Mixed-layer deepening due to Langmuir circulation
J. Phys. Oceanogr., 27, 121-132, 1997.
The interaction between wind-driven Langmuir circulation and pre-existing
stratification is examined in order to elucidate its role
in the deepening of the ocean surface mixed layer. For
linear stratification, a numerical model suggests that Langmuir cells
initially engulf water and create a homogeneous surface layer. The depth
h of this layer can be understood in terms of a Froude number
Fr = w_dn / (N h) where w_dn is the maximum
downwelling velocity generated by Langmuir circulation in homogeneous
water and N is the buoyancy frequency. Numerical results show that
Fr is a constant (approx 0.6). Using computed values
of w_dn, this implies that the rapid mixed-layer
deepening stops at h = c u_* / N in which u_* is the
water friction velocity and the coefficient c is about 10 for fully
developed seas. Alternatively, the deepening is arrested
when the buoyancy jump (delta b) at the mixed-layer base reaches
about 50 u_*^2 / h . The above formula, compared with the
PWP (Price, Weller and Pinkel 1986) value of 0.65 for the bulk Richardson
number R_b associated with shear mixing, suggests that
engulfment by Langmuir circulation dominates mixed-layer deepening if
the velocity difference |delta u| across the base of the
mixed layer is less than about 0.01 U_w , where U_w is the wind speed.
The buoyancy jump criterion is tested for two-layer stratification profiles
and found to be a robust formula suitable for incorporation into
one-dimensional mixed layer models.
The possibility of further mixed-layer deepening through shear instability
is studied by examining the distribution of the gradient Richardson number
Ri_g, particularly in a transition region beneath the
mixed layer. It has great variability across wind,
reaching minimum values beneath downwelling jets, but can fall
below 0.25, indicating the onset of shear instability. Thus Langmuir cells
may facilitate shear instability in a horizontally confined region
beneath downwelling jets, although further study will require
allowance for a different background shear.
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