|
Level-0
|
\(\overline {\mathbf {V}^{*} p^{*}} - \nabla ^{*} \times [(\overline {p^{*} \varphi ^{*}})/2+ (\overline {u^{*}_{t^{*}t^{*}}\varphi ^{*}})/\beta ^{*}]\mathbf {z}\)
|
(15a), (17b), (23a)
|
Solid black
|
–
|
|
Level-1
|
\(\overline {\mathbf {V}^{*} p^{*}} - \nabla ^{*} \times [(\overline {p^{*} \varphi ^{\mathrm {app*}}})/2+ (\overline {u^{*}_{t^{*}t^{*}}\varphi ^{\mathrm {app*}}})/\beta ^{*}]\mathbf {z}\)
|
(18b), (26b)
|
Dashed orange
|
–
|
|
Level-2
|
\(\overline {\mathbf {V}^{*} p^{*}} - \nabla ^{*} \times (\overline {p^{*} \varphi ^{\mathrm {app*}}})/2\mathbf {z}\)
|
(18c), (26c)
|
Solid blue
|
(c)
|
|
QG
|
\(\overline {\mathbf {V}^{*} p^{*}} -\nabla ^{*} \times [\overline {{p^{*}}^{2}}/(2f^{*})]\mathbf {z}\)
|
(5), (6)
|
–
|
(b)
|
|
f-Plane
|
\(\overline {\mathbf {V}^{*} p^{*}}\)
|
(3), (4)
|
Dashed green
|
(a)
|
| |
Definition of EPV-based streamfunctions
| | | |
| |
\(\nabla ^{*2} \varphi ^{*} - (f^{*}/c^{*})^{2} \varphi ^{*} - (3/c^{*2})\varphi ^{*}_{t^{*} t^{*}} = q^{*}\),
|
(15b), (16), (17a), (23c)
| | |
| | ∇∗2
φ
app∗−(f
∗/c
∗)2
φ
app∗=q
∗,
|
(18a), (26a)
| | |
