Nonlocal Transport and Implied Viscosity and Diffusivity throughout the Boundary Layer in LES of the Southern Ocean with Surface Waves

2019 ◽  
Vol 49 (10) ◽  
pp. 2631-2652
Author(s):  
William G. Large ◽  
Edward G. Patton ◽  
Peter P. Sullivan
Keyword(s):  
Boundary Layer ◽  
Southern Ocean ◽  
Wind Stress ◽  
Momentum Flux ◽  
Similarity Theory ◽  
Stress Component ◽  
Stable Stratification ◽  
Shear Component ◽  
Wide Range ◽  
Surface Buoyancy

AbstractObservations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes) forcing for large-eddy simulation (LES) of deep Southern Ocean boundary layers. Almost everywhere there is a nonzero angle Ω between the shear and the stress vectors. Also, with unstable forcing there is usually a depth where there is stable stratification, but zero buoyancy flux and often a number of depths above where there is positive flux, but neutral stratification. These features allow nonlocal transports of buoyancy and of momentum to be diagnosed, using either the Eulerian or Lagrangian shear. The resulting profiles of nonlocal diffusivity and viscosity are quite similar when scaled according to Monin–Obukhov similarity theory in the surface layer, provided the Eulerian shear is used. Therefore, a composite shape function is constructed that may be generally applicable. In contrast, the deeper boundary layer appears to be too decoupled from the Stokes component of the Lagrangian shear. The nonlocal transports can be dominant. The diagnosed across-shear momentum flux is entirely nonlocal and is highly negatively correlated with the across-shear component of the wind stress, just as nonlocal and surface buoyancy fluxes are related. Furthermore, in the convective limit the scaling coefficients become essentially identical, with some consistency with atmospheric experience. The nonlocal contribution to the along-shear momentum flux is proportional to (1 − cosΩ) and is always countergradient, but is unrelated to the aligned wind stress component.

scholarly journals A New Value of the von Kármán Constant: Implications and Implementation

2009 ◽  
Vol 48 (5) ◽  
pp. 923-944 ◽  
Author(s):  
Edgar L. Andreas
Keyword(s):  
Boundary Layer ◽  
Similarity Theory ◽  
Stable Stratification ◽  
Transfer Coefficients ◽  
Obukhov Length ◽  
Von Karman ◽  
Roughness Lengths ◽  
Experimental Values ◽  
Definition Of ◽  
Von Kármán

Abstract The von Kármán constant k occurs throughout the mathematics that describe the atmospheric boundary layer. In particular, because k was originally included in the definition of the Obukhov length, its value has both explicit and implicit effects on the functions of Monin–Obukhov similarity theory. Although credible experimental evidence has appeared sporadically that the von Kármán constant is different than the canonical value of 0.40, the mathematics of boundary layer meteorology still retain k = 0.40—probably because the task of revising all of this math to implement a new value of k is so daunting. This study therefore outlines how to make these revisions in the nondimensional flux–gradient relations; in variance, covariance, and dissipation functions; and in structure parameters of Monin–Obukhov similarity theory. It also demonstrates how measured values of the drag coefficient (CD), the transfer coefficients for sensible (CH) and latent (CE) heat, and the roughness lengths for wind speed (z0), temperature (zT), and humidity (zQ) must be modified for a new value of the von Kármán constant. For the range of credible experimental values for k, 0.35–0.436, revised values of CD, CH, CE, z0, zT, and zQ could be quite different from values obtained assuming k = 0.40, especially if the original measurements were made in stable stratification. However, for the value of k recommended here, 0.39, no revisions to the transfer coefficients and roughness lengths should be necessary. Henceforth, use the original measured values of transfer coefficients and roughness lengths but do use similarity functions modified to reflect k = 0.39.

The Importance of Nonlinear Cross-Shelf Momentum Flux during Wind-Driven Coastal Upwelling*

2004 ◽  
Vol 34 (11) ◽  
pp. 2444-2457 ◽  
Author(s):  
Steven J. Lentz ◽  
David C. Chapman
Keyword(s):  
Boundary Layer ◽  
Wind Stress ◽  
Momentum Flux ◽  
Coastal Upwelling ◽  
Bottom Boundary Layer ◽  
Return Flow ◽  
Flux Divergence ◽  
Bottom Boundary ◽  
Shelf Circulation ◽  
The Cross

