Verification of the Malkus hypothesis regarding the stability of turbulent flows

Gol'dshtik, M. A.; Sapozhnikov, V. A.; Shtern, V. N.

doi:10.1007/bf01017309

Cited by 1 publication

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“…This description clearly illustrates that instability mechanisms, mean velocity profiles and torques are closely connected. The connection is most explicit in marginal stability theory, initially described for thermal convection (Malkus 1954;Howard 1966), and later extended to channel flow (Malkus 1956(Malkus , 1983Reynolds & Tiederman 1967;Gol'dshtik et al 1970) and TC flow with stationary outer cylinder (King et al 1984;Marcus 1984b;Barcilon & Brindley 1984). We will here present an extension of previous TC studies to the case of independently rotating cylinders, and will focus in particular on the rotation dependence of the torque, with its characteristic non-monotonic behaviour.…”

Section: Introductionmentioning

confidence: 94%

Marginally stable and turbulent boundary layers in low-curvature Taylor–Couette flow

Brauckmann

Eckhardt

2017

J. Fluid Mech.

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Marginal stability arguments are used to describe the rotation-number dependence of torque in Taylor-Couette (TC) flow for radius ratios η 0.9 and shear Reynolds number Re S = 2 × 10 4 . With an approximate representation of the mean profile by piecewise linear functions, characterized by the boundary-layer thicknesses at the inner and outer cylinder and the angular momentum in the center, profiles and torques are extracted from the requirement that the boundary layers represent marginally stable TC subsystems and that the torque at the inner and outer cylinder coincide. This model then explains the broad shoulder in the torque as a function of rotation number near R Ω ≈ 0.2. For rotation numbers R Ω < 0.07 the TC stability conditions predict boundary layers in which shear Reynolds numbers are very large. Assuming that the TC instability is bypassed by some shear instability, a second maximum in torque appears, in very good agreement with numerical simulations. The results show that, despite the shortcomings of marginal stability theory in other cases, it can explain quantitatively the non-monotonic torque variation with rotation number for both the broad maximum as well as the narrow maximum.

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