Kimmo K. Kahma

Estimates of Kinetic Energy Dissipation under Breaking Waves

Abstract The dissipation of kinetic energy at the surface of natural water bodies has important consequences for many Physical and biochemical processes including wave dynamics, gas transfer, mixing of nutrients and pollutants, and photosynthetic efficiency of plankton. Measurements of dissipation close to the surface obtained in a large lake under conditions of strong wind forcing are presented that show a layer of enhanced dissipation exceeding wall layer values by one or two orders of magnitude. The authors propose a scaling for the rate of dissipation based on wind and wave parameters, and conclude that the dissipation rate under breaking waves depends on depth, to varying degrees, in three stages. Very near the surface, within one significant height, the dissipation rate is high (an order of magnitude greater than that predicted by wall layer theory) and roughly constant. Below this is an intermediate region where the dissipation decays as z−2. The thickness of this layer (relative to the significant...

Reconciling Discrepancies in the Observed Growth of Wind-generated Waves

Abstract Spectra from various wave-growth experiments have been collected into a database, and the data have been reanalyzed to explain the differences in the observed growth rates. For one of the experiments (Joint North Sea Wave Project: JONSWAP), the extensive wind data allowed the authors to perform a detailed analysis of the time history of the wind at a point moving with the group velocity of the peak of the wave spectrum. Using the average of the wind speed at this moving point, removing spectra that according to this wind estimate were not measured in steady or increasing wind, and taking into account the atmospheric stratification, the previously large discrepancy in the growth rates between JONSWAP and two other experiments (Bothnian Sea, Lake Ontario) was removed. The analysis revealed significant differences between the spectra in different groups. Peak enhancement was higher in the Bothnian Sea data than in the other datasets at the same dimensionless fetch. Equally high peak enhancement coul...

A Study of the Growth of the Wave Spectrum with Fetch

Abstract The development of the wave spectrum with fetch in a steady wind has been studied with a line of consecutive wave buoys in the Bothnian Sea in 1976 and 1979. The relationship that was found between dimensionless peak frequency ωm (=ωmU10/g) and dimensionless fetch X (=gX/U102) was close to previous observations. The dimensionless energy ¯σ2 (=g2ω2/U104) was about twice that observed in the JONSWAP experiment. In the saturation range when ¯ω>4 the frequency spectrum was found to have the form S(ω) = αuU10gω−4 where αu=4.5 × 10−3, independent of the dimensionless fetch X. The deviation from the Phillips −5 power law could not be explained by the influence of currents or finite depth. Near the peak, the spectra were satisfactorily described by the JONSWAP spectrum; above frequencies twice the peak frequency the difference becomes significant. A qualitative explanation is proposed for the dependence of the spectrum on the wind speed in the saturation range. The semi-theoretical method of Longuet-Hi...

A case study of air-sea interaction during swell conditions

Air-sea interaction data from a situation with pronounced unidirectional swell have been analyzed. Measurements of turbulence at three levels (10, 18, and 26 m above mean sea level) together with directional wave buoy data from the site Ostergarnsholm in the Baltic Sea were used. The situation, which lasted for ∼48 hours, appeared in the aftermath of a gale. The wind direction during the swell situation turned slowly within a 90° sector. Both during the gale phase and the swell phase the over-water fetch was >150 km. The wind speed during the swell phase was typically 4 m s−1. During the swell phase a wind maximum near or below the lowest wind speed measuring level 10 m was observed. The net momentum flux was very small, resulting in CD values ∼0.7 × 10−3. Throughout the lowest 26 m, covered by the tower measurements, turbulence intensities in all three components remained high despite the low value of the kinematic momentum flux -u′w′¯ resulting in a reduction of the correlation coefficient for the longitudinal and vertical velocity from its typical value around −0.35 to between −0.2 and 0 (and with some positive values at the higher measuring levels), appearing abruptly at wave age c0/U10 equal to 1.2. Turbulence spectra of the horizontal components were shown not to scale with height above the water surface, in contrast to vertical velocity spectra for which such a variation was observed in the low-frequency range. In addition, spectral peaks in the horizontal wind spectra were found at a frequency as low as 10−3 Hz. From a comparison with results from a previous study it was concluded that this turbulence is of the “inactive” kind, being brought down from the upper parts of the boundary layer by pressure transport.

On momentum flux and velocity spectra over waves

Data from a research tower in Lake Ontario are used to study the validity of Monin--Obukhov scaling in the marine atmospheric boundary layer under various wave conditions. It is found that over pure wind seas, the velocity spectra and cospectra follow established universal scaling laws. However, in the presence of swells outrunning weak winds, velocity spectra and cospectra no longer satisfy universal spectral shapes. Here, Monin–Obukhov similarity theory, and the classical logarithmic boundary layers, are no longer valid. It is further shown that, in the presence of such swells, the momentum flux can be significantly modified in comparison to pure wind sea values. The implications of these findings for bulk flux estimations and on the inertial dissipation method for calculating fluxes are discussed.

