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M. S. Longuet-Higgins

Abstract

It is shown that the vertical acceleration of a particle beneath the crest of a step gravity wave does not always decrease monotonically with depth in the fluid. When the wave steepness ak exceeds 0.4, the acceleration at first increases with depth, and is a maximum at points slightly below the free surface. The result may have implications for the motions of a floating buoy.

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M. S. Longuet-Higgins

Abstract

Surface accelerations can be measured in at least two ways: 1) by a fixed vertical wave guage, 2) by a free-floating buoy. This gives rise to two different vertical accelerations, called respectively “apparent” and “real”, or Langrangian. This paper presents the first accurate calculations of the two types of acceleration, for symmetric waves of finite steepness.

The apparent upwards accelerations is always less than 0.24g, but the apparent downwards acceleration is unlimited. The real vertical acceleration is smoother than the apparent acceleration, and always lies between 0.30g and −0.39g.

The (real) horizontal acceleration is studied, and shown to be greater in amplitude than the real vertical acceleration.

The results are discussed in relation to proposed limits on the acceleration in random seas.

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M. S. Longuet-Higgins

Abstract

Sunlight reflected from a wind-roughened sea surface produces a glitter pattern in which the region of maximum intensity tends to be shifted horizontally by an apparent angle Δ, depending on the wind speed. It is shown that Δ is related directly to the skewness of the distribution of surface slopes. From the observed data of Cox and Munk (1956) it is possible to deduce a simple correlation between Δ and the wind stress τ.

The physical mechanism underlying slope skewness is investigated. The skewness which results from damping of individual waves is shown to be negligible. A two-scale model is proposed, in which damped ripples or short gravity waves ride on the surface of longer gravity waves. The model is found to give skewness of the observed magnitude. The sign of the skewness depends on the angle between the wind maintaining the ripples and the direction of the longer waves, in agreement with observation.

Certain theoretical relations between Δ and the phase γ of the short-wave modulation may be of interest in interpreting observations of the sea surface by other types of remote sensing.

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J. A. Ewing, M. S. Longuet-Higgins, and M. A. Srokosz

Abstract

Recent theoretical studies of the accelerations in regular gravity waves of finite steepness have shown striking differences between the Eulerian and the Lagrangian accelerations (those measured by fixed instruments or freely floating instruments, respectively). In the present paper, attention is directed to field observations of accelerations in random seas. Two sets of data are analyzed, representing Eulerian and Lagrangian measurements. The Eulerian accelerations are found to be notably asymmetric, with maximum downwards accelerators exceeding −1.6g. The Lagrangian acceleration histograms are narrower and more symmetric, in general. As might be expected, the acceleration variance is highly sensitive to the high-frequency cutoff, in both types of data.

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