An individual-component approximation to quadratic stress for flow-decomposition analysis

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An individual-component approximation to quadratic stress for flow-decomposition analysis

Militello, A. / Kraus, N.C.

An individual-component approximation (ICA) to the one-dimensional quadratic stress is presented for analysis of hydrodynamic systems that contain multiple-frequency fluid motion such as tidal current and nearshore currents. Criteria governing development of the approximation are accuracy, symmetry. and preservation of contributions (magnitude and direction) of individual and coupled velocity components. Preservation of directionality is required to isolate functioning of individual terms for flow-decomposition analysis. The ICA is compared with the small-amplitude approximation analytically and through numerical examination for two velocity components. The two approximations differ at second order within the range of validity of the small-amplitude approximation. The ICA is exact in the limits of components with large magnitudes and components of equal magnitudes. Based on calculations comparing the exact numerical solution for velocity components with a wide range of relative magnitudes, relative periods, and phase differences, the ICA is accurate except in restricted regions of small-magnitude quadratic velocity. The ICA is generalized to multiple components without restriction on magnitude, period, or phase, and example calculations are given for flows comprised of three components and six components. The method is applied to velocity tidal constituents for Galveston Bay, Texas, and Tampa Bay, Florida.