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Sub-critical transition to turbulence. The explosive or subcritical
onset of turbulence is an important unsolved problem in fluid dynamics.
By subcritical, we mean that a flow passes abruptly from a laminar or spatially
ordered state to turbulence when the Reynolds number is increased past
a critical value. Turbulent bursts take the form of isolated spots
or patches of turbulence that are randomly created in time and space.
In open flows, such as channel and pipe flows and boundary layer flows
over flat plates, the turbulent bursts decay or advect out of the experimental
apparatus. In closed systems, such as Rayleigh-Benard convection
or the flow between rotating cylinders (Taylor-Couette
flow), the turbulent bursts are characterised by a decay time that
becomes longer as a critical Reynolds number is approached, reminiscent
of phase transition behaviour. Furthermore, for certain parameter
values the bursting takes the form of a repetitive laminar-turbulent burst
cycle.
Turbulent bursts (of energy and mass) also occur in plasma confinement
systems, such as the earth's magnetosphere, the solar corona,
accretion disks and, in the laboratory, tokamaks.