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Lagrangian Surface Wave Motion and Stokes Drift Fluctuations

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  • 1 NorthWest Research Associates, El Granada, California
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Abstract

Nonlinear effects in Lagrangian sea surface motions are important to understanding variability in wave-induced mass transport, wave-driven diffusion processes, and the interpretation of measurements obtained with moored or free-drifting buoys. This study evaluates the Lagrangian vertical and horizontal motions of a particle at the surface in a natural, random sea state using second-order, finite-depth wave theory. In deep water, the predicted low-frequency (infragravity) surface height fluctuations are much larger than Eulerian bound wave motions and of the opposite sign. Comparison to surface elevation bispectra observed with a moored buoy in steady, high-wind conditions shows good agreement and confirms that—in contrast to the Eulerian sea surface motion with predominant phase coupling between the spectral peak and double-frequency harmonic components—nonlinearity in Lagrangian wave observations is dominated by phase-coupled infragravity motions. Sea surface skewness estimates obtained from moored buoys in deep and shallow sites, over a wide range of wind–sea and swell conditions, are in good agreement with second-order theory predictions. Theory and field data analysis of surface drift motions in deep water reveal energetic [O(10) cm s−1] infragravity velocity fluctuations that are several orders of magnitude larger and 180° out of phase with Eulerian infragravity motions. These large fluctuations in Stokes drift may be important in upper-ocean diffusion processes.

Corresponding author address: Dr. Thomas H. C. Herbers, NorthWest Research Associates, P.O. Box 1533, El Granada, CA 94018. E-mail: thcherbers@gmail.com

Abstract

Nonlinear effects in Lagrangian sea surface motions are important to understanding variability in wave-induced mass transport, wave-driven diffusion processes, and the interpretation of measurements obtained with moored or free-drifting buoys. This study evaluates the Lagrangian vertical and horizontal motions of a particle at the surface in a natural, random sea state using second-order, finite-depth wave theory. In deep water, the predicted low-frequency (infragravity) surface height fluctuations are much larger than Eulerian bound wave motions and of the opposite sign. Comparison to surface elevation bispectra observed with a moored buoy in steady, high-wind conditions shows good agreement and confirms that—in contrast to the Eulerian sea surface motion with predominant phase coupling between the spectral peak and double-frequency harmonic components—nonlinearity in Lagrangian wave observations is dominated by phase-coupled infragravity motions. Sea surface skewness estimates obtained from moored buoys in deep and shallow sites, over a wide range of wind–sea and swell conditions, are in good agreement with second-order theory predictions. Theory and field data analysis of surface drift motions in deep water reveal energetic [O(10) cm s−1] infragravity velocity fluctuations that are several orders of magnitude larger and 180° out of phase with Eulerian infragravity motions. These large fluctuations in Stokes drift may be important in upper-ocean diffusion processes.

Corresponding author address: Dr. Thomas H. C. Herbers, NorthWest Research Associates, P.O. Box 1533, El Granada, CA 94018. E-mail: thcherbers@gmail.com
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