Michael L. Banner

Modeling Wave-Enhanced Turbulence in the Ocean Surface Layer

Abstract Until recently, measurements below the ocean surface have tended to confirm “law of the wall” behavior, in which the velocity profile is logarithmic, and energy dissipation decays inversely with depth. Recent measurements, however, show a sublayer, within meters of the surface, in which turbulence is enhanced by the action of surface waves. In this layer, dissipation appears to decay with inverse depth raised to a power estimated between 3 and 4.6. The present study shows that a conventional model, employing a “level 2½” turbulence closure scheme predicts near-surface dissipation decaying as inverse depth to the power 3.4. The model shows agreement in detail with measured profiles of dissipation. This is despite the fact that empirical constants in the model are determined for situations very different from this near-surface application. The action of breaking waves is modeled by a turbulent kinetic energy input at the surface. In the wave-enhanced layer, the downward flux of turbulent kinetic en...

On the separation of air flow over water waves

Conditions leading to the onset of air-flow separation over a mobile air-water interface are discussed. It is argued that, in a frame of reference in which the interfacial boundary assumes a steady shape, the occurrence of separation requires a stagnation point on the interface. In the case of air blowing over water waves, this corresponds to the onset of wave breaking. These arguments are strongly supported by flow visualization and pressure measurements carried out in a laboratory wind-wave flume. Furthermore, the pressure measurements show a greatly enhanced interfacial shear stress for a breaking wave compared with that over an unbroken wave of the same wavelength. The implications of these findings for wind-wave generation are discussed.

Breaking Probability for Dominant Waves on the Sea Surface

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 aerod...

Tangential stress beneath wind-driven air–water interfaces

The detailed structure of the aqueous surface sublayer flow immediately adjacent to the wind-driven air-water interface is investigated in a laboratory wind-wave flume using particle image velocimetry (PIV) techniques. The goal is to investigate quantitatively the character of the flow in this crucial, very thin region which is often disrupted by microscale breaking events. In this study, we also examine critically the conclusions of Okuda, Kawai & Toba (1977), who argued that for very short, strongly forced wind-wave conditions, shear stress is the dominant mechanism for transmitting the atmospheric wind stress into the water motion - waves and surface drift currents. In strong contrast, other authors have more recently observed very substantial normal stress contributions on the air side. The availability of PIV and associated image technology now permits a timely re-examination of the results of Okuda et al., which have been influential in shaping present perceptions of the physics of this dynamically important region. The PIV technique used in the present study overcomes many of the inherent shortcomings of the hydrogen bubble measurements, and allows reliable determination of the fluid velocity and shear within 200 μm of the instantaneous wind-driven air-water interface. The results obtained in this study are not in accord with the conclusions of Okuda et al. that the tangential stress component dominates the wind stress. It is found that prior to the formation of wind waves, the tangential stress contributes the entire wind stress, as expected. With increasing distance downwind, the mean tangential stress level decreases marginally, but as the wave field develops, the total wind stress increases significantly. Thus, the wave form drag, represented by the difference between the total wind stress and the mean tangential stress, also increases systematically with wave development and provides the major proportion of the wind stress once the waves have developed beyond their early growth stage. This scenario reconciles the question of relative importance of normal and tangential stresses at an air-water interface. Finally, consideration is given to the extrapolation of these detailed laboratory results to the field, where the present findings suggest that the sea surface is unlikely to become fully aerodynamically rough, at least for moderate to strong winds.

Wave-Follower Field Measurements of the Wind-Input Spectral Function. Part II: Parameterization of the Wind Input

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, U10/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 winddriven 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.

THE INFLUENCE OF WAVE BREAKING ON THE SURFACE PRESSURE DISTRIBUTION IN WIND-WAVE INTERACTIONS

In reviewing the current status of our understanding of the mechanisms underlying wind-wave generation, it is apparent that existing theories and models are not applicable to situations where the sea surface is disturbed by breaking waves, and that the available experimental data on this question are sparse. In this context, this paper presents the results of a detailed study of the effects of wave breaking on the aerodynamic surface pressure distribution and consequent wave-coherent momentum flux, as well as its influence on the total wind stress. Two complementary experimental configurations were used to focus on the details and consequences of the pressure distribution over breaking waves under wind forcing. The first utilized a stationary breaking wave configuration and confirmed the presence of significant phase shifting, due to air flow separation effects, between the surface pressure and surface elevation (and slope) distributions over a range of wind speeds. The second configuration examined the pressure distribution, recorded at a fixed height above the mean water surface just above the crest level, over short mechanically triggered waves which were induced to break almost continuously under wind forcing. This allowed a very detailed comparison of the form drag for actively breaking waves and for waves of comparable steepness just prior to breaking (‘incipiently’ breaking waves). For these propagating steep-wave experiments, the pressure phase shifts and distributions closely paralleled the stationary configuration findings. Moreover, a large increase (typically 100%) in the total windstress was observed for the breaking waves, with the increase corresponding closely to the comparably enhanced form drag associated with the actively breaking waves. In addition to further elucidating some fundamental features of wind-wave interactions for very steep wind waves, this paper provides a useful data set for future model calculations of wind flow over breaking waves. The results also provide the basis for a parameterization of the wind input source function applicable for a wave field undergoing active breaking, an important result for numerical modelling of short wind waves.

