Search Results

You are looking at 1 - 10 of 31 items for

  • Author or Editor: Tetsu Hara x
  • Refine by Access: All Content x
Clear All Modify Search
Tobias Kukulka and Tetsu Hara

Abstract

This is the second part of a two-part investigation of a coupled wind and wave model that includes the enhanced form drag of breaking waves. The model is based on the wave energy balance and the conservation of air-side momentum and energy. In Part I, coupled nonlinear advance–delay differential equations were derived, which govern the wave height spectrum, the distribution of breaking waves, and vertical air side profiles of the turbulent stress and wind speed. Numeric solutions were determined for mature seas. Here, numeric solutions for a wide range of wind and wave conditions are obtained, including young, strongly forced wind waves. Furthermore, the “spatial sheltering effect” is introduced so that smaller waves in airflow separation regions of breaking longer waves cannot be forced by the wind. The solutions strongly depend on the wave height curvature spectrum at high wavenumbers (the “threshold saturation level”). As the threshold saturation level is reduced, the effect of breaking waves becomes stronger. For young strongly forced waves (laboratory conditions), breaking waves close to the spectral peak dominate the wind input and previous solutions of a model with only input to breaking waves are recovered. Model results of the normalized roughness length are generally consistent with previous laboratory and field measurements. For field conditions, the wind stress depends sensitively on the wave height spectrum. The spatial sheltering may modify the number of breaking shorter waves, in particular, for younger seas.

Full access
Tobias Kukulka and Tetsu Hara

Abstract

This is the first of a two-part investigation of a coupled wind and wave model that includes the enhanced form drag of breaking waves. In Part I here the model is developed and applied to mature seas. Part II explores the solutions in a wide range of wind and wave conditions, including growing seas. Breaking and nonbreaking waves induce air-side fluxes of momentum and energy above the air–sea interface. By balancing air-side momentum and energy and by conserving wave energy, coupled nonlinear advance–delay differential equations are derived, which govern simultaneously the wave and wind field. The system of equations is closed by introducing a relation between the wave height spectrum and wave dissipation due to breaking. The wave dissipation is proportional to nonlinear wave interactions, if the wave curvature spectrum is below the “threshold saturation level.” Above this threshold the wave dissipation rapidly increases so that the wave height spectrum is limited. The coupled model is applied to mature wind-driven seas for which the wind forcing only occurs in the equilibrium range away from the spectral peak. Modeled wave height curvature spectra as functions of wavenumber k are consistent with observations and transition from k 1/2 at low wavenumbers to k 0 at high wavenumbers. Breaking waves affect only weakly the wave height spectrum. Furthermore, the wind input to waves is dominated by nonbreaking waves closer to the spectral peak. Shorter breaking waves, however, can support a significant fraction, which increases with wind speed, of the total air–sea momentum flux.

Full access
Erik J. Bock and Tetsu Hara

Abstract

A description of a new scanning laser slope gauge (SLSG) is given and the results obtained from both laboratory wind-wave tank and field measurements are presented. The device relies on the measurements of two components of surface slope to compute spatial and temporal lags that are used to estimate the full three-dimensional slope spectrum. The device is capable of resolving frequencies up to 34.7 Hz and wavelengths in the range between 7.9 × 10−3 and 3.08 × 10−1 m. The technique makes use of a two-dimensional laser scanner that samples the perimeter of a circle of 0.154-m diameter (an unfilled aperture). Both laboratory and field results indicate the device is well suited to measure the full three-dimensional spectra of capillary-gravity waves and is capable of providing ground-truthing measurements for the verification of remotely sensed ocean surface features.

