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## 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.

## 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.

## Abstract

Upper-ocean turbulence results from a complex set of interactions between submesoscale turbulence and local boundary layer processes. The interaction between larger-scale currents and turbulent fluctuations is two-way: large-scale shearing motions generate turbulence, and the resulting coherent turbulent fluxes of momentum and buoyancy feed back onto the larger flow. Here we examine the evolution and role of turbulence in the intensification, instability, arrest, and decay (i.e., the life cycle) of a dense filament undergoing frontogenesis in the upper-ocean boundary layer, i.e., cold filament frontogenesis (CFF). This phenomenon is examined in large-eddy simulations (LES) with resolved turbulent motions in large horizontal domains using 10^{9} grid points. The boundary layer turbulence is generated by surface buoyancy loss (cooling flux) and is allowed to freely interact with an initially imposed cold filament, and the evolution is followed through the frontal life cycle. Two control parameters are explored: the initial frontal strength *M*
^{2} = ∂*
_{x}b* and the surface flux

## Abstract

Upper-ocean turbulence results from a complex set of interactions between submesoscale turbulence and local boundary layer processes. The interaction between larger-scale currents and turbulent fluctuations is two-way: large-scale shearing motions generate turbulence, and the resulting coherent turbulent fluxes of momentum and buoyancy feed back onto the larger flow. Here we examine the evolution and role of turbulence in the intensification, instability, arrest, and decay (i.e., the life cycle) of a dense filament undergoing frontogenesis in the upper-ocean boundary layer, i.e., cold filament frontogenesis (CFF). This phenomenon is examined in large-eddy simulations (LES) with resolved turbulent motions in large horizontal domains using 10^{9} grid points. The boundary layer turbulence is generated by surface buoyancy loss (cooling flux) and is allowed to freely interact with an initially imposed cold filament, and the evolution is followed through the frontal life cycle. Two control parameters are explored: the initial frontal strength *M*
^{2} = ∂*
_{x}b* and the surface flux

## 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.

## 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.

## 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.

## 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.

## Abstract

Direct numerical simulations (DNS) of turbulent Couette flow are combined with Lagrangian point-particle tracking to investigate the effects of a dispersed phase on bulk passive heat transport when the two phases can exchange both momentum and sensible heat. The idealized setup allows a fixed number of particles, without the influence of gravity, to be transported by carrier-phase motions across the mean velocity and temperature gradients that exist between the solid boundaries of turbulent Couette flow. In this way, the setup serves as a model of spray in a shear-dominated layer in the immediate vicinity of the water surface and provides insight into the ability of spray to enhance sensible heat fluxes. The authors find that the dispersed phase contributes a relatively large amount of vertical heat transport and increases the total heat flux across the domain by 25% or greater. Particles that accumulate in regions associated with wall-normal ejections efficiently carry heat across the channel. Furthermore, the authors find that the relative contribution of the dispersed-phase heat flux becomes larger with Reynolds number, suggesting an importance at atmospheric scales.

## Abstract

Direct numerical simulations (DNS) of turbulent Couette flow are combined with Lagrangian point-particle tracking to investigate the effects of a dispersed phase on bulk passive heat transport when the two phases can exchange both momentum and sensible heat. The idealized setup allows a fixed number of particles, without the influence of gravity, to be transported by carrier-phase motions across the mean velocity and temperature gradients that exist between the solid boundaries of turbulent Couette flow. In this way, the setup serves as a model of spray in a shear-dominated layer in the immediate vicinity of the water surface and provides insight into the ability of spray to enhance sensible heat fluxes. The authors find that the dispersed phase contributes a relatively large amount of vertical heat transport and increases the total heat flux across the domain by 25% or greater. Particles that accumulate in regions associated with wall-normal ejections efficiently carry heat across the channel. Furthermore, the authors find that the relative contribution of the dispersed-phase heat flux becomes larger with Reynolds number, suggesting an importance at atmospheric scales.

