## Abstract

Study of a schematic linear, wind-driven, inertio–gravity wave model in the upper ocean finds resonant, near-inertial waves of finite horizontal wavelength to have both horizontal and vertical motions. The mean product of these horizontal motions with the vertical motion yields an internal vertical Reynolds stress that is zero at the sea surface and nonzero at the base of the mixed layer and in the main pycnocline below. Assuming near-inertial waves of finite wavelength to be generated by finite wavelength disturbances in the atmosphere, advected by the mean wind, the internal vertical Reynolds stress at the base of the mixed layer is directed 45° to the right of the mean wind direction. Below the mixed layer, near-inertial waves in the mixed layer. This generation mechanism produces an internal vertical stress throughout the main pycnocline, directed initially 45° to the right of the mean wind direction, but rotating into it with increasing depth. The divergence of this internal vertical Reynolds stress produces an Eulerian mean flow. In the mixed layer, the Eulerian mean flow (vertically averaged) is directed 45° to the left of the mean with direction. Below the mixed layer, the Eulerian mean flow is directed principally upwind over the upper portion of the main pycnocline. For wavelength scales of O(100 km), The Eulerian mean flow is of the same order of magnitude as the Ekman mean flow driven by the synoptic mean wind. This means that Eulerian measurements (e.g., current meter observations) of wind-driven currents in the upper ocean may have to consider the Eulerian mean motion from this source. In this linear situation, that Eulerian mean flow is equal, but opposite to the Stokes drift associated with these near-inertial waves; consequently, the net Lagrangian particle motion is zero everywhere in the column.

Analysis of the Lagrangian mean motions in this schematic model establishes that measurement systems which are traditionally considered Lagrangian (e.g., drogued drifters) and Eulerian (e.g., moored current meters) may in fact be mixed. Drogued drifters are found to act like Lagrangian tracers with respect to horizontal displacements, but not with respect to vertical displacements. In the context of the present model, this inability to follow the particle vertically yields considerable downwind mean motion of the drogued drifter over the lower half of the mixed layer. This motion has not dynamical significance (i.e., it is not related to the transport of volume, heat, salt, etc.), but it is larger than the crosswind Ekman flow and may explain why drogued drifters prefer downwind motion. Moored current meters may taken on quasi-Lagrangian character by being displaced vertically in response to mooring motion. This can have an effect upon the measured mean motion that is as large as the purely Eulerian mean flow past the mooring.