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Cesar B. Rocha
,
William R. Young
, and
Ian Grooms

Abstract

This study investigates the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. This study extends two existing Galerkin approaches (A and B) and develops a new Galerkin approximation (C). Approximation A, due to Flierl, represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith, represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the boundaries are isopycnal surfaces. The authors discuss the advantages and limitations of approximations A, B, and C in terms of mathematical rigor and conservation laws and illustrate their relative efficiency by solving linear stability problems with nonzero surface buoyancy. With moderate number of modes, B and C have superior accuracy than A at high wavenumbers. Because B lacks the conservation of energy, this study recommends approximation C for constructing solutions to the surface active QG equations using the Galerkin series with standard vertical modes.

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Michael L. Banner
,
Alexander V. Babanin
, and
Ian R. Young

Abstract

The breaking probability is investigated for the dominant surface waves observed in three geographically diverse natural bodies of water: Lake Washington, the Black Sea, and the Southern Ocean. The breaking probability is taken as the average number of breaking waves passing a fixed point per wave period. The data covered a particularly wide range of dominant wavelengths (3–300 m) and wind speeds (5–20 m s−1). In all cases, the wave breaking events were detected visually. It was found that the traditional approach of relating breaking probability to the wind speed or wave age provided reasonable correlations within individual datasets, but when the diverse datasets are combined, these correlations are significantly degraded.

Motivated by the results of recent computational studies of breaking onset in wave groups, the authors investigated the hypothesis that nonlinear hydrodynamic processes associated with wave groups are more fundamental to the process of breaking than previously advocated aerodynamic properties, such as the wind speed or wave age. Further, these computational studies suggest that the significant wave steepness is an appropriate parameter for characterizing the nonlinear group behavior.

Based on this approach, analysis of the data revealed that the probability of dominant wave breaking is strongly correlated with the significant wave steepness for the broad range of wave conditions investigated. Of particular interest is a threshold of this parameter below which negligible dominant wave breaking occurs. Once this threshold is exceeded, a near-quadratic dependence of the breaking probability on the significant wave steepness was observed, with a correlation coefficient of 0.78. The inclusion of parameters representing the secondary influence of wind forcing and background current shear improved the correlation only marginally to 0.81.

The applicability of the breaking probability dependence found for the dominant waves was investigated for higher-frequency bins up to twice the spectral peak frequency f p . The Black Sea data were used for this analysis, in which shorter breaking wave statistics were also measured. It was found that the maximum of the composite breaking frequency distribution gradually shifts from about 1.6f p for lower values of the peak steepness parameter to f p for higher values of this parameter. The breaking probability in a comparable higher frequency band has a similar dependence on significant steepness to that found for the dominant waves.

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Ian R. Young
,
Emmanuel Fontaine
,
Qingxiang Liu
, and
Alexander V. Babanin

Abstract

The wave climate of the Southern Ocean is investigated using a combined dataset from 33 years of altimeter data, in situ buoy measurements at five locations, and numerical wave model hindcasts. The analysis defines the seasonal variation in wind speed and significant wave height, as well as wind speed and significant wave height for a 1-in-100-year return period. The buoy data include an individual wave with a trough to crest height of 26.4 m and suggest that waves in excess of 30 m would occur in the region. The extremely long fetches, persistent westerly winds, and procession of low pressure systems that traverse the region generate wave spectra that are unique. These spectra are unimodal but with peak frequencies that propagate much faster than the local wind. This situation results in a unique energy balance in which waves at the spectra peak grow as a result of nonlinear transfer without any input from the local wind.

