How we compute N matters to estimates of mixing in stratified flows

• Published in: Journal of fluid mechanics 2017-11, Vol.831, Article R2
• Main Authors: Arthur, Robert S., Venayagamoorthy, Subhas K., Koseff, Jeffrey R., Fringer, Oliver B.
• Format: Article
• Language: English
• Subjects: Brunt-vaisala frequency; Computational fluid dynamics; Computer simulation; Density field; Density profiles; Density stratification; Direct numerical simulation; Efficiency; Energy; ENGINEERING; Environmental engineering; Estimates; Fluid flow; Fluids; GEOSCIENCES; Internal waves; Laboratories; Mathematical models; MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Ocean models; Rapids; Reynolds number; Richardson number; Slope; Stratification; stratified turbulence; Turbulence; Turbulent mixing
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2017.679

Most commonly used models for turbulent mixing in the ocean rely on a background stratification against which turbulence must work to stir the fluid. While this background stratification is typically well defined in idealized numerical models, it is more difficult to capture in observations. Here, a potential discrepancy in ocean mixing estimates due to the chosen calculation of the background stratification is explored using direct numerical simulation data of breaking internal waves on slopes. Two different methods for computing the buoyancy frequency $N$ , one based on a three-dimensionally sorted density field (often used in numerical models) and the other based on locally sorted vertical density profiles (often used in the field), are used to quantify the effect of $N$ on turbulence quantities. It is shown that how $N$ is calculated changes not only the flux Richardson number $R_{f}$ , which is often used to parameterize turbulent mixing, but also the turbulence activity number or the Gibson number $Gi$ , leading to potential errors in estimates of the mixing efficiency using $Gi$ -based parameterizations.