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

From: Towards a seamlessly diagnosable expression for the energy flux associated with both equatorial and mid-latitude waves

Approx. Energy flux vector Equation Figs. 2 & 3 Figs. 6 & 7
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)