$dFxydx=x$ derivative of ${}_{}$Fxy

fbar $=$ mean cyclic wave frequency

$F_x=x$ component of the wave energy flux

$F_y=y$ component of the wave energy flux

$h=$ water depth

$H_s=$ significant wave height

$Sxx=$ component of radiation stress

$S_{xy}=$ component of radiation stress

$S_{yy}=$ component of radiation stress

$t=$ time $($days$)$

${}_{wx}=x$ component of wind stress

${}_{wy}=y$ component of wind stress

$=$ wave direction $($relative to the $x$ axis$)$

$U=$ mean on$-$offshore Eulerian velocity at $0\mathrm{.}7m$ above bottom

uu$=$ variance of on$-$offshore velocity

$uv=$ covariance of on$-$offshore and alongshore velocity

$V=$ mean alongshore Eulerian velocity at $0\mathrm{.}7m$ above bottom

$vv=$ variance of alongshore velocity

a$.$ Test the relationships between the estimates of uu$,$ uv$,$ vv$,$ Fx$,$ Fy$,$ Sxx$,$ Sxy$,$ Syy that are in the csv file and the corresponding estimates that are obtained from $h,$ fbar, $H_s,$ and $,$ assuming that all of the energy is at the cyclic frequency fbar and the direction theta.