Mathematical description
67
Summary
Processes with the smallest time scales are expected to be most dominant in steady balances. Ratio’s of time scales lead to dimensional
parameters and indicate whether balances in a flow can occur between
different processes. A process with a small time scale is expected to
lead to a large contribution to the vorticity balance in a flow.
For flows with a characteristic horizontal length scale L and a vertical
length scale D, near a certain latitude θ 0 (with f 0 =2 Ω s i n θ 0 )i n
water with a vertical density gradient set by the buoyancy frequency
N , important scales are the inertial time scale τ f , the inverse buoyancy
frequency τ s and the internal and external radii of deformation (L D
and R D , respectively), defined by
τ f =
1
f 0
; τ s =
1
N
; L D =
ND
f 0
; R D =
√ gD
f 0
In a stratified, rotating flow with a characteristic horizontal velocity U
the most important dimensionless parameters are the Rossby number
ǫ, the Burger number S and the rotational Froude number F defined
by
ǫ =
U
f 0 L
; S =
N 2 D 2
f 2
0 L 2 ; F =
f 2
0 L 2
gD