ToO9OOJ1Ww

A shimmering metallic finish highlights the textured basket-weave of a breezy peep-toe sandal elevated by a chunky stacked heel. Style Name: Very Volatile Starla Woven Sandal (Women). Style Number: 5634771. Available in stores.

National Accessibility Customer Service
Skip to Main Content

Use arrow keys to access sub-menus and sub-menu links, this may require a mode change

S/R
CD_CODE_SCHEME
,
Roberto Del Carlo Circular Heel Boots Calf Leather Leather Black kh7s1M

,
Vince Camuto Plus Floral Long Sleeve Button Dress Aqua Glow SWL0z4AU

G
C
o
r
u
,
G
C
o
r
v
: ( local to
MOM_FLUXFORM.F
)

The most commonly used coordinate system on the sphere is the geographic system ( λ , φ ) . The curvilinear nature of these coordinates on the sphere lead to some “metric” terms in the component momentum equations. Under the thin-atmosphere and hydrostatic approximations these terms are discretized:

(2.101)
¶
A
w
Δ
r
f
h
w
G
m
e
t
r
i
c
u
=
¯
¯
u
i
a
tan
φ
A
c
Δ
r
f
h
c
¯
v
j
i

(2.102)
Alberta Ferretti Handbags Purple Nbju5hq

A s Δ r f h s G m e t r i c v = − ¯ ¯ u i a tan φ A c Δ r f h c ¯ u i j

A s Δ r f h s G m e t r i c v = − ¯ ¯ u i a tan φ A c Δ r f h c ¯ u i j

(2.103)
¶
G
m
e
t
r
i
c
w
=
0

where a is the radius of the planet (sphericity is assumed) or the radial distance of the particle (i.e. a function of height). It is easy to see that this discretization satisfies all the properties of the discrete Coriolis terms since the metric factor u a tan φ can be viewed as a modification of the vertical Coriolis parameter: f → f + u a tan φ .

δ
i
:
δ
i
Φ
=
Φ
i
+
1
/
2
−
Φ
i
−
1
/
2

−
i
:
¯
Φ
i
=
(
Φ
i
+
1
/
2
+
Φ
i
−
1
/
2
)
/
2

δ
x
:
δ
x
Φ
=
1
Δ
x
δ
i
Φ

¯
∇
= horizontal gradient operator :
¯
∇
Φ
=
{
δ
x
Φ
,
δ
y
Φ
}

¯
∇
⋅
= horizontal divergence operator :
¯
∇
⋅
→
f
=
1
A
{
δ
i
Δ
y
f
x
+
δ
j
Δ
x
f
y
}

¯
∇
2
= horizontal Laplacian operator :
¯
∇
2
Φ
=
¯
∇
⋅
¯
∇
Φ

The equations of motion integrated by the model involve four prognostic equations for flow, u and v , temperature, θ , and salt/moisture, S , and three diagnostic equations for vertical flow, w , density/buoyancy, ρ / b , and pressure/geo-potential, ϕ h y d . In addition, the surface pressure or height may by described by either a prognostic or diagnostic equation and if non-hydrostatics terms are included then a diagnostic equation for non-hydrostatic pressure is also solved. The combination of prognostic and diagnostic equations requires a model algorithm that can march forward prognostic variables while satisfying constraints imposed by diagnostic equations.

Since the model comes in several flavors and formulation, it would be confusing to present the model algorithm exactly as written into code along with all the switches and optional terms. Instead, we present the algorithm for each of the basic formulations which are:

In all the above configurations it is also possible to substitute the Adams-Bashforth with an alternative time-stepping scheme for terms evaluated explicitly in time. Since the over-arching algorithm is independent of the particular time-stepping scheme chosen we will describe first the over-arching algorithm, known as the pressure method, with a rigid-lid model in
Section 2.3
. This algorithm is essentially unchanged, apart for some coefficients, when the rigid lid assumption is replaced with a linearized implicit free-surface, described in
Tods Leather Penny Loafers DkBrown f0OGb8Oc

. These two flavors of the pressure-method encompass all formulations of the model as it exists today. The integration of explicit in time terms is out-lined in
Section 2.5
and put into the context of the overall algorithm in
Veja V 12 B Mesh Sneakers White gR3clnM

and
Diane von Furstenberg Short Dresses Dark Blue kB3SgD

. Inclusion of non-hydrostatic terms requires applying the pressure method in three dimensions instead of two and this algorithm modification is described in
SelfPortrait Azaelea Guipure Lace Midi Dress Sky Blue Usd kyIDahns

. Finally, the free-surface equation may be treated more exactly, including non-linear terms, and this is described in
Section 2.10.2
.

The horizontal momentum and continuity equations for the ocean (
(1.98)
and
La Canadienne Jojo Black Suede Womens Boots AmlNBJ2TJ

), or for the atmosphere (
(1.45)
and
(1.47)
), can be summarized by:

Connect with Us