Kukulka Tobias

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Kukulka

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The effect of breaking waves on a coupled model of wind and ocean surface waves. Part II : growing seas

(American Meteorological Society, 2008-10) Kukulka, Tobias ; Hara, Tetsu

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.
Rapid mixed layer depening by the combination of Langmuir and shear instabilities : a case study

(American Meteorological Society, 2010-11) Kukulka, Tobias ; Plueddemann, Albert J. ; Trowbridge, John H. ; Sullivan, Peter P.

Langmuir circulation (LC) is a turbulent upper-ocean process driven by wind and surface waves that contributes significantly to the transport of momentum, heat, and mass in the oceanic surface layer. The authors have previously performed a direct comparison of large-eddy simulations and observations of the upper-ocean response to a wind event with rapid mixed layer deepening. The evolution of simulated crosswind velocity variance and spatial scales, as well as mixed layer deepening, was only consistent with observations if LC effects are included in the model. Based on an analysis of these validated simulations, in this study the fundamental differences in mixing between purely shear-driven turbulence and turbulence with LC are identified. In the former case, turbulent kinetic energy (TKE) production due to shear instabilities is largest near the surface, gradually decreasing to zero near the base of the mixed layer. This stands in contrast to the LC case in which at middepth range TKE production can be dominated by Stokes drift shear. Furthermore, the Eulerian mean vertical shear peaks near the base of the mixed layer so that TKE production by mean shear flow is elevated there. LC transports horizontal momentum efficiently downward leading to an along-wind velocity jet below LC downwelling regions at the base of the mixed layer. Locally enhanced vertical shear instabilities as a result of this jet efficiently erode the thermocline. In turn, enhanced breaking internal waves inject cold deep water into the mixed layer, where LC currents transport temperature perturbation advectively. Thus, LC and locally generated shear instabilities work intimately together to facilitate strongly the mixed layer deepening process.
Significance of Langmuir circulation in upper ocean mixing : comparison of observations and simulations

(American Geophysical Union, 2009-05-28) Kukulka, Tobias ; Plueddemann, Albert J. ; Trowbridge, John H. ; Sullivan, Peter P.

Representing upper ocean turbulence accurately in models remains a great challenge for improving weather and climate projections. Langmuir circulation (LC) is a turbulent process driven by wind and surface waves that plays a key role in transferring momentum, heat, and mass in the oceanic surface layer. We present a direct comparison between observations and large eddy simulations, based on the wave-averaged Navier-Stokes equation, of an LC growth event. The evolution of cross-wind velocity variance and spatial scales, as well as mixed layer deepening are only consistent with simulations if LC effects are included in the model. Our results offer a validation of the large eddy simulation approach to understanding LC dynamics, and demonstrate the importance of LC in ocean surface layer mixing.
The effect of breaking waves on a coupled model of wind and ocean surface waves. Part I : mature seas

(American Meteorological Society, 2008-10) Kukulka, Tobias ; Hara, Tetsu

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 k1/2 at low wavenumbers to k0 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.
The influence of crosswind tidal currents on Langmuir circulation in a shallow ocean

(American Geophysical Union, 2011-08-04) Kukulka, Tobias ; Plueddemann, Albert J. ; Trowbridge, John H. ; Sullivan, Peter P.

Langmuir circulation (LC) is a turbulent process driven by wind and surface waves that plays a key role in transferring momentum, heat, and mass in the oceanic surface layer. On the coastal shelves the largest-scale LC span the whole water column and thus couple the surface and bottom boundary layers and enhance turbulent mixing. Observations and large eddy simulations (LES) of a shallow coastal ocean demonstrate that these relatively large scale Langmuir cells are strongly influenced by crosswind tidal currents. Two mechanisms by which crosswind tidal shear may distort and disrupt Langmuir cells are proposed. The first mechanism involves cell shearing due to differential advection across the whole cell. For the second mechanism, middepth vertical LC currents advect sheared mean crosswind current, leading to the attraction of upwelling and downwelling regions, so that LC cells are unsustainable when both regions overlap. Scaling arguments indicate that LC cells are more susceptible to crosswind shear distortion for smaller LC surface velocity convergence and greater cell aspect ratio (vertical to horizontal LC scale), which is consistent with the results obtained from the observations and LES. These results imply that scaling of LC characteristics in a coastal ocean differs from that in the open ocean, which has important practical implications for parameterizing enhanced mixing due to LC.
Wind fetch and direction effects on Langmuir turbulence in a coastal ocean

(American Geophysical Union, 2022-04-20) Wang, Xingchi ; Kukulka, Tobias ; Plueddemann, Albert J.

