Non-linear wave-number interaction in near-critical two-dimensional flows

摘要: This paper deals with a system of equations which includes as special cases the governing such hydrodynamic stability problems Taylor problem, Benard and plane parallel flow. A non-linear analysis is made disturbances to basic The flow depends on single co-ordinate η. that are considered represented superposition many functions each periodic in ξ normal η independent third direction. considers disturbance energy initially concentrated denumerable set ‘most dangerous’ modes whose wave-numbers close critical wave-number selected by linear theory. It major result this concentration persists time passes. Because problem can be reduced study partial differential equation for Fourier transform modal amplitudes. striking feature present work wide class reduces fundamental does not essentially depend specific forms ofthe operators original equations. Certain general conclusions drawn from equation, example some there exist multi-modal steady solutions combination number different spatial periods. (Whether any stable remains an open question.) also shown other circumstances (at least interval time) travelling waves kinematic behaviour clarified concept group speed.