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Comparison of Methods for Estimating Nearshore Shear Wave Variance

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  • 1 Center for Coastal Studies, Scripps Institution of Oceanography, La Jolla, California
  • | 2 Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
  • | 3 Naval Postgraduate School, Monterey, California
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Abstract

Shear waves (instabilities of the breaking wave–driven mean alongshore current) and gravity waves both contribute substantial velocity fluctuations to nearshore infragravity motions (periods of a few minutes). Three existing methods of estimating the shear wave contribution to the infragravity velocity variance are compared using extensive field observations. The iterative maximum likelihood estimator (IMLE) and the direct estimator (DE) methods use an alongshore array of current meters, and ascribe all the velocity variance at non–gravity wavenumbers to shear waves. The ratio (R) method uses a collocated pressure gauge and current meter, and assumes that shear wave pressure fluctuations are small, and that the kinetic and potential energies of gravity waves are equal. The shear wave velocity variance 〈q2sw〉 is estimated from the relative magnitudes of the total (shear plus gravity wave) pressure and velocity variances. Estimates of root-mean-square shear wave velocity fluctuations q2sw from all three methods are generally in good agreement (correlations > 0.96), supporting the validity of their underlying assumptions. When q2sw is greater than a few centimeters per second, IMLE and DE estimates of q2sw differ by less than 10%. The R estimates of q2sw are usually higher than the IMLE and DE estimates, and on average the R method attributes 15% more of the total horizontal velocity variance to shear waves than is attributed by the IMLE method. When mean currents and shear waves are weak, all three estimators are noisy and biased high.

Corresponding author address: Dr. T. James Noyes, Scripps Institution of Oceanography, 9500 Gilman Drive, No. 209, La Jolla, CA 92093-0209. Email: jnoyes@coast.ucsd.edu

Abstract

Shear waves (instabilities of the breaking wave–driven mean alongshore current) and gravity waves both contribute substantial velocity fluctuations to nearshore infragravity motions (periods of a few minutes). Three existing methods of estimating the shear wave contribution to the infragravity velocity variance are compared using extensive field observations. The iterative maximum likelihood estimator (IMLE) and the direct estimator (DE) methods use an alongshore array of current meters, and ascribe all the velocity variance at non–gravity wavenumbers to shear waves. The ratio (R) method uses a collocated pressure gauge and current meter, and assumes that shear wave pressure fluctuations are small, and that the kinetic and potential energies of gravity waves are equal. The shear wave velocity variance 〈q2sw〉 is estimated from the relative magnitudes of the total (shear plus gravity wave) pressure and velocity variances. Estimates of root-mean-square shear wave velocity fluctuations q2sw from all three methods are generally in good agreement (correlations > 0.96), supporting the validity of their underlying assumptions. When q2sw is greater than a few centimeters per second, IMLE and DE estimates of q2sw differ by less than 10%. The R estimates of q2sw are usually higher than the IMLE and DE estimates, and on average the R method attributes 15% more of the total horizontal velocity variance to shear waves than is attributed by the IMLE method. When mean currents and shear waves are weak, all three estimators are noisy and biased high.

Corresponding author address: Dr. T. James Noyes, Scripps Institution of Oceanography, 9500 Gilman Drive, No. 209, La Jolla, CA 92093-0209. Email: jnoyes@coast.ucsd.edu

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