Full access
Tetsu Hara and Andrey V. Karachintsev

Abstract

Nonlinearity and directionality of an evolving open-ocean surface wave field are investigated under increasing wind forcing. In addition to the frequency wave elevation spectrum, the frequency wave slope spectrum, the bicoherence of the wave elevation time series, and the peak wavenumber at a given frequency estimated by the maximum likelihood method are examined. As the wave field matures, an increasing portion of the high-frequency components of the wave elevation spectrum becomes phase correlated with the dominant wave component. This observation clearly suggests that the contribution to the frequency spectrum from the higher harmonics generated by steep dominant waves becomes increasingly important relative to the contribution from free waves that propagate at their own phase speed predicted by the dispersion relation. The observation therefore invalidates the common assumption that an ocean surface wave spectrum is a superposition of linear surface wave components of different frequencies. In addition, close examination of the frequency slope spectra and the peak wavenumber estimates suggests that the observed phase-coupled modes are generated by short-crested two-dimensional dominant wave patterns rather than by long-crested dominant waves.

Full access
Tetsu Hara and Stephen E. Belcher

Abstract

The mean wind profile and the Charnock coefficient, or drag coefficient, over mature seas are investigated. A model of the wave boundary layer, which consists of the lowest part of the atmospheric boundary layer that is influenced by surface waves, is developed based on the conservation of momentum and energy. Energy conservation is cast as a bulk constraint, integrated across the depth of the wave boundary layer, and the turbulence closure is achieved by parameterizing the dissipation rate of turbulent kinetic energy. Momentum conservation is accounted for by using the analytical model of the equilibrium surface wave spectra developed by Hara and Belcher. This approach allows analytical expressions of the Charnock coefficient to be obtained and the results to be examined in terms of key nondimensional parameters. In particular, simple expressions are obtained in the asymptotic limit at which effects of viscosity and surface tension are small and the majority of the stress is supported by wave drag. This analytical model allows us to identify the conditions necessary for the Charnock coefficient to be a true constant, an assumption routinely made in existing bulk parameterizations.

Full access
Tetsu Hara and Peter P. Sullivan

Abstract

Accurate predictions of the sea state–dependent air–sea momentum flux require a thorough understanding of the wave boundary layer turbulence over surface waves. A set of momentum and energy equations is derived to formulate and analyze wave boundary layer turbulence. The equations are written in wave-following coordinates, and all variables are decomposed into horizontal mean, wave fluctuation, and turbulent fluctuation. The formulation defines the wave-induced stress as a sum of the wave fluctuation stress (because of the fluctuating velocity components) and a pressure stress (pressure acting on a tilted surface). The formulations can be constructed with different choices of mapping. Next, a large-eddy simulation result for wind over a sinusoidal wave train under a strongly forced condition is analyzed using the proposed formulation. The result clarifies how surface waves increase the effective roughness length and the drag coefficient. Specifically, the enhanced wave-induced stress close to the water surface reduces the turbulent stress (satisfying the momentum budget). The reduced turbulent stress is correlated with the reduced viscous dissipation rate of the turbulent kinetic energy. The latter is balanced by the reduced mean wind shear (satisfying the energy budget), which causes the equivalent surface roughness to increase. Interestingly, there is a small region farther above where the turbulent stress, dissipation rate, and mean wind shear are all enhanced. The observed strong correlation between the turbulent stress and the dissipation rate suggests that existing turbulence closure models that parameterize the latter based on the former are reasonably accurate.

Full access
Nobuhiro Suzuki, Tetsu Hara, and Peter P. Sullivan

Abstract

A neutrally stratified turbulent airflow over a very young sea surface at a high-wind condition was investigated using large-eddy simulations. In such a state, the dominant drag at the sea surface occurs over breaking waves, and the relationship between the dominant drag and local instantaneous surface wind is highly stochastic and anisotropic. To model such a relationship, a bottom boundary stress parameterization was proposed for the very young sea surface resolving individual breakers. This parameterization was compared to the commonly used parameterization for isotropic surfaces. Over both the young sea and isotropic surfaces, the main near-surface turbulence structure was wall-attached, large-scale, quasi-streamwise vortices. Over the young sea surface, these vortices were more intense, and the near-surface mean velocity gradient was smaller. This is because the isotropic surface weakens the swirling motions of the vortices by spanwise drag. In contrast, the young sea surface exerts little spanwise drag and develops more intense vortices, resulting in greater turbulence and mixing. The vigorous turbulence decreases the mean velocity gradient in the roughness sublayer below the logarithmic layer. Thus, the enhancement of the air–sea momentum flux (drag coefficient) due to breaking waves is caused not only by the streamwise form drag over individual breakers but also by the enhanced vortices. Furthermore, contrary to an assumption used in existing wave boundary layer models, the wave effect may extend as high as 10–20 times the breaking wave height.

