127 research outputs found
A Consistent One-Dimensional Model for the Turbulent Tachocline
The first consistent model for the turbulent tachocline is presented, with
the turbulent diffusivity computed within the model instead of being specified
arbitrarily. For the origin of the 3D turbulence a new mechanism is proposed.
Owing to the strongly stable stratification, the mean radial shear is stable,
while the horizontal shear is expected to drive predominantly horizontal,
quasi-2D motions in thin slabs. Here I suggest that a major source of 3D
overturning turbulent motions in the tachocline is the secondary shear
instability due to the strong, random vertical shear arising between the
uncorrelated horizontal flows in neighbouring slabs. A formula for the vertical
diffusivity due to this turbulence, equation (9), is derived and applied in a
simplified 1D model of the tachocline. It is found that Maxwell stresses due to
an oscillatory poloidal magnetic field of a few hundred gauss are able to
confine the tachocline to a thickness below 5 Mm. The integral scale of the 3D
overturning turbulence is the buoyancy scale, on the order of 10 km and its
velocity amplitude is a few m/s, yielding a vertical turbulent diffusivity on
the order of 10^8 cm^2/s.Comment: 16 pages, 2 figure
Oscillator Models of the Solar Cycle and the Waldmeier Effect
We study the behaviour of the van der Pol oscillator when either its damping
parameter or its nonlinearity parameter is subject to additive or
multiplicative random noise. Assuming various power law exponents for the
relation between the oscillating variable and the sunspot number, for each case
we map the parameter plane defined by the amplitude and the correlation time of
the perturbation and mark the parameter regime where the sunspot number
displays solar-like behaviour. Solar-like behaviour is defined here as a good
correlation between the rise rate and cycle amplitude {\it and} the lack of a
good correlation between the decay rate and amplitude, together with
significant (\ga 10\,%) r.m.s. variation in cycle lengths and cycle
amplitudes. It is found that perturbing alone the perturbed van der Pol
oscillator does not show solar-like behaviour. When the perturbed variable is
, solar-like behaviour is displayed for perturbations with a correlation
time of about 3--4 years and significant amplitude. Such studies may provide
useful constraints on solar dynamo models and their parameters.Comment: 4 pages, 2 figure
An analytic interface dynamo over a shear layer of finite depth
Parker's analytic Cartesian interface dynamo is generalized to the case of a
shear layer of finite thickness and low resistivity ("tachocline"), bounded by
a perfect conductor ("radiative zone") on the one side, and by a highly
diffusive medium ("convective zone") supporting an -effect on the other
side. In the limit of high diffusivity contrast between the shear layer and the
diffusive medium, thought to be relevant for the Sun, a pair of exact
dispersion relations for the growth rate and frequency of dynamo modes is
analytically derived. Graphic solution of the dispersion relations displays a
somewhat unexpected, non-monotonic behaviour, the mathematical origin of which
is elucidated. The dependence of the results on the parameter values (dynamo
number and shear layer thickness) is investigated. The implications of this
result for the solar dynamo problem are discussed.Comment: 11 pages, 4 figures Geophys. Astrophys. Fluid Dyn., in pres
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