A compact representation of ocean wave directionality

Nonlinear dynamics of steep waves in water of finite depth are analyzed. The most unstable Benjamin‐Feir sidebands are found for a number of values of carrier wave steepness and water depth. The long‐time evolution of a three‐wave system, consisting of the carrier and the two most unstable sidebands, is then studied. Such a wave system undergoes periodic recurrence. It is shown that the slow‐time modulation leads to a corresponding periodic variation in the radiation stress when the propagation directions of the sidebands differ from that of the carrier. The variation of the radiation stress, in turn, results in slow‐time modulation of longshore current.

Section: Some Experimental Resultsmentioning

confidence: 99%

Slow‐time modulation of finite‐depth nonlinear water waves: Relation to longshore current oscillations

Shemer¹,

Dodd²,

Thornton³

1991

“…Indeed, from (5), The above argument is not exactly suitable to (37), since it is impossible to find a coordinate system for cI)vv being zero as long as the wave energy is not restricted in one single direction. However, when B 2 = 0, the x axis coincides with the dominant wave direction and the principal axes of the radiation stress tensor [Higgins et al, 1981]. Therefore in this coordinate system, cI)v• will become minimized.…”

Section: Estimates Of A4 and B4mentioning

confidence: 99%

Error‐reducing strategies for estimates of high‐resolution directional spectra using closely spaced sensors

Shyu¹

1995

When an array of closely spaced sensors is applied, even if the number of sensors is very large, the error magnification phenomenon will render some cross spectra of wave records useless to the estimates of directional spectra because these cross spectra contain about the same information as others. Consequently, only few cospectra or quadrature (quad) spectra can provide truly useful information about the directional distribution when the ordinary spectral analysis procedures are applied. In this paper the sources of certain magnified errors are identified and several error‐reducing strategies are developed so that three more cospectra or quad spectra become useful to the estimates of directional spectra when a compact array with three closely spaced biaxial current meters plus a wave staff is utilized. While most of the strategies are directly relevant to reduction of the random errors, the influences of other data acquisition and processing errors are also fully taken into account. These error‐reducing strategies can improve the directional resolution of all estimators. Their effectiveness is illustrated through a series of model tests with the truncated Fourier series method (TFSM) and the Long and Hasselmann (1979) and Herbers and Guza (1990) minimum nastiness methods. In the TFSM analysis the additional three cospectra or quad spectra allow determination of the third and fourth angular harmonics of directional spectra, after which even the fifth and sixth harmonics can be determined approximately by a simple iterative scheme in most cases. For the modern Long and Hasselmann and Herbers and Guza techniques, the improvements by the present strategies are a bit marginal when the nonnegativity constraint of these techniques can very effectively optimize the estimates, but this may depend on the array geometry, and in some cases there is a clear improvement.

“…Measurements of these stresses have practical value to coastal engineers and are routinely collected at various coastal sites. These data are often obtained with a "slope array," a small square array of four bottom-mounted pressure sensors [Higgins et al, 1981;Seymour et al, 1985]. where x and y are the two horizontal dimensions, f is the wave frequency, 0 is the propagation direction (measured counterclockwise from the positive x axis), n (f) is the ratio of group to phase speed, p is the density of seawater, and g is the acceleration of gravity.…”

Section: Introductionmentioning

confidence: 99%

“…The slope array is a bottom-mounted device that gives pitch and roll type information for surface waves. Higgins et al [1981 ], Pawka et al [1983], Oltman-Shay and Guza [1984], and others approximate surface slopes essentially by dividing the differential pressure (converted to surface elevation by linear theory) of two sensors by their separation. The error introduced by the curvature of the sea surface between the sensors is minimized by very small sensor separations, but this makes the slope measurements sensitive to noise.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Estimation of wave radiation stresses from slope array data

Herbers¹,

Guza²

1989

A compact array of four bottom‐mounted pressure sensors arranged in a square, a slope array, is frequently used to obtain estimates of the wave radiation stresses in shallow water. For wavelengths long in comparison with the array dimension (L), existing processing methods (Higgins et al., 1981) have bias errors of O(kL)2, with k the wavenumber. An estimator for wave radiation stresses and energy fluxes is derived here that reduces the bias to O(kL)4, thus considerably extending the frequency range of accurate estimates of a slope array. The stability of the new estimator to statistical fluctuations in the cross spectra is similar to the method of Higgins et al. [1981].