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Authors:
(1) Scott Conn, California Institute of Technology, Pasadena, California;
(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;
(3) Jorn Callies, California Institute of Technology, Pasadena, California.
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APPENDIX A
YBJ kinetic energy Budget
The YBJ kinetic energy budget may be formed by multiplying (2) by −𝑀∗ /2 and adding the complex conjugate. Using integration by parts, the resulting kinetic energy budget can be written as
where
We are free to choose C as a boundary condition on the new field 𝐴, i.e., we can choose 𝐴 at 𝑧 = −𝐻 as the solution of (A4) for some specified C. A sensible choice for the transformation is thus setting C = 0 and
Under this transformation, the kinetic energy budget becomes (4), with the horizontal and vertical fluxes given by
The divergence of the flux terms vanishes when the budget is integrated over the entire domain, and the only terms that can alter the domain-integrated kinetic energy are the wind work and dissipation:
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This paper is available on arxiv under CC 4.0 license.
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