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Pramod Kumar Jangir
,
Kevin C. Ewans
, and
Ian R. Young

Abstract

Accurate ocean wave measurements are needed for the safe design and operation of offshore facilities, but despite many ocean wave measurements, the accuracy of wave measurement systems remains an ongoing issue. Of paramount importance are measurements during extreme sea states. This paper examines wave measurements made with an Optech Laser (Laser), a Rosemount WaveRadar (Radar), and a Datawell Waverider buoy at North Rankin A (NRA) platform, Australia; Ekofisk, North Sea; and several South China Sea locations. We evaluate the relative performance of these instruments based upon various frequency domain comparisons, including comparisons of their 1D frequency spectra using spectrograms, spectral moments, high-frequency tail slopes, and significant wave heights derived from their wave spectra. A spectral relationship (transfer function) in terms of mean spectral ratio of the instruments is developed, which can be used for spectral calibration. On average, Laser and Waverider spectral estimates agree well at all sea states. However, at low wind speeds, the higher-frequency spectral levels of the Laser are relatively high and noisy compared with the other two instruments. Radar higher-frequency spectral estimates are relatively low compared to the other two instruments, particularly at lower sea states. In addition, the higher-frequency tail slopes of all three instruments vary between f −4 and f −5. However, at higher sea states, the Waverider tail slopes become steeper than f −5. The Radar produces the lowest significant wave heights (Hm 0) compared to the Laser and Waverider, but its second-moment period (Tm 02) estimates are longer than the Laser and Waverider.

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Pramod Kumar Jangir
,
Kevin C. Ewans
, and
Ian R. Young

Abstract

Accurate measurements of ocean waves underpin efficient offshore operations and optimal offshore structure design, helping to ensure the offshore industry can operate both safely and economically. Popular instruments used by the offshore industry are the Rosemount WaveRadar (Radar) and the Waverider Buoy. The Optech Laser has been used at some locations for specific studies. Recent reports indicate systematic differences of order 10% among the wave measurements made by these instruments. This paper examines the relative performance of these instruments based upon various time-domain comparisons, including results from a quality control (QC) procedure, capabilities of measuring the wave surface profile (skewness), and crest heights for varying wind sea and swell conditions. The QC check provides good-quality data that can be further investigated with an assurance of error-free data, suggesting that the Waverider produces the best-quality data with the lowest failure rate compared to the Laser and Radar. A significant number of the Waverider surface elevation records have negative skewness, particularly at higher sea states, affecting its crest height measurements, which are lower than those from the Laser and Radar. Additionally, the significant wave height (H 1/3) estimates of the Radar are lower than the Laser and Waverider, but its zero-crossing wave periods (TZ ), on average, are longer than the Laser and the Waverider. The significant heights (H 1/3) of Laser and Waverider are in good agreement for all three datasets, but the Waverider’s zero-crossing wave period (TZ ) estimates are significantly longer than the Laser.

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Alberto Meucci
,
Ian R. Young
,
Ole Johan Aarnes
, and
Øyvind Breivik

Abstract

The trends in marine 10-m wind speed U 10 and significant wave height H s found in two century-long reanalyses are compared against a model-only integration. Reanalyses show spurious trends due to the assimilation of an increasing number of observations over time. The comparisons between model and reanalyses show that the areas where the discrepancies in U 10 and H s trends are greatest are also the areas where there is a marked increase in assimilated observations. Large differences in the yearly averages call into question the quality of the observations assimilated by the reanalyses, resulting in unreliable U 10 and H s trends before the 1950s. Four main regions of the world’s oceans are identified where the trends between model and reanalyses deviate strongly. These are the North Atlantic, the North Pacific, the Tasman Sea, and the western South Atlantic. The trends at +24-h lead time are markedly weaker and less correlated with the observation count. A 1985–2010 comparison with an extensive dataset of calibrated satellite altimeters shows contrasting results in H s trends but similar U 10 spatial trend distributions, with general agreement between model, reanalyses, and satellite altimeters on a broad increase in wind speed over the Southern Hemisphere.

Open access
Ali Tamizi
,
Ian R. Young
,
Agustinus Ribal
, and
Jose-Henrique Alves

Abstract

A very large database containing 24 years of scatterometer passes is analyzed to investigate the surface wind fields within tropical cyclones. The analysis confirms the left–right asymmetry of the wind field with the strongest winds directly to the right of the tropical cyclone center (Northern Hemisphere). At values greater than 2 times the radius to maximum winds, the asymmetry is approximately equal to the storm velocity of forward movement. Observed wind inflow angle (i.e., storm motion not subtracted) is shown to vary both radially and azimuthally within the tropical cyclone. The smallest observed wind inflow angles are found in the left-front quadrant with the largest values in the right-rear quadrant. As the velocity of forward movement increases and the central pressure decreases, observed inflow angles ahead of the storm decrease and those behind the storm increase. In the right-rear quadrant, the observed inflow angle increases with radius from the storm center. In all other quadrants, the observed inflow angle is approximately constant as a function of radial distance.

