Table 3 List of energy flux vectors and EPV-based streamfunctions in dimensional form and their location in the text and figures

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)