Fluid dynamics equations typically are of the
form
| ut |
= |
aux |
+ |
buy |
+ |
cuz |
+ |
euxx |
+ |
fuyy |
+ |
guzz |
|
|
|<--
|
Transport
terms
(Primary) |
-->|
|
|
|<---
|
Diffusion
terms
(Secondary) |
--->|
|
Transport
terms: |
In quasi-steady flows,
these tend to cancel. This
happens both in reality and in the model. However, the balance of vertical
and horizontal terms will differ between model and reality due to truncation
errors. So will the circulation. |
Diffusion
terms: |
The main error source here is
numerically induced diapycnal
mixing. It can be suppressed by aligning the axes of the mixing tensor
with (locally referenced) isopycnals. Rotating the tensor axes, unfortunately,
does not reduce transport errors. |
By suppressing the term cuz
and evaluating (aux + buy )
along isopycnals,
isopycnic coordinate models ...
-
avoid inconsistencies between vertical and horizontal transport
terms that cause (among other things) false diapycnal mixing;
-
hide truncation errors associated with horizontal transport
behind the "smoke screen" of isopycnal mixing.
|