Spectrally Resolved Energy Dissipation Rate and Momentum Flux of Breaking Waves

Abstract Video observations of the ocean surface taken from aboard the Research Platform FLIP reveal the distribution of the along-crest length and propagation velocity of breaking wave crests that generate visible whitecaps. The key quantity assessed is Λ(c)dc, the average length of breaking crests per unit area propagating with speeds in the range (c, c + dc). Independent of the wave field development, Λ(c) is found to peak at intermediate wave scales and to drop off sharply at larger and smaller scales. In developing seas breakers occur at a wide range of scales corresponding to phase speeds from about 0.1 cp to cp, where cp is the phase speed of the waves at the spectral peak. However, in developed seas, breaking is hardly observed at scales corresponding to phase speeds greater than 0.5 cp. The phase speed of the most frequent breakers shifts from 0.4 cp to 0.2 cp as the wave field develops. The occurrence of breakers at a particular scale as well as the rate of surface turnover are well correlated w...

On Determining the Onset and Strength of Breaking for Deep Water Waves. Part I: Unforced Irrotational Wave Groups

Abstract Finding a robust threshold variable that determines the onset of breaking for deep water waves has been an elusive problem for many decades. Recent numerical studies of the unforced evolution of two-dimensional nonlinear wave trains have highlighted the complex evolution to recurrence or breaking, together with the fundamental role played by nonlinear intrawave group dynamics. In Part I of this paper the scope of two-dimensional nonlinear wave group calculations is extended by using a wave-group-following approach applied to a wider class of initial wave group geometries, with the primary goal of identifying the differences between evolution to recurrence and to breaking onset. Part II examines the additional influences of wind forcing and background shear on these evolution processes. The present investigation focuses on the long-term evolution of the maximum of the local energy density along wave groups. It contributes a more complete picture, both long-term and short-term, of the approach to b...

Performance of a Saturation-Based Dissipation-Rate Source Term in Modeling the Fetch-Limited Evolution of Wind Waves

Abstract A new formulation of the spectral dissipation source term Sds for wind-wave modeling applications is investigated. This new form of Sds is based on a threshold behavior of deep-water wave-breaking onset associated with nonlinear wave-group modulation. It is expressed in terms of the azimuth-integrated spectral saturation, resulting in a nonlinear dependence of dissipation rates on the local wave spectrum. Validation of the saturation-based Sds is made against wave field parameters derived from observations of fetch-limited wind-wave evolution. Simulations of fetch-limited growth are made with a numerical model featuring an exact nonlinear form of the wave–wave-interactions source term Snl. For reference, the performance of this saturation-based Sds is compared with the performance of the wave-dissipation source-term parameterization prescribed for the Wave Modeling Project (WAM) wind-wave model. Calculations of integral spectral parameters using the saturation-based model for Sds agree closely wi...

Wave breaking onset and strength for two-dimensional deep-water wave groups

The numerical study of J. Song & M. L. Banner (J. Phys. Oceanogr. vol. 32, 2002, p. 254) proposed a generic threshold parameter for predicting the onset of breaking within two-dimensional groups of deep-water gravity waves. Their parameter provides a non-dimensional measure of the wave energy convergence rate and geometrical steepening at the maximum of an evolving nonlinear wave group. They also suggested that this parameter might control the strength of breaking events. The present paper presents the results of a detailed laboratory observational study aimed at validating their proposals. For the breaking onset phase of this study, wave potential energy was measured at successive local envelope maxima of nonlinear deep-water wave groups propagating along a laboratory wave tank. These local maxima correspond alternately to wave group geometries with the group maximum occurring at an extreme carrier wave crest elevation, followed by an extreme carrier wave trough depression. As the nonlinearity increases, these crest and trough maxima can have markedly different local energy densities owing to the strong crest–trough asymmetry. The local total energy density was reconstituted from the potential energy measurements, and made dimensionless using the square of the local (carrier wave) wavenumber. A mean non-dimensional growth rate reflecting the rate of focusing of wave energy at the envelope maximum was obtained by smoothing the local fluctuations. For the cases of idealized nonlinear wave groups investigated, the observations confirmed the evolutionary trends of the modelling results of Song & Banner (2002) with regard to predicting breaking onset. The measurements confirmed the proposed common breaking threshold growth rate of 0.0014 ± 0.0001, as well as the predicted key evolution times: the time taken to reach the energy maximum for recurrence cases; and the time to reach the breaking threshold and then breaking onset, for breaking cases. After the initiation and subsequent cessation of breaking, the measured wave packet mean energy losses and loss rates associated with breaking produced an unexpected finding: the post-breaking mean wave energy did not decrease to the mean energy level corresponding to maximum recurrence, but remained significantly higher. Therefore, pre-breaking absolute wave energy or mean steepness do not appear to be the most fundamental determinants of post-breaking wave packet energy density. However, the dependence of the fractional breaking energy loss of wave packets on the parametric growth rate just before breaking onset proposed by Song & Banner (2002) was found to provide a plausible collapse to our laboratory data sets, within the experimental uncertainties. Further, when the results for the energy loss rate per unit width of breaking front were expressed in terms of a breaker strength parameter b multiplying the fifth power of the wave speed, it is found that b was also strongly