Abstract
We formulate an expression for the turbulent kinetic energy dissipation
rate, $\epsilon$, associated with shear–generated
turbulence in terms of readily measured properties of the flow or easily
derived quantities in models. The expression depends on the turbulent
vertical length scale, $\ell_v$, the inverse time
scale $N$ and the Richardson number $Ri=N^2/S^2$, where $S$
is the vertical shear, with $\ell_v$ scaled in a way
consistent with theories and observations of stratified turbulence.
Unlike previous studies the focus is not so much on the functional form
of $Ri$, but the vertical variation of the length scale
$\ell_v$. Using data from two $\sim$7
day time series in the western equatorial Pacific the scaling is
compared with the observed $\epsilon$. The scaling
works well with the estimated $\epsilon$ capturing the
differences in amplitude and vertical distribution of the observed
$\epsilon$ between the two times series. Much of those
differences are attributable to changes in the vertical distribution of
the length scale $\ell_v$, and in particular the
associated turbulent velocity scale, $u_t$. We relate $u_t$ to a
measure of the fine-scale variations in velocity,
$\tilde{u}$. Our study highlights the need to
consider the length scale and its estimation in environmental flows. The
implications for the vertical variation of the associated turbulent
diffusivity are discussed.