On the stages of vortex decay in an impulsively stopped, rotating cylinder

Turbulence generation and decay in the Taylor–Couette system due to an abrupt stoppage

“…Our results are in very good agreement with the results of Kaiser et al (2020) and Euteneuer & Karlsruhe (1972) whose unstable zone grows as the square root of time. Following the idea that the vortices appear in the unstable zone as interpenetrating spirals do in the unstable zone between the inner cylinder and the nodal surface (the cylindrical surface where u θ = 0) in counter-rotating TC flow, we can consider that δ t z approximately corresponds to the size of the unstable zone of the flow.…”

“…The present study shares some similarities with the works on impulsive spin-down in a cylinder (Euteneuer & Karlsruhe 1972;Neitzel & Davis 1981;Neitzel 1982;Mathis & Neitzel 1985;Savas 1992;Kim & Choi 2004Kim, Song & Choi 2008;Kaiser et al 2020) or Couette flow decay in the TC system (Tillmann 1967;Neitzel 1982;Kohuth & Neitzel 1988). While the geometry of the first case differs, it can be seen as a particular case of the TC system (with the radius ratio, η = 0) and Kohuth & Neitzel (1988) have shown that the inner cylinder of the TC system has no influence on the onset of the instability at large Reynolds number.…”

“…This combination of averaging processes appeared to be sufficient to obtain converged data. The convergence was mainly achieved by the spatial averaging, as also observed by Kaiser et al (2020) in their numerical work. We did not perform an ensemble average of multiple repetitions for the same Re o = ω o r o d/ν, the outer Reynolds number based on the outer cylinder velocity, but we checked that two independent repetitions had the same behaviour, as shown in figure 4(a).…”

“…Thus, what happens at the very beginning when the cylinder is stopped can be compared to what happens in the TC system when the outer cylinder is stopped. The whole process of the generation and decay of turbulence has been described in the direct numerical simulations by Kaiser et al (2020). They considered an infinitely long cylinder in solid-body rotation (SBR) and impulsively stopped for a wide range of Reynolds numbers.…”

Смещения Предела Устойчивости Течения При Модуляции Скорости Вращения

“…В то же время результаты исследований устойчивости течений под влиянием периодических во времени граничных условий приводят к различным выводам. Так, течение Тэйлора−Куэтта в цилиндрическом зазоре становится неустойчивым при меньших, чем при стационарном вращении, числах Рейнольдса как при модуляции скорости вращения [7], так и при ее ступенчатом изменении [8,9]. Наоборот, в плоском течении Куэтта в случае осцилляций стенок в направлении поперек течения обнаружены его стабилизация и затягивание перехода к турбулентности [10].…”