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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.

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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.

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Chin-Hoh Moeng
and
Peter P. Sullivan

Abstract

Planetary boundary layer (PBL) flows are known to exhibit fundamental differences depending on the relative combination of wind shear and buoyancy forces. These differences are not unexpected in that shear instabilities occur locally, while buoyancy force sets up vigorous thermals, which result in nonlocal transport of heat and momentum. At the same time, these two forces can act together to modify the flow field. In this study, four large-eddy simulations (LESs) spanning the shear and buoyancy flow regimes were generated; two correspond to the extreme cases of shear and buoyancy-driven PBLs, while the other two represent intermediate PBLs where both forces are important. The extreme cases are used to highlight and quantify the basic differences between shear and convective PBLs in 1) flow structures, 2) overall statistics, and 3) turbulent kinetic energy (TKE) budget distributions. Results from the two intermediate LES cases are used to develop and verify a velocity scaling and a TKE budget model, which are proposed for the intermediate PBL. The velocity variances and the variance fluxes (i.e., third moments) normalized by this velocity scaling are shown to become quantities on the order of one, and to lie mostly between those of the two extreme PBL cases. The proposed TKE budget model is shown to adequately reproduce the profiles of the TKE budget terms and the TKE.

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Dmitrii V. Mironov
and
Peter P. Sullivan

Abstract

The effect of horizontal temperature heterogeneity of the underlying surface on the turbulence structure and mixing intensity in the stably stratified boundary layer (SBL) is analyzed using large-eddy simulation (LES). Idealized LESs of flows driven by fixed winds and homogeneous and heterogeneous surface temperatures are compared. The LES data are used to compute statistical moments, to estimate budgets of the turbulence kinetic energy (TKE), of the temperature variance and of the temperature flux, and to assess the relative importance of various terms in maintaining the budgets. Unlike most previous studies, the LES-based second-moment budgets are estimated with due regard for the subgrid-scale contributions.

The SBL over a heterogeneous surface is more turbulent with larger variances (and TKE), is better vertically mixed, and is deeper compared to its homogeneous counterpart. The most striking difference between the cases is exhibited in the temperature variance and its budget. Because of surface heterogeneity, the turbulent transport term (divergence of the third-order moment) not only redistributes the temperature variance vertically but is a net gain. The increase in the temperature variance near the heterogeneous surface explains the reduced magnitude of the downward buoyancy flux and the ensuing increase in TKE that leads to more vigorous mixing. Analysis of the temperature flux budget shows that the transport term contributes to net production/destruction. Importantly, the role of the third-order transport cannot be elucidated if the budgets are computed based solely on resolved-scale fields. Implications for modeling (parameterizing) the SBL over thermally heterogeneous surfaces are discussed.

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Nobuhiro Suzuki
,
Tetsu Hara
, and
Peter P. Sullivan

Abstract

Large-eddy simulation (LES) is used to investigate how dominant breaking waves in the ocean under hurricane-force winds affect the drag and near-surface airflow turbulence. The LES explicitly resolves the wake turbulence produced by dominant-scale breakers. Effects of unresolved roughness such as short breakers, nonbreaking waves, and sea foam are modeled as the subgrid-scale drag. Compared to the laboratory conditions previously studied using the same method, dominant-scale breakers in open-ocean conditions are less frequent, and the subgrid-scale drag is more significant. Nevertheless, dominant-scale breakers are more fully exposed to high winds and produce more intense wakes individually. As a result, they support a large portion of the total drag and significantly influence the turbulence for many ocean conditions that are likely to occur. The intense wake turbulence is characterized by flow separation, upward bursts of wind, and upward flux of the turbulent kinetic energy (TKE), all of which may influence sea spray dispersion. Similarly to the findings in the laboratory conditions, high production of wake turbulence shortcuts the inertial energy cascade, causes high TKE dissipation, and contributes to the reduction of the drag coefficient. The results also indicate that if the drag coefficient decreases with increasing wind at very high winds, as some recent observations suggest, then the unresolved roughness must also decrease.

