TY - JOUR
T1 - Global linear stability of the boundary-layer flow over a rotating sphere
AU - Barrow, A.
AU - Garrett, Stephen
AU - Peake, N.
PY - 2015
Y1 - 2015
N2 - We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°–65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk.
AB - We consider the linear global stability of the boundary-layer flow over a rotating sphere. Our results suggest that a self-excited linear global mode can exist when the sphere rotates sufficiently fast, with properties fixed by the flow at latitudes between approximately 55°–65° from the pole (depending on the rotation rate). A neutral curve for global linear instabilities is presented with critical Reynolds number consistent with existing experimentally measured values for the appearance of turbulence. The existence of an unstable linear global mode is in contrast to the literature on the rotating disk, where it is expected that nonlinearity is required to prompt the transition to turbulence. Despite both being susceptible to local absolute instabilities, we conclude that the transition mechanism for the rotating-sphere flow may be different to that for the rotating disk.
UR - https://www.sciencedirect.com/science/article/pii/S0997754614000338?via%3Dihub
U2 - 10.1016/j.euromechflu.2014.02.012
DO - 10.1016/j.euromechflu.2014.02.012
M3 - Article
VL - 49
SP - 301
EP - 307
JO - European Journal of Mechanics - B/Fluids
JF - European Journal of Mechanics - B/Fluids
IS - Part B
ER -