## Abstract

A massively parallel large-eddy simulation (LES) code for planetary boundary layers (PBLs) that utilizes pseudospectral differencing in horizontal planes and solves an elliptic pressure equation is described. As an application, this code is used to examine the numerical convergence of the three-dimensional time-dependent simulations of a weakly sheared daytime convective PBL on meshes varying from 32^{3} to 1024^{3} grid points. Based on the variation of the second-order statistics, energy spectra, and entrainment statistics, LES solutions converge provided there is adequate separation between the energy-containing eddies and those near the filter cutoff scale. For the convective PBL studied, the majority of the low-order moment statistics (means, variances, and fluxes) become grid independent when the ratio *z _{i}
*/(

*C*Δ

_{s}*) > 310, where*

_{f}*z*is the boundary layer height, Δ

_{i}*is the filter cutoff scale, and*

_{f}*C*is the Smagorinsky constant. In this regime, the spectra show clear Kolmogorov inertial subrange scaling. The bulk entrainment rate determined from the time variation of the boundary layer height

_{s}*w*=

_{e}*dz*/

_{i}*dt*is a sensitive measure of the LES solution convergence;

*w*becomes grid independent when the vertical grid resolution is able to capture both the mean structure of the overlying inversion and the turbulence. For all mesh resolutions used, the vertical temperature flux profile varies linearly over the interior of the boundary layer and the minimum temperature flux is approximately −0.2 of the surface heat flux. Thus, these metrics are inadequate measures of solution convergence. The variation of the vertical velocity skewness and third-order moments expose the LES’s sensitivity to grid resolution.

_{e}## Abstract

A massively parallel large-eddy simulation (LES) code for planetary boundary layers (PBLs) that utilizes pseudospectral differencing in horizontal planes and solves an elliptic pressure equation is described. As an application, this code is used to examine the numerical convergence of the three-dimensional time-dependent simulations of a weakly sheared daytime convective PBL on meshes varying from 32^{3} to 1024^{3} grid points. Based on the variation of the second-order statistics, energy spectra, and entrainment statistics, LES solutions converge provided there is adequate separation between the energy-containing eddies and those near the filter cutoff scale. For the convective PBL studied, the majority of the low-order moment statistics (means, variances, and fluxes) become grid independent when the ratio *z _{i}
*/(

*C*Δ

_{s}*) > 310, where*

_{f}*z*is the boundary layer height, Δ

_{i}*is the filter cutoff scale, and*

_{f}*C*is the Smagorinsky constant. In this regime, the spectra show clear Kolmogorov inertial subrange scaling. The bulk entrainment rate determined from the time variation of the boundary layer height

_{s}*w*=

_{e}*dz*/

_{i}*dt*is a sensitive measure of the LES solution convergence;

*w*becomes grid independent when the vertical grid resolution is able to capture both the mean structure of the overlying inversion and the turbulence. For all mesh resolutions used, the vertical temperature flux profile varies linearly over the interior of the boundary layer and the minimum temperature flux is approximately −0.2 of the surface heat flux. Thus, these metrics are inadequate measures of solution convergence. The variation of the vertical velocity skewness and third-order moments expose the LES’s sensitivity to grid resolution.

_{e}## 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.

## 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.

## Abstract

The characteristics of wind profiles in a neutral atmospheric boundary layer and their dependence on the geostrophic wind speed *U*
_{
g
}, Coriolis parameter *f*, and surface roughness length *z*
_{0} are examined utilizing large-eddy simulations. These simulations produce a constant momentum flux layer and a log-law layer above the surface characterized by a logarithmic increase of wind speed with height. The von Kármán constant derived from the mean wind profile is around 0.4 over a wide range of control parameters. The depths of the simulated boundary layer, constant-flux layer, and surface log-law layer tend to increase with the wind speed and decrease with an increasing Coriolis parameter. Immediately above the surface log-law layer, a second log-law layer has been identified from these simulations. The depth of this upper log-law layer is comparable to its counterpart in the surface layer, and the wind speed can be scaled as *h* is the boundary layer depth. An analytical model is proposed to assist in the interpretation of the log laws in a typical Ekman boundary layer. The physics and implications of the upper log-law layer are discussed.

## Abstract

The characteristics of wind profiles in a neutral atmospheric boundary layer and their dependence on the geostrophic wind speed *U*
_{
g
}, Coriolis parameter *f*, and surface roughness length *z*
_{0} are examined utilizing large-eddy simulations. These simulations produce a constant momentum flux layer and a log-law layer above the surface characterized by a logarithmic increase of wind speed with height. The von Kármán constant derived from the mean wind profile is around 0.4 over a wide range of control parameters. The depths of the simulated boundary layer, constant-flux layer, and surface log-law layer tend to increase with the wind speed and decrease with an increasing Coriolis parameter. Immediately above the surface log-law layer, a second log-law layer has been identified from these simulations. The depth of this upper log-law layer is comparable to its counterpart in the surface layer, and the wind speed can be scaled as *h* is the boundary layer depth. An analytical model is proposed to assist in the interpretation of the log laws in a typical Ekman boundary layer. The physics and implications of the upper log-law layer are discussed.