Wave-Induced Wind in the Marine Boundary Layer

Recent field observations and large-eddy simulations have shown that the impact of fast swell on the marine atmospheric boundary layer (MABL) might be stronger than previously assumed. For low to moderate winds blowing in the same direction as the waves, swell propagates faster than the mean wind. The momentum flux above the sea surface will then have two major components: the turbulent shear stress, directed downward, and the swell-induced stress, directed upward. For sufficiently high wave age values, the wave-induced component becomes increasingly dominant, and the total momentum flux will be directed into the atmosphere. Recent field measurements have shown that this upward momentum transfer from the ocean into the atmosphere has a considerable impact on the surface layer flow dynamics and on the turbulence structure of the overall MABL. The vertical wind profile will no longer exhibit a logarithmic shape because an acceleration of the airflow near the surface will take place, generating a low-level wave-driven wind maximum (a wind jet). As waves propagate away from their generation area as swell, some of the wave momentum will be returned to the atmosphere in the form of wave-driven winds. A model that qualitatively reproduces the wave-following atmospheric flow and the wave-generated wind maximum, as seen from measurements, is proposed. The model assumes a stationary momentum and turbulent kinetic energy balance and uses the dampening of the waves at the surface to describe the momentum flux from the waves to the atmosphere. In this study, simultaneous observations of wind profiles, turbulent fluxes, and wave spectra during swell events are presented and compared with the model. In the absence of an established model for the linear damping ratio during swell conditions, the model is combined with observations to estimate the wave damping. For the cases in which the observations showed a pronounced swell signal and almost no wind waves, the agreement between observed and modeled wind profiles is remarkably good. The resulting attenuation length is found to be relatively short, which suggests that the estimated damping ratios are too large. The authors attribute this, at least partly, to processes not accounted for by the model, such as the existence of an atmospheric background wind. In the model, this extra momentum must be supplied by the waves in terms of a larger damping ratio.

The Atmospheric Boundary Layer during Swell: A Field Study and Interpretation of the Turbulent Kinetic Energy Budget for High Wave Ages

Analysis of the turbulent kinetic energy (TKE) budget for five slightly unstable cases with swell has been performed based on measurements of mechanical production, buoyancy production, turbulent transport, and dissipation at five levels over the sea, from 2.5 to 26 m. The time rate of change and advection of TKE were found to be small, so the TKE residual is interpreted as an estimate of the pressure transport term (Tp). In two cases with high wave age, the Tp term is a gain at all heights. For three cases with smaller wave age, Tp is a loss in the TKE budget below 5–10 m and a gain for greater heights, where the decrease is exponential, thus showing the combined effects of swell waves and a range of waves traveling slower than the wind. The TKE budget for a case with growing sea but similar wind speed and stability as some of the swell cases has Tp close to zero at all heights. It is shown that the observed characteristic wind profile with either a low-level maximum in the 5–10-m range or a distinct ‘‘knee’’ at that height is an effect of the Tp term.

Observational Study of Marine Atmospheric Boundary Layer Characteristics during Swell

By combining simultaneous data from an instrumented Air–Sea Interaction Spar (ASIS) buoy and a 30-m tower, profiles of wind and turbulence characteristics have been obtained at several heights from about 1 to 30 m above the water surface during swell conditions. Five cases formed as averages over time periods ranging from 2.5 to 9.5 h, representing quasi-steady conditions, have been selected. They represent a range of typical wave age and include wind-following swell cases and cross-swell cases. For relatively large wave age, the wind profile exhibits a well-defined maximum in the height range 5–10 m; for more modest wave age, this maximum turns into a sharp ‘‘knee’’ in the wind profile. Below the maximum (or knee), the wind increases rapidly with height; above that point the wind is very nearly constant up to the highest measuring level on the tower, 30 m. Analysis of balloon data from one day with swell indicates that the layer with constant wind in fact extends to the top of the boundary layer, in this case ;200 m. Analysis of the complete swell dataset from the 45 days of the 2003 Baltic Swell experiment shows that the results concerning wind profile shape obtained from the selected cases are generally valid in this experiment. Analysis of the nondimensional wind profile fm shows that Monin–Obukhov scaling is not valid during swell. Wind and turbulence characteristics are found not to vary to a significant degree with the wind/swell angle within the range of angles encountered, 6908.

Shore protection manual's wave prediction reviewed

Empirical steady-state wave prediction methods given in the 1984 version of the Shore Protection Manual (SPM) are compared with measured wave data and with three other wave prediction formulas including the one used in 1977 and earlier versions of the SPM. Fetch-limited wave data and overwater wind data from several sources comprise the data set. The other wave prediction formulas are those of Sverdrup-Munk-Bretschneider, Jonswap and Donelan. Results indicate that the 1984 version of the SPM, which uses an adjusted wind speed factor based on friction velocity, tends to overpredict wave height and period and, statistically, is the poorest predictor of the four methods tested. Use of the adjusted wind speed factor and other wind modifications are discussed.

Apparatus for Atmospheric Surface Layer Measurements over Waves

Abstract This paper describes an apparatus developed for simultaneously measuring water elevation and static and dynamic pressure, momentum, and heat fluxes above waves close to the interface. The apparatus was used successfully at the Lake Ontario wave research tower of the Canada Centre for Inland Waters. The principle and purpose of the various sensors used, calibration procedures, and data-gathering processes are described. Simultaneous measurements of the atmospheric surface layer’s physical quantities are presented. All the quantities necessary to close the kinetic energy budget in the atmospheric surface layer have been measured.