DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

diagram. Although S stars might be an intermediate
stage of evolution between oxygen-rich
(M stars) and carbon rich (C stars) AGB stars,
it is possible that they are an end stage and will
not go through a carbon rich phase. It has been
shown that some S stars have undergone mass
transfer from a companion and have white dwarf
companions.
stability frequency See buoyancy frequency.
stability of the water column The strength
of the stratification of a water column is expressed
in terms of the intrinsic buoyancy frequency
N, that a parcel experiences. The stability
is given by
N 2 =−gρ −1 (∂ρ/∂z)
=g(α∂/∂z − β∂S/∂z
+ additional terms)
where g is gravitational acceleration, ρ density, z
vertical coordinate (positive upward), α thermal
expansivity, β saline contraction coefficient,
potential temperature and S salinity. Additional
terms may become relevant, when (1) stability
is very low (e.g., gradient of gases, such as CO2
or CH4, or silica in deep lakes), or when (2) inflowing
river water or bottom boundary water
contain high particle concentrations. N 2 varies
over 10 orders of magnitude in natural waters
from 10 −11 s −2 (in well-mixed bottom layers
or double-diffusive layers) to 1 s −2 in extreme
halocline (merging fresh and salt water).
stability ratio The non-dimensional ratio
of the stability due to the stabilizing compo-
nent divided by the destabilizing component of
the stratification: Rρ = or Rρ =
α∂T/∂z
βs∂S/∂z
−1
α∂T/∂z
βs∂S/∂z
(see double diffusion). Here T is
the temperature, S is the salinity, and z is the vertical
coordinate. The thermal and saline expansion
coefficients of sea water, α and β, respectively,
are defined such that they are always positive.
Hence, the value of Rρ indicates the type of
the stability of the water column. The density
of sea water is a function of temperature and
salinity, and their vertical gradients determine
the stability of the water column. In the oceans,
temperature generally decreases with depth and
© 2001 by CRC Press LLC
stable causality
salinity increases with depth (i.e., for z positive
upward, ∂T/∂z > 0 and ∂S/∂z < 0). A
value of Rρ in the open interval (−∞, 0) indicates
a stable stratification, while a Rρ > 1
indicates an unstable water column. Vice versa,
if ∂T/∂z < 0, then −∞ 1 indicates
stable stratification.
In a two-layer situation in which two water
masses of different salt and temperature composition
are stacked vertically, a value of Rρ
in the interval between 0 and approximately 3
indicates the possibility of a double diffusive instability.
For ∂T/∂z > 0 the double diffusion
will be in the form of salt fingers, for ∂T/∂z < 0
in the form of layering.
Rρ ∂T/∂z > 0 ∂T/∂z < 0
−∞ 1 Unstable Stable
0