Stability Analysis of the Karman Boundary-Layer Flow

The Karman boundary-layer has been numerically investigated for the disturbance wave number, wave velocity, azimuth angle and radius (Reynolds number, Re). The disturbed flow over rotating disk can lead to transition at a much lower Re than that of the well-known Type I instability. This early transition is due to the excitation of the Type II. Presented are the neutral stability results concerning these instabilities by solving newly formulated stability equations with consideration of whole convective terms. When the present numerical results are compared with the previously known results, the value of critical Re corresponding to Type I is moved from ${Re}_{c.1}$=285.3 to 270.2 and the value corresponding to Type II from ${Re}_{c.2}$=69.4 to 36.9, respectively. Also, the corresponding wave number is moved fro)m $k_1$=0.378 to 0.386 for Type I; from $k_2$=0.279 to 0.385 for Type II. For Type II, the upped limit of wave number and azimuth angle is $k_u$=0.5872, $\varepsilon_u$=$-17.5^{\circ}$, while its lower limit is near $k_u$=0, $\varepsilon_u$=$-28.4^{\circ}$. This implies that the disturbances will be relatively fast amplified at small Re and within narrow bands of wave number compared with the previous results.