Waves on a shearing current: a uniformly valid asymptotic solution

McKee, W. D.

doi:10.1017/s0305004100048490

Cited by 23 publications

(20 citation statements)

References 7 publications

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“…Apparently, wave energy is reflected at wave directions larger than the reflecting energy. Such a reflection in a straight shear current is a well-known phenomenon [e.g., Kenyon, 1971;McKee, 1974McKee, , 1975McKee, , 1977Smith, 1976;Jonsson and Skovgaard, 1978;Hayes, 1980;Smith, 1983 Figure 4) and reflection is even more important than in the swell case. This is evident in the relatively large decrease of the computed significant wave height near the center of the Gulf Stream.…”

Section: Storm From the Ne Direction In The Ne Storm Case The Signifmentioning

confidence: 99%

“…Several studies have been carried out to model the effects of such shear currents on the propagation of waves. Some of these studies consider both refraction and diffraction [e.g., McKee, 1974McKee, , 1975McKee, , 1977Smith, 1976;Booij, 1981;Smith, 1983] whereas others (given below) ignore diffraction. In the following we also ignore diffraction as the corresponding effects are dominated by the short-crested, random nature of the waves (at least at the scales considered here).…”

Section: Introductionmentioning

confidence: 99%

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Effects of the Gulf Stream on ocean waves

Holthuijsen

Tolman

1991

J. Geophys. Res.

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In the present study a third-generation numerical wave model is used to study effects of a straight Gulf Stream and a Gulf Stream ring on ocean waves in swell and storm conditions. The model accounts for all relevant processes of propagation, generation, and dissipation of the waves (including current effects) without imposing a priori restraints on the spectral development of the waves. The dominating mechanism affecting the waves appears to be current-induced refraction even though the shortcrestedness of the incoming waves tends to mask its effects (also in swell conditions). Depending on wind and wave conditions, refraction may trap locally generated waves in the straight Gulf Stream or it may reflect wave energy back to the open ocean. In the Gulf Stream ring, refraction induces a considerable variation in significant wave height and short-crestedness, but it hardly affects the mean wave direction. In storm conditions the processes of generation and dissipation are considerably enhanced in countercurrent situations and reduced following-current situations.1.

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Section: Storm From the Ne Direction In The Ne Storm Case The Signifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effects of the Gulf Stream on ocean waves

Holthuijsen

Tolman

1991

J. Geophys. Res.

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“…The fluid‐mechanical problem of surface wave interaction with currents has a long history, see reviews by Peregrine [1976] and Peregrine and Jonsson [1983]. Significant insights have been obtained by theoretical analysis of waves on currents with velocity depending on only one coordinate [ Longuet‐Higgins and Stewart , 1960, 1961; McKee , 1974; Basovich and Talanov , 1977; Hughes , 1978; Basovich et al , 1987; Thompson et al , 1988; Gotwols et al , 1988; Trulsen et al , 1990; Maltseva et al , 1995; van der Kooij et al , 1995]. Direct numerical integration of equations governing wave train trajectories and wave action balance has been used when simulating surface wave interaction with currents variable in two dimensions [ Irvine and Tilley , 1988; Liu et al , 1989; Brissette et al , 1993; Wang et al , 1994].…”

Section: Introductionmentioning

confidence: 99%

A perturbation model of radiometric manifestations of oceanic currents

Godin

Irisov

2003

Radio Science

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[1] Extracting quantitative oceanographic information from microwave images of the ocean surface requires a physical understanding and an efficient mathematical model of surface wave interaction with currents. In this paper, we consider ''weak'' currents (with velocities up to a few tens of centimeters per second) and discuss a perturbation approach that leads to numerically efficient models of surface roughness modulation by the current fields with arbitrary dependence on horizontal coordinates and time. With the wave-atmosphere interaction being described within the relaxation approximation, closed-form analytic expressions are obtained for surface roughness modulation. The hydrodynamic theory is combined with an electromagnetic model based on the small-slope approximation to simulate microwave emission from the ocean surface. Analysis of the theoretical results demonstrates that the physics of surface wave interaction with time-dependent currents, which are inhomogeneous in two spatial dimensions, is more rich and complex than is suggested by the one-dimensional models considered theoretically in the past. Of particular interest for remote sensing is the finding that realistic two-dimensionally inhomogeneous currents, unlike their onedimensional models, can produce perturbations in microwave brightness temperature that extend well beyond the current field itself. Our model suggests that microwave brightness temperature measurements should be a sensitive tool of observing and quantitatively evaluating surface currents in the ocean.INDEX TERMS: 0659 Electromagnetics: Random media and rough surfaces; 4275 Oceanography: General: Remote sensing and electromagnetic processes (0689); 4512 Oceanography: Physical: Currents; 4560 Oceanography: Physical: Surface waves and tides (1255); 6959 Radio Science: Radio oceanography; KEYWORDS: wave-current interaction, microwave remote sensing, surface roughness modulation, thermal radiation, small-slope approximation, surface wave spectrum Citation: Godin, O. A., and V. G. Irisov, A perturbation model of radiometric manifestations of oceanic currents,

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“…Thus a non-singular description of short surface gravity waves near a caustic can provide a useful supplement to the ray solution as well as being of interest in its own right. A particular class of problems for which uniformly valid descriptions of small amplitude short waves near caustics have been obtained is steady parallel flows with the caustic along a streamline (9,11). The intention of this paper is to seek another class of problems for which it is tractable to obtain a non-singular description of small amplitude short waves near a caustic.…”

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confidence: 99%