1 - 10 of 11 Chapters
[The physics problem of the mutual influences of rapidly oscillating surface gravity waves and more slowly evolving upper-ocean currents is well-studied.]
[Consider a uniform-density fluid with an upper free surface at z = η and a flat bottom at z = − H.]
[In this chapter the QL theory for wave–current interaction is developed with only the assumptions that η is small enough to allow a Taylor series expansion about the mean surface elevation of z = 0]
[As discussed in Chap. 1, a QL theory, on the one hand, is an ansatz, where wave-wave nonlinear advection is neglected because its effects, while important for small- but finite-𝜖 wave evolution, are not necessarily of primary importance for the WEC and CEW interactions, even when wave...
[To solve the WQL equations (3.3)–(3.4), a perturbative approach is taken assuming small μ.]
[The WQL and CQL equations can be integrated on the slow time of current evolution (n.b., Eq. (4.2)) after solving the elliptical problem (5.18) for P. This latter step is what distinguishes this wave–current interaction theory from previous ones (e.g., CL76 et seq.) that only include the...
[For a given current field u and primary wave specified by (a, k), consider an expanded representation of the leading-order wave field]
[Four examples of different current shapes are considered here and, at greater length, in Appendix J. In each case a current is specified and presumed to remain “frozen” in time, and the corresponding CEW and WEC effects are evaluated.]
[The examples in Chap. 8 are all for narrow-banded wave and current fields, i.e., with only a few horizontal wavenumber k components]
[Surface gravity waves are mostly uninfluenced by interior density and material concentration variations. A scale estimate (Chap. 4) of the buoyancy force is smaller than the leading-order wave pressure-gradient force by the ratio Δρ∕ρ near the surface, i.e., ∼ 10−3.]
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