Mixing processes in the upper ocean play a key role in transferring heat, momentum, and matter in the ocean. These mixing processes are significantly enhanced by wave-driven Langmuir turbulence (LT). Based on a paired analysis of observations and simulations, this study investigates wind fetch and direction effects on LT at a coastal site south of the island Martha’s Vineyard (MA, USA). Our results demonstrate that LT is strongly influenced by wind fetch and direction in coastal oceans, both of which contribute to controlling turbulent coastal transport processes. For northerly offshore winds, land limits the wind fetch and wave development, whereas southerly winds are associated with practically infinite fetch. Observed and simulated two-dimensional wave height spectra reveal persistent southerly swell and substantially more developed wind-driven waves from the south. For oblique offshore winds, waves develop more strongly in the alongshore direction with less limited fetch, resulting in significant wind and wave misalignments. Observations of coherent near-surface crosswind velocities indicate that LT is only present for sufficiently developed waves. The fetch-limited northerly winds inhibit wave developments and the formation of LT. In addition to limited fetch, strong wind–wave misalignments prevent LT development. Although energetic and persistent, swell waves do not substantially influence LT activity during the observation period because these relatively long swell waves are associated with small Stokes drift shear. These observational results agree well with turbulence-resolving large eddy simulations (LESs) based on the wave-averaged Navier–Stokes equation, validating the LES approach to coastal LT in the complex wind and wave conditions.
Nonlocal transport due to Langmuir circulation in a coastal ocean

(American Geophysical Union, 2012-12-11) Kukulka, Tobias ; Plueddemann, Albert J. ; Sullivan, Peter P.

We present observations and simulations of large-scale velocity structures associated with turbulent boundary layer dynamics of a coastal ocean. Special purpose acoustic Doppler current profiler measurements revealed that such structures were frequently present, in spite of complex coastal environmental conditions. Large eddy simulation results are only consistent with these observations if the Langmuir circulation (LC) effect due to wave-current interaction is included in the model. Thus, model results indicate that the observed large-scale velocity structures are due to LC. Based on these simulations, we examine the shift of energetics and transport from a local regime for purely shear-driven turbulence to a nonlocal regime for turbulence with LC due to coherent large-scale motions that span the whole water column. Without LC, turbulent kinetic energy (TKE) dissipation rates approximately balance TKE shear production, consistent with solid wall boundary layer turbulence. This stands in contrast to the LC case for which the vertical TKE transport plays a dominant role in the TKE balance. Conditional averages argue that large-scale LC coherent velocity structures extract only a small fraction of energy from the wavefield but receive most of their energy input from the Eulerian shear. The analysis of scalar fields and Lagrangian particles demonstrates that the vertical transport is significantly enhanced with LC but that small-scale mixing may be reduced. In the presence of LC, vertical scalar fluxes may be up gradient, violating a common assumption in oceanic boundary layer turbulence parameterizations.
Observations of turbulence in the ocean surface boundary layer : energetics and transport

(American Meteorological Society, 2009-05) Gerbi, Gregory P. ; Trowbridge, John H. ; Terray, Eugene A. ; Plueddemann, Albert J. ; Kukulka, Tobias

Observations of turbulent kinetic energy (TKE) dynamics in the ocean surface boundary layer are presented here and compared with results from previous observational, numerical, and analytic studies. As in previous studies, the dissipation rate of TKE is found to be higher in the wavy ocean surface boundary layer than it would be in a flow past a rigid boundary with similar stress and buoyancy forcing. Estimates of the terms in the turbulent kinetic energy equation indicate that, unlike in a flow past a rigid boundary, the dissipation rates cannot be balanced by local production terms, suggesting that the transport of TKE is important in the ocean surface boundary layer. A simple analytic model containing parameterizations of production, dissipation, and transport reproduces key features of the vertical profile of TKE, including enhancement near the surface. The effective turbulent diffusion coefficient for heat is larger than would be expected in a rigid-boundary boundary layer. This diffusion coefficient is predicted reasonably well by a model that contains the effects of shear production, buoyancy forcing, and transport of TKE (thought to be related to wave breaking). Neglect of buoyancy forcing or wave breaking in the parameterization results in poor predictions of turbulent diffusivity. Langmuir turbulence was detected concurrently with a fraction of the turbulence quantities reported here, but these times did not stand out as having significant differences from observations when Langmuir turbulence was not detected.
Inhibited upper ocean restratification in nonequilibrium swell conditions

