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Estimating the Eddy Viscosity Profile from Velocity Spirals in the Ekman Boundary Layer

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  • 1 Graduate School of Science, Kyoto University, Kyoto, Japan
  • 2 University of Tokyo Ocean Alliance, University of Tokyo, Tokyo, Japan
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Abstract

Turbulent mixing induced by tidal currents near the sea bottom plays a key role in coastal and shallow sea environments. Many attempts have been made to quantify turbulent mixing near the seabed, such as velocity microstructure measurements with microstructure profilers and turbulent Reynolds stress measurements using acoustic Doppler current profilers (ADCPs). This study proposes an alternative method in which the Ekman balance equations are solved with measured velocity spirals to estimate the eddy viscosity profile. Three schemes (schemes 1, 2, and 3) are described in this paper; schemes 1 and 2 were used in previous studies, while scheme 3 is newly proposed in the present study. The performance of the three schemes was tested using velocity spirals simulated with an idealized eddy viscosity profile, showing that scheme 2 is useful if the random measurement errors are small, while scheme 3 is useful when the errors in the Ekman balance are small. The performance was also evaluated using measured velocity spirals. This method utilizes velocity measured with standard ADCPs operated in normal modes, allowing for easier and more frequent quantifications of the mixing averaged over longer periods.

Corresponding author address: Yutaka Yoshikawa, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwake, Sakyo, Kyoto 606-8502, Japan. E-mail: yosikawa@kugi.kyoto-u.ac.jp

Abstract

Turbulent mixing induced by tidal currents near the sea bottom plays a key role in coastal and shallow sea environments. Many attempts have been made to quantify turbulent mixing near the seabed, such as velocity microstructure measurements with microstructure profilers and turbulent Reynolds stress measurements using acoustic Doppler current profilers (ADCPs). This study proposes an alternative method in which the Ekman balance equations are solved with measured velocity spirals to estimate the eddy viscosity profile. Three schemes (schemes 1, 2, and 3) are described in this paper; schemes 1 and 2 were used in previous studies, while scheme 3 is newly proposed in the present study. The performance of the three schemes was tested using velocity spirals simulated with an idealized eddy viscosity profile, showing that scheme 2 is useful if the random measurement errors are small, while scheme 3 is useful when the errors in the Ekman balance are small. The performance was also evaluated using measured velocity spirals. This method utilizes velocity measured with standard ADCPs operated in normal modes, allowing for easier and more frequent quantifications of the mixing averaged over longer periods.

Corresponding author address: Yutaka Yoshikawa, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwake, Sakyo, Kyoto 606-8502, Japan. E-mail: yosikawa@kugi.kyoto-u.ac.jp
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