value. Thus, arising mode insufficient reproduce field frequency.