**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.

## Table of Links

## 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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