Free access
Ali Tamizi
,
Jose-Henrique Alves
, and
Ian R. Young

Abstract

A series of numerical experiments with the WAVEWATCH III spectral wave model are used to investigate the physics of wave evolution in tropical cyclones. Buoy observations show that tropical cyclone wave spectra are directionally skewed with a continuum of energy between locally generated wind-sea and remotely generated waves. These systems are often separated by more than 90°. The model spectra are consistent with the observed buoy data and are shown to be governed by nonlinear wave–wave interactions that result in a cascade of energy from the wind-sea to the remotely generated spectral peak. The peak waves act in a “parasitic” manner taking energy from the wind-sea to maintain their growth. The critical role of nonlinear processes explains why one-dimensional tropical cyclone spectra have characteristics very similar to fetch-limited waves, even though the generation system is far more complex. The results also provide strong validation of the critical role nonlinear interactions play in wind-wave evolution.

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Mark A. Donelan
,
Alexander V. Babanin
,
Ian R. Young
, and
Michael L. Banner

Abstract

Nearly all of the momentum transferred from wind to waves comes about through wave-induced pressure acting on the slopes of waves: known as form drag. Direct field measurements of the wave-induced pressure in airflow over water waves are difficult and consequently rare. Those that have been reported are for deep water conditions and conditions in which the level of forcing, measured by the ratio of wind speed to the speed of the dominant (spectral peak) waves, is quite weak, U 10/cp < 3. The data reported here were obtained over a large shallow lake during the Australian Shallow Water Experiment (AUSWEX). The propagation speeds of the dominant waves were limited by depth and the waves were correspondingly steep. This wider range of forcing and concomitant wave steepness revealed some new aspects of the rate of wave amplification by wind, the so-called wind input source function, in the energy balance equation for wind-driven water waves. It was found that the exponential growth rate parameter (fractional energy increase per radian) depended on the slope of the waves, ak, vanishing as ak → 0. For very strong forcing a condition of “full separation” occurs, where the airflow detaches from the crests and reattaches on the windward face leaving a separation zone over the leeward face and the troughs. In a sense, the outer flow does not “see” the troughs and the resulting wave-induced pressure perturbation is much reduced, leading to a reduction in the wind input source function relative to that obtained by extrapolation from more benign conditions. The source function parameterized on wave steepness and degree of separation is shown to be in agreement with previous field and laboratory data obtained in conditions of much weaker forcing and wave steepness. The strongly forced steady-state conditions of AUSWEX have enabled the authors to define a generalized wind input source function that is suitable for a wide range of conditions.

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Alexander V. Babanin
,
Michael L. Banner
,
Ian R. Young
, and
Mark A. Donelan

Abstract

This is the third in a series of papers describing wave-follower observations of the aerodynamic coupling between wind and waves on a large shallow lake during the Australian Shallow Water Experiment (AUSWEX). It focuses on the long-standing problem of the aerodynamic consequences of wave breaking on the wind–wave coupling. Direct field measurements are reported of the influence of wave breaking on the wave-induced pressure in the airflow over water waves, and hence the energy flux to the waves. The level of forcing, measured by the ratio of wind speed to the speed of the dominant (spectral peak) waves, covered the range of 3–7. The propagation speeds of the dominant waves were limited by the water depth and the waves were correspondingly steep. These measurements allowed an assessment of the magnitude of any breaking-induced enhancement operative for these field conditions and provided a basis for parameterizing the effect. Overall, appreciable levels of wave breaking occurred for the strong wind forcing conditions that prevailed during the observational period. Associated with these breaking wave events, a significant phase shift is observed in the local wave-coherent surface pressure. This produced an enhanced wave-coherent energy flux from the wind to the waves with a mean value of 2 times the corresponding energy flux to the nonbreaking waves. It is proposed that the breaking-induced enhancement of the wind input to the waves can be parameterized by the sum of the nonbreaking input and the contribution due to the breaking probability.

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