TY - JOUR

T1 - Local instability of a rotating flow driven by precession of arbitrary frequency

AU - Naing, Me Me

AU - Fukumoto, Y.

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/10

Y1 - 2011/10

N2 - We revisit the local stability, to three-dimensional disturbances, of rotating flows with circular streamlines, whose rotation axis executes constant precessional motion about an axis perpendicular to itself. In the rotating frame, the basic flow is steady velocity field linear in coordinates in an unbounded domain constructed by Kerswell (1993 Geophys. Astrophys. Fluid Dyn. 72 107-44), and admits the use of the Wentzel-Kramers-Brillouin (WKB) method. For a small precession frequency, we recover Kerswell's result. A novel instability is found at a large frequency for which the axial wavenumber executes an oscillation around zero; significant growth of the disturbance amplitude occurs in a very short time interval only around the time when the axial wavenumber vanishes. In the limit of infinite precession frequency, the growth rate exhibits singular behavior with respect to a parameter characterizing the tilting angle of the wave vector.

AB - We revisit the local stability, to three-dimensional disturbances, of rotating flows with circular streamlines, whose rotation axis executes constant precessional motion about an axis perpendicular to itself. In the rotating frame, the basic flow is steady velocity field linear in coordinates in an unbounded domain constructed by Kerswell (1993 Geophys. Astrophys. Fluid Dyn. 72 107-44), and admits the use of the Wentzel-Kramers-Brillouin (WKB) method. For a small precession frequency, we recover Kerswell's result. A novel instability is found at a large frequency for which the axial wavenumber executes an oscillation around zero; significant growth of the disturbance amplitude occurs in a very short time interval only around the time when the axial wavenumber vanishes. In the limit of infinite precession frequency, the growth rate exhibits singular behavior with respect to a parameter characterizing the tilting angle of the wave vector.

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U2 - 10.1088/0169-5983/43/5/055502

DO - 10.1088/0169-5983/43/5/055502

M3 - Article

AN - SCOPUS:80054103733

VL - 43

JO - Fluid Dynamics Research

JF - Fluid Dynamics Research

SN - 0169-5983

IS - 5

M1 - 055502

ER -