TY - JOUR
T1 - Exploding solutions for three-dimensional rimming flows
AU - Benilov, Eugene S.
AU - Lacey, S. M.
AU - O'Brien, S. B.G.
PY - 2005/11
Y1 - 2005/11
N2 - We examine the linear stability of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. Unlike previous models, both axial and azimuthal components of the hydrostatic pressure gradient are taken into account, which yields solutions which collapse in both dimensions. Two types of such solutions are found: disturbances with zero and non-zero net mass (the former have greater explosion rates, that is, their amplitudes grow faster than those of the latter). It is also shown that, despite the existence of exploding disturbances, all solutions with harmonic dependence on time (eigenmodes) are neutrally stable.
AB - We examine the linear stability of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. Unlike previous models, both axial and azimuthal components of the hydrostatic pressure gradient are taken into account, which yields solutions which collapse in both dimensions. Two types of such solutions are found: disturbances with zero and non-zero net mass (the former have greater explosion rates, that is, their amplitudes grow faster than those of the latter). It is also shown that, despite the existence of exploding disturbances, all solutions with harmonic dependence on time (eigenmodes) are neutrally stable.
UR - http://www.scopus.com/inward/record.url?scp=29544433405&partnerID=8YFLogxK
U2 - 10.1093/qjmam/hbi020
DO - 10.1093/qjmam/hbi020
M3 - Article
AN - SCOPUS:29544433405
SN - 0033-5614
VL - 58
SP - 563
EP - 576
JO - Quarterly Journal of Mechanics and Applied Mathematics
JF - Quarterly Journal of Mechanics and Applied Mathematics
IS - 4
ER -