General circulation models (e.g. Samelson, 1998) indicate that the thermohaline circulation is highly sensitive to the global magnitude and distribution of mixing. Recent observations (e.g. Polzin et al 1997) highlight the inhomogeneity of mixing. Therefore, a global map of mixing would benefit climate modeling, as well as our understanding of biological productivity and pollutant dispersal. Since global measurements of mixing are impractical, another way of estimating the global mixing distribution is to map the energy flux into internal waves, and then to measure their subsequent long-range propagation.
Figure 1: (top) Depth-integrated, annual-mean near-inertial energy-flux vectors are plotted from 60 historical moored records. The length of each arrow is logarithmic, with references indicated at upper left. Moorings with |F|< 0.1 kW/m appear as a black dot without an arrow; white dots indicate moorings which were unusable. The few instances of poleward propagation are plotted in white. Color map indicates annual-mean energy-flux from the wind to near-inertial mixed-layer motions from Alford (2001). The color scale is logarithmic and is indicated at upper left. The box in the NW Pacific is discussed in the text.
(bottom) Arrows are as in (a) but for the M2-tidal band. Color map denotes internal-tide conversion using the TPXO5 model (Egbert and Ray, 2000), courtesy of G. D. Egbert. The lines in the western Pacific and near Hawaii are discussed in the text. The inset in each panel shows a histogram of the poleward component of the flux for all moorings.
The first step is to map the distribution of the two primary internal-wave sources, the wind, which generates near-inertial waves, and surface-tidal flow over topography (Egbert and Ray, 2000), leading to internal tides. The wind-flux portion is calculated (Alford, 2001) by using the NCEP/NCAR reanalysis wind fields, which incorporate observations over many years and locations into a dynamically consistent framework, to drive a simple model of the mixed-layer response. The energy flux is then given by the scalar product of the wind stress and the mixed-layer current. Ongoing work involves examining the high-latitude dependence of the fluxes (as the response gets faster at high latitude, the NCEP winds become more and more inadequate for the job), and the interannual variability of the fluxes.
The global distribution of the energy flux available for internal waves is plotted below for the wind (top) and the tides (bottom, courtesy of G. Egbert). The greatest wind inputs occur at midlatitudes during wintertime, associated with travelling storms. Large tidal inputs (red regions) occur where the surface tide flows perpendicular to rough bottom features.
The subsequent horizontal flux for each can be measured using historical moored records by solving for the lowest two modes and computing <u'p'>, where u' is the baroclinic velocity and p' is the baroclinic pressure anomaly. Near-inertial fluxes are large following wintertime storms, and are equatorward, since waves generated at the inertial frequency become evanescent poleward of their generation site. The tidal fluxes are usually directed away from strong topography.
Since then, Zhongxiang Zhao and I have been working on further refining our estimates of the global distribution of internal-tide energy flux from both moorings and altimetry, which has resulted in a series of papers and an exciting new NSF proposal.
Harper Simmons and I are working together to compare models and observations in order to determine the analogous fate of the near-inertial motions.