Gravity and Shear Wave Contributions to Nearshore Infragravity Motions

T. C. Lippmann Center for Coastal Studies, Scripps Institution of Oceanography, La Jolla, California

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T. H. C. Herbers Department of Oceanography, Naval Postgraduate School, Monterey, California

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E. B. Thornton Department of Oceanography, Naval Postgraduate School, Monterey, California

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Abstract

Data from a cross-shore array of nine collocated pressure sensors and bidirectional current meters, extending from the shoreline to approximately 4.5-m depth, are used to estimate the relative contributions of gravity waves (e.g., edge and leaky waves) and instabilities of the alongshore current (shear waves) to motions in the infragravity (frequencies nominally 0.004–0.05 Hz) band. The ratio between frequency-integrated velocity and pressure variances is shown to be approximately equal to g/h for a broad spectrum of gravity waves independent of the mode mix of edge and leaky waves. Since shear waves have velocity to pressure variance ratios ≫ g/h, this ratio can be used to estimate the relative contributions of gravity and shear waves to the infragravity band. Outside the surf zone where the shear in the alongshore current is relatively weak, the observed velocity to pressure variance ratios are approximately equal to g/h, consistent with a gravity-dominated wave field. Inside the surf zone where alongshore currents are strongly sheared, these ratios are up to a factor of 4 larger, indicating that shear waves contribute as much as 75% of the velocity variance in the infragravity band. Observed shear-wave-dominated infragravity band motions are confined to a narrow region of strong shear on the seaward side of the alongshore current maximum, and their cross-shore structure appears to be insensitive to changes in the beach profile, qualitatively consistent with theoretical predictions by linear stability analysis.

Corresponding author address: Dr. Thomas C. Lippman, Center for Coastal Studies, 0209, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0209.

Abstract

Data from a cross-shore array of nine collocated pressure sensors and bidirectional current meters, extending from the shoreline to approximately 4.5-m depth, are used to estimate the relative contributions of gravity waves (e.g., edge and leaky waves) and instabilities of the alongshore current (shear waves) to motions in the infragravity (frequencies nominally 0.004–0.05 Hz) band. The ratio between frequency-integrated velocity and pressure variances is shown to be approximately equal to g/h for a broad spectrum of gravity waves independent of the mode mix of edge and leaky waves. Since shear waves have velocity to pressure variance ratios ≫ g/h, this ratio can be used to estimate the relative contributions of gravity and shear waves to the infragravity band. Outside the surf zone where the shear in the alongshore current is relatively weak, the observed velocity to pressure variance ratios are approximately equal to g/h, consistent with a gravity-dominated wave field. Inside the surf zone where alongshore currents are strongly sheared, these ratios are up to a factor of 4 larger, indicating that shear waves contribute as much as 75% of the velocity variance in the infragravity band. Observed shear-wave-dominated infragravity band motions are confined to a narrow region of strong shear on the seaward side of the alongshore current maximum, and their cross-shore structure appears to be insensitive to changes in the beach profile, qualitatively consistent with theoretical predictions by linear stability analysis.

Corresponding author address: Dr. Thomas C. Lippman, Center for Coastal Studies, 0209, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0209.

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