# A Fourier approximation method for steady water waves

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...(34) is related to the wavenumber by the dispersion equation, x(2) 1⁄4 gk tanhðkdÞ: ð36Þ Even with small wave heights, free-surface waves show slightly non-sinusoidal form and comparisons are made with the highly accurate stream function theory of Rienecker and Fenton [24] based on Fourier approximations....

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...(34) is related to the wavenumber by the dispersion equation, x2 ¼ gk tanhðkdÞ: ð36Þ Even with small wave heights, free-surface waves show slightly non-sinusoidal form and comparisons are made with the highly accurate stream function theory of Rienecker and Fenton [24] based on Fourier approximations....

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...Regular waves are generated by a piston-type paddle for several periods and wave heights; velocities and pressures are then compared against accurate stream-function theory [24]....

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