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Nobuhiro Suzuki
,
Tetsu Hara
, and
Peter P. Sullivan

Abstract

The effects of breaking waves on near-surface wind turbulence and drag coefficient are investigated using large-eddy simulation. The impact of intermittent and transient wave breaking events (over a range of scales) is modeled as localized form drag, which generates airflow separation bubbles downstream. The simulations are performed for very young sea conditions under high winds, comparable to previous laboratory experiments in hurricane-strength winds. The results for the drag coefficient in high winds range between about 0.002 and 0.003. In such conditions more than 90% of the total air–sea momentum flux is due to the form drag of breakers; that is, the contributions of the nonbreaking wave form drag and the surface viscous stress are small. Detailed analysis shows that the breaker form drag impedes the shear production of the turbulent kinetic energy (TKE) near the surface and, instead, produces a large amount of small-scale wake turbulence by transferring energy from large-scale motions (such as mean wind and gusts). This process shortcuts the inertial energy cascade and results in large TKE dissipation (integrated over the surface layer) normalized by friction velocity cubed. Consequently, the large production of wake turbulence by breakers in high winds results in the small drag coefficient obtained in this study. The results also suggest that common parameterizations for the mean wind profile and the TKE dissipation inside the wave boundary layer, used in previous Reynolds-averaged Navier–Stokes models, may not be valid.

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Peter G. Hess
and
Donal O'sullivan

Abstract

The two phases of the quasi-biennial oscillation in ozone are simulated using winds generated by a three-dimensional mechanistic stratospheric model input into an off-line ozone transport model. Ozone chemistry is parameterized in the off-line model. The mechanistic model is run with either easterly or westerly zonal winds in the lower equatorial stratosphere, so as to model the equatorial wind structure during the two phases of the equatorial quasi-biennial oscillation (QBO). When forcing is applied at the lower model boundary in the winter hemisphere, the mechanistic model simulates differences in the global circulation between the easterly and westerly phases of the QBO. The resulting modeled total ozone is larger in the polar regions during the easterly phase of the QBO than during the westerly phase, in agreement with observations. Using the residual-mean formalism the authors find that the difference in the modeled budget of ozone between the two phases of the QBO is due to a modulation of the extratropical planetary wave structure, and consequently the ozone transport, by the equatorial zonal-mean winds. Differences in the residual-mean velocities between the two phases of the QBO explain most of the differences in the ozone transport.

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Kirsty Hanley
,
Stephen Belcher
, and
Peter Sullivan
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Peter P. Sullivan
and
James C. McWilliams

Abstract

Imagery and numerical modeling show an abundance of submesoscale oceanic eddies in the upper ocean. Large-eddy simulation (LES) is used to elucidate eddy impacts on the atmospheric boundary layer (ABL) forced by winds, convection, and an eddy with varying radius; the maximum azimuthal eddy speed is 1 m s−1. Simulations span the unstable regime −1/L = [0, ∞], where L is the Monin–Obukhov (M–O) stability parameter. A linearized Ekman model and the LES couple ABL winds to an eddy through rough-wall M–O boundary conditions. The eddy currents cause a surface stress anomaly that induces Ekman pumping in a dipole horizontal pattern. The dipole is understood as a consequence of surface winds aligned or opposing surface currents. In free convection a vigorous updraft is found above the eddy center and persists over the ABL depth. Heterogeneity in surface temperature flux is responsible for the full ABL impact. With winds and convection, current stress coupling generates a dipole in surface temperature flux even with constant sea surface temperature. Wind, pressure, and temperature anomalies are sensitive to an eddy under light winds. The eddy impact on ABL secondary circulations is on the order of the convective velocity scale w * but grows with increasing current speed, decreasing wind, or increasing convection. Flow past an isolated eddy develops a coherent ABL “wake” and secondary circulations for at least five eddy radii downwind. Kinetic energy exchanges by wind work indicate an eddy-killing effect on the oceanic eddy current, but only a spatial rearrangement of the atmospheric wind work.

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Peter P. Sullivan
and
Edward G. Patton
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