Diagnosing diapycnal mixing from passive tracers

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  • 1 Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

Turbulent mixing across density surfaces transforms abyssal ocean waters into lighter waters and is vital to close the deepest branches of the global overturning circulation. Over the last twenty years, mixing rates inferred from in-situ microstructure profilers and tracer release experiments (TREs) have provided valuable insights in the connection between small-scale mixing and large-scale ocean circulation. Problematically, estimates based on TREs consistently exceed those from collocated in-situ microstructure measurements. These differences have been attributed to a low bias in the microstructure estimates which can miss strong, but rare, mixing events. Here we demonstrate that TRE estimates can suffer from a high bias, because of the approximations generally made to interpret the data. We first derive formulas to estimate mixing from the temporal growth of the second moment of a tracer patch by extending Taylor’s celebrated formula to account for both density stratification and variations in mixing rates. The formulas are validated with tracers released in numerical simulations of turbulent flows and then used to discuss biases in the interpretation of TREs based estimates and how to possibly overcome them.

Corresponding author address: Xiaozhou Ruan, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139. E-mail: xruan@mit.edu

Abstract

Turbulent mixing across density surfaces transforms abyssal ocean waters into lighter waters and is vital to close the deepest branches of the global overturning circulation. Over the last twenty years, mixing rates inferred from in-situ microstructure profilers and tracer release experiments (TREs) have provided valuable insights in the connection between small-scale mixing and large-scale ocean circulation. Problematically, estimates based on TREs consistently exceed those from collocated in-situ microstructure measurements. These differences have been attributed to a low bias in the microstructure estimates which can miss strong, but rare, mixing events. Here we demonstrate that TRE estimates can suffer from a high bias, because of the approximations generally made to interpret the data. We first derive formulas to estimate mixing from the temporal growth of the second moment of a tracer patch by extending Taylor’s celebrated formula to account for both density stratification and variations in mixing rates. The formulas are validated with tracers released in numerical simulations of turbulent flows and then used to discuss biases in the interpretation of TREs based estimates and how to possibly overcome them.

Corresponding author address: Xiaozhou Ruan, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139. E-mail: xruan@mit.edu
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