Wind-based models for estimating the dissipation rates of turbulent energy in aquatic environments: empirical comparisons

• Published in: Marine ecology. Progress series (Halstenbek) Vol. 94; no. 3; pp. 207 - 216
• Main Authors: MacKenzie, B. R., Leggett, W. C.
• Format: Journal Article
• Language: English
• Published: Inter-Research 1993
• Subjects: Boundary layers; Datasets; Marine; Mixing layers; Phytoplankton; Plankton; Surface layers; Turbulence; Turbulence models; Upwelling water; Wind velocity; Northern Hemisphere Oceans
• ISSN: 0171-8630; 1616-1599
• DOI: 10.3354/meps094207

The rate at which turbulent kinetic energy is dissipated influences growth, encounter probability, coagulation rates and vertical distribution of plankton. In this study we quantified the effectiveness with which boundary (wall) layer theory represents turbulent dissipation rates (ε, W m−3) measured within natural surface mixing layers. This model explained 58 % of the variance in 818 literature-derived estimates of turbulent dissipation rates measured at 11 different geographic sites. The residual mean square error (RMSE) associated with the regression of log10 observed dissipation rate vs log10 predicted dissipation rate showed that ca 68 % of surface layer dissipation rates observed in nature were within a factor ± 5.2-fold of dissipation rates estimated using boundary layer theory. Dissipation rates in more complex mixing environments, where turbulence was known to be caused by additional hydrographic phenomena (free convection, breaking of waves in the upper 1.5 m of the water column, current shear, upwelling), exceeded the boundary layer prediction by 1.5- to 26-fold depending on the mechanism associated with turbulence-generation. We found no evidence that turbulence near the surface (0 to 5 or 0 to 10 m) during high winds (≥7.5 or ≥ 10 m s−1) was higher than the boundary layer prediction. When all data were combined into one data set, n = 1088), a multiple regression model having wind speed (W) and sampling depth (z) as inputs (log ε = 2.688logW − 1.322logz − 4.812) explained 54 % of the variance in surface layer turbulent dissipation rates (RMSE = ± 5.5-fold). The potential for developing more precise empirical models of mixing layer turbulent dissipation rates is high and can be achieved by reporting wind conditions prior to, and during, turbulence measurements more thoroughly, and by collecting replicate turbulence profiles. The existing theoretical and empirical models are, however, adequate for many biological applications such as estimating the nature and magnitude of interactions among, and distributions of, many plankton taxa as a result of wind forcing.