(John Wiley & Sons, 2013-07-30) Kukulka, Tobias ; Plueddemann, Albert J. ; Sullivan, Peter P.

Diurnal restratification of the ocean surface boundary layer (OSBL) represents a competition between mixing of the OSBL and solar heating. Langmuir turbulence (LT) is a mixing process in the OSBL, driven by wind and surface waves, that transfers momentum, heat, and mass. Observations in nonequilibrium swell conditions reveal that the OSBL does not restratify despite low winds and strong solar radiation. Motivated by observations, we use large-eddy simulations of the wave-averaged Navier-Stokes equations to show that LT is capable of inhibiting diurnal restratification of the OSBL. Incoming heat is redistributed vertically by LT, forming a warmer OSBL with a nearly uniform temperature. The inhibition of restratification is not reproduced by two common Reynolds-averaged Navier-Stokes equation models, highlighting the importance of properly representing sea-state dependent LT dynamics in OSBL models.
Distribution of surface plastic debris in the eastern Pacific Ocean from an 11-Year data set

(American Chemical Society, 2014-04-07) Law, Kara L. ; Moret-Ferguson, Skye E. ; Goodwin, Deborah S. ; Zettler, Erik R. ; DeForce, Emelia A. ; Kukulka, Tobias ; Proskurowski, Giora

We present an extensive survey of floating plastic debris in the eastern North and South Pacific Oceans from more than 2500 plankton net tows conducted between 2001 and 2012. From these data we defined an accumulation zone (25 to 41°N, 130 to 180°W) in the North Pacific subtropical gyre that closely corresponds to centers of accumulation resulting from the convergence of ocean surface currents predicted by several oceanographic numerical models. Maximum plastic concentrations from individual surface net tows exceeded 106 pieces km–2, with concentrations decreasing with increasing distance from the predicted center of accumulation. Outside the North Pacific subtropical gyre the median plastic concentration was 0 pieces km–2. We were unable to detect a robust temporal trend in the data set, perhaps because of confounded spatial and temporal variability. Large spatiotemporal variability in plastic concentration causes order of magnitude differences in summary statistics calculated over short time periods or in limited geographic areas. Utilizing all available plankton net data collected in the eastern Pacific Ocean (17.4°S to 61.0°N; 85.0 to 180.0°W) since 1999, we estimated a minimum of 21 290 t of floating microplastic.
Langmuir turbulence controls on observed diurnal warm layer depths

(American Geophysical Union, 2023-05-24) Wang, Xingchi ; Kukulka, Tobias ; Farrar, J. Thomas ; Plueddemann, Albert J. ; Zippel, Seth F.

The turbulent ocean surface boundary layer (OSBL) shoals during daytime solar surface heating, developing a diurnal warm layer (DWL). The DWL significantly influences OSBL dynamics by trapping momentum and heat in a shallow near‐surface layer. Therefore, DWL depth is critical for understanding OSBL transport and ocean‐atmosphere coupling. A great challenge for determining DWL depth is considering wave‐driven Langmuir turbulence (LT), which increases vertical transport. This study investigates observations with moderate wind speeds (4–7 m/s at 10 m height) and swell waves for which breaking wave effects are less pronounced. By employing turbulence‐resolving large eddy simulation experiments that cover observed wind, wave, and heating conditions based on the wave‐averaged Craik‐Lebovich equation, we develop a DWL depth scaling unifying previous approaches. This scaling closely agrees with observed DWL depths from a year‐long mooring deployment in the subtropical North Atlantic, demonstrating the critical role of LT in determining DWL depth and OSBL dynamics.

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