Full access
Yalin Fan, Isaac Ginis, and Tetsu Hara

Abstract

In this paper, the wind–wave–current interaction mechanisms in tropical cyclones and their effect on the surface wave and ocean responses are investigated through a set of numerical experiments. The key element of the authors’ modeling approach is the air–sea interface model, which consists of a wave boundary layer model and an air–sea momentum flux budget model. The results show that the time and spatial variations in the surface wave field, as well as the wave–current interaction, significantly reduce momentum flux into the currents in the right rear quadrant of the hurricane. The reduction of the momentum flux into the ocean consequently reduces the magnitude of the subsurface current and sea surface temperature cooling to the right of the hurricane track and the rate of upwelling/downwelling in the thermocline. During wind–wave–current interaction, the momentum flux into the ocean is mainly affected by reducing the wind speed relative to currents, whereas the wave field is mostly affected by refraction due to the spatially varying currents. In the area where the current is strongly and roughly aligned with wave propagation direction, the wave spectrum of longer waves is reduced, the peak frequency is shifted to a higher frequency, and the angular distribution of the wave energy is widened.

Full access
Il-Ju Moon, Isaac Ginis, and Tetsu Hara

Abstract

Effects of new drag coefficient (Cd) parameterizations on WAVEWATCH III (WW3) model surface wave simulations are investigated. The new parameterizations are based on a coupled wind–wave model (CWW) and a wave tank experiment, and yields reduced Cd at high wind speeds. Numerical experiments for uniform winds and Hurricane Katrina (2005) indicate that the original Cd parameterization used in WW3 overestimates drag at high wind speeds compared to recent observational, theoretical, and numerical modeling results. Comparisons with buoy measurements during Hurricane Katrina demonstrate that WW3 simulations with the new Cd parameterizations yield more accurate significant wave heights compared to simulations with the original Cd parameterization, provided that accurate high-resolution wind forcing fields are used.

Full access
Tobias Kukulka, Tetsu Hara, and Stephen E. Belcher

Abstract

Under high-wind conditions, breaking surface waves likely play an important role in the air–sea momentum flux. A coupled wind–wave model is developed based on the assumption that in the equilibrium range of surface wave spectra the wind stress is dominated by the form drag of breaking waves. By conserving both momentum and energy in the air and also imposing the wave energy balance, coupled equations are derived governing the turbulent stress, wind speed, and the breaking-wave distribution (total breaking crest length per unit surface area as a function of wavenumber). It is assumed that smaller-scale breaking waves are sheltered from wind forcing if they are in airflow separation regions of longer breaking waves (spatial sheltering effect). Without this spatial sheltering, exact analytic solutions are obtained; with spatial sheltering asymptotic solutions for small- and large-scale breakers are derived. In both cases, the breaking-wave distribution approaches a constant value for large wavenumbers (small-scale breakers). For low wavenumbers, the breaking-wave distribution strongly depends on wind forcing. If the equilibrium range model is extended to the spectral peak, the model yields the normalized roughness length (Charnock coefficient) of growing seas, which increases with wave age and is roughly consistent with earlier laboratory observations. However, the model does not yield physical solutions beyond a critical wave age, implying that the wind input to the wave field cannot be dominated by breaking waves at all wavenumbers for developed seas (including field conditions).

Full access