A study of the spatial amplification of the $K{\acute{a}}rm{\acute{a}}n$ boundary-layer

$K{\acute{a}}rm{\acute{a}}n$ 경계층 유동의 공간증폭에 관한 이론적 연구

The hydrodynamic instability of the three-dimensional boundary layer on a rotating disk introduces a periodic modulation of the mean flow in the form of stationary cross flow vortices. Detailed numerical values of the growth rates, neutral curves and other characteristics of the two instabilities have been calculated over a wide range of parameters. Presented are the neutral stability results concerning the two instability modes by solving new linear stability equations reformulated not only by considering whole convective terms but by correcting some errors in the previous stability equations. The present stability results are agree with the previously known ones within reasonable limit. The flow is found to be always stable for a disturbance whose dimensionless wave number at Re=1200 is greater than 0.75. Also, the spatial amplification contours have been calculated for the moving disturbance wave, whose azimuth angle is between ${\varepsilon}=15^{\circ}$ and $12.5^{\circ}$.