Geoscience Reference
In-Depth Information
Chapter 7
A Numerical Model for the Ice/Ocean Boundary
Layer
Abstract: A numerical model approach for simulating the IOBL is presented in this
chapter. The staggered grid and implicit solution algorithms are patterned closely
on techniques I learned while collaborating with George Mellor when we were both
occupying visiting research chairs at the Naval Postgraduate School in Monterey,
California. They were first used to model the IOBL with the Mellor-Yamada “level
2
1
/
2
” second-moment closure (Mellor and Yamada 1982; Mellor et al. 1986) and
later adapted to the first-order closure based on similarity scaling (McPhee et al.
1987). The latter is accomplished by expressing eddy viscosity and eddy diffusivity
as the product of a local scale velocity and mixing length. It is essentially an im-
plementation of the scaling principles described in Chapter 5, and will hereafter be
referred to as
local turbulence closure
(LTC). LTC differs from the Mellor-Yamada
and so-called
k
(e.g., Burchard and Baumert 1995) models in that the length
scales are based on a combination of measurements and similarity theory, rather
than derived from separate TKE and master length scale conservation equations. A
practical impact is that the LTC model eliminates the need to carry these equations
in the solution.
We start with a review of a fairly standard leap-frog-in-time, implicit solution
technique on a staggered vertical grid, and explore various approaches to specify-
ing boundary conditions. We then discuss the algorithms for calculating the mixing
length and eddy viscosity under varying conditions of buoyancy flux in the IOBL,
and match the fluid model to an algorithm implementing the interface conditions
described in Chapter 6. The model is exercised for several examples in Chapter 8.
−
ε
7.1 Difference Equations
The partial differential equation for a conserved quantity in a horizontally homoge-
neous fluid is
F
z
Q
θ
θ
t
=
−
+
(7.1)
