2007
DOI: 10.1090/s0033-569x-07-01050-x
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Non-linear and non-stationary modes of the lower branch of the incompressible boundary layer flow due to a rotating disk

Abstract: Abstract. In this paper a theoretical study is undertaken to investigate the structure of the lower branch neutral stability modes of three-dimensional small disturbances imposed on the incompressible Von Karman's boundary layer flow due to a rotating disk. Particular attention is given to the short-wavelength non-linear non-stationary crossflow vortex modes at sufficiently high Reynolds numbers with reasonably small scaled frequencies. [497][498][499][500][501][502][503][504][505][506][507][508][509][510][51… Show more

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Cited by 11 publications
(33 citation statements)
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“…Hence, decreasing ψ is found to destabilize the flow. Similar comparisons for the rotating disk have been given recently for stationary and non-stationary neutral solutions by Turkyilmazoglu (2006Turkyilmazoglu ( , 2007. Figure 12 shows a comparison between the predicted onset of the two instability modes found in the numerical investigation for stationary vortices and the observed onset of spiral vortices as measured in three experimental investigations: Kreith et al (1962), Kappesser et al (1973) and Kobayashi & Izumi (1983).…”
Section: Comparison Between the Asymptotic And Numerical Investigationssupporting
confidence: 75%
“…Hence, decreasing ψ is found to destabilize the flow. Similar comparisons for the rotating disk have been given recently for stationary and non-stationary neutral solutions by Turkyilmazoglu (2006Turkyilmazoglu ( , 2007. Figure 12 shows a comparison between the predicted onset of the two instability modes found in the numerical investigation for stationary vortices and the observed onset of spiral vortices as measured in three experimental investigations: Kreith et al (1962), Kappesser et al (1973) and Kobayashi & Izumi (1983).…”
Section: Comparison Between the Asymptotic And Numerical Investigationssupporting
confidence: 75%
“…In spite of the fact that Figure 2 (a-d) represents specific cases of a suction and injection (and restricted Mach numbers), the general trend for values ofs > 0 ands < 0 is similar to those in Figure 2 (a-d). The trends calculated for zero-suction incompressible modes in [40] are preserved here for large blowing, while an opposite behavior is seen for the large suctioning, in particular for an isothermal wall as the Mach number increases. An immediate conclusion to be drawn from Figure 2 (a-d) is that the non-linear effects are destabilizing for a linearly unstable disturbance for all of the Mach numbers within which the neutral stationary or non-stationary waves exist, since B is positive for both suction and injection.…”
Section: Linear Resultsmentioning
confidence: 68%
“…Regardless of whether the adiabatic or isothermal wall conditions are considered, there exists a region of positive frequencies (and also negative frequencies for the modes under strong wall cooling with suction) that are always unstable. Moreover, much less initial amplitude disturbance is sufficient than for that of the stationary modes determined in [2] and [1], if the perturbations have positive frequencies, an outcome that is also in line with that of [40]. In addition to this, the appearance of double modes for the lower branch curves having positive frequencies as encountered in the numerical stability solution of non-stationary incompressible flow in [24] is clarified here, whose interval of occurrence is particularly increased in the case of suction but reduced in the presence of wall cooling together with injection.…”
Section: Suction/blowing Influences On the Finite Amplitude Disturbanmentioning
confidence: 59%
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