Abstract A simple theory is proposed for steady, two-dimensional, wind-driven coastal upwelling that relates the dynamics and the structure of the cross-shelf circulation to the stratification, bathymetry, and wind stress. The new element is an estimate of the nonlinear cross-shelf momentum flux divergence due to the wind-driven cross-shelf circulation acting on the vertically sheared geostrophic alongshelf flow. The theory predicts that the magnitude of the cross-shelf momentum flux divergence relative to the wind stress depends on the Burger number S = αN/f, where α is the bottom slope, N is the buoyancy frequency, and f is the Coriolis parameter. For S ≪ 1 (weak stratification), the cross-shelf momentum flux divergence is small, the bottom stress balances the wind stress, and the onshore return flow is primarily in the bottom boundary layer. For S ≈ 1 or larger (strong stratification), the cross-shelf momentum flux divergence balances the wind stress, the bottom stress is small, and the onshore return flow is in the interior. Estimates of the cross-shelf momentum flux divergence using moored observations from four coastal upwelling regions (0.2 ≤ S ≤ 1.5) are substantial relative to the wind stress when S ≈ 1 and exhibit a dependence on S that is consistent with the theory. Two-dimensional numerical model results indicate that the cross-shelf momentum flux divergence can be substantial for the time-dependent response and that the onshore return flow shifts from the bottom boundary layer for small S to just below the surface boundary layer for S ≈ 1.5–2.

scholarly journals Turbulence Process Domination under the Combined Forcings of Wind Stress, the Langmuir Vortex Force, and Surface Cooling

2014 ◽  
Vol 44 (1) ◽  
pp. 44-67 ◽  
Author(s):  
A. E. Gargett ◽  
C. E. Grosch
Keyword(s):  
Boundary Layer ◽  
Wind Stress ◽  
Vertical Velocity ◽  
Ocean Surface ◽  
The Other ◽  
Surface Boundary ◽  
Langmuir Circulation ◽  
Surface Cooling ◽  
Wide Range ◽  
Velocity Variance

Abstract Turbulence in the ocean surface layer is generated by time-varying combinations of destabilizing surface buoyancy flux, wind stress forcing, and wave forcing through a vortex force associated with the surface wave field. Observations of time- and depth-averaged vertical velocity variance of full-depth turbulence in shallow unstratified water columns under destabilizing buoyancy forcing are used to determine when process domination can be assigned over a wide range of mixed forcings. The properties of two turbulence archetypes, one representing full-depth Langmuir circulations and the other representing full-depth convection, are described in detail. It is demonstrated that these archetypes lie in distinct regions of the plane of , where and are Langmuir and Rayleigh numbers, respectively, derived from scaling with surface stress velocity and a time scale characteristic of the growth of Langmuir circulation , where and are mean and Stokes velocities, respectively. Situations in which neither process dominates lie between the two end members, with relative dominance given by proximity to one or the other. Cases dominated by direct stress forcing are conspicuous by their absence. In cases of Langmuir domination, surface Stokes velocity is linearly related to , making it impossible to differentiate between scaling depth-averaged vertical velocity variance with , and any other scaling involving both and . A third nondimensional parameter is introduced and used to assess the importance of bottom boundary layer turbulence in a depth-limited system. Questions of time dependence and applicability of results to the open ocean surface boundary layer are considered.

scholarly journals A Model of the Zonally Averaged Stratification and Overturning in the Southern Ocean

2005 ◽  
Vol 35 (7) ◽  
pp. 1190-1205 ◽  
Author(s):  
Dirk Olbers ◽  
Martin Visbeck
Keyword(s):  
Southern Ocean ◽  
Wind Stress ◽  
Analytical Models ◽  
Small Scale ◽  
Intermediate Water ◽  
Near Surface ◽  
Eddy Transport ◽  
Circumpolar Current ◽  
Baroclinic Transport ◽  
Surface Buoyancy

Abstract The ocean area south of the Antarctic Circumpolar Current (ACC) frontal system is a region of major watermass modification. Influx of North Atlantic Deep Water (NADW), small-scale mixing, eddy transport and diffusion, as well as the fluxes of momentum and buoyancy at the sea surface combine in a complex array of processes to generate the unique stratification of the Southern Ocean with its southward uprising isopycnals and northward flux of Antarctic Intermediate Water (AAIW) and Antarctic Bottom Water. Comprehensive analytical models of this scenario are rare. The authors develop and apply a model based on zonally and temporally averaged theory to explain the conversion of NADW into AAIW with all of the aforementioned processes contained in an extremely simplified way. Eddies appear via a transformed Eulerian mean (TEM) approach with a conventional downgradient parameterization of the meridional density flux. The structure of the eddy coefficient is estimated from hydrographic and wind stress data by a simple inverse approach. Mixing is limited to a near-surface layer and is treated in a most simple entrainment form. The model determines the zonal mean density stratification in the Southern Ocean and the baroclinic transport of the ACC from the applied wind stress and the surface density flux and unravels the role and importance of the different processes responsible for shaping the stratification (Ekman and eddy-induced advection and pumping, mixing, surface buoyancy flux, and eddy-induced diffusion). All of these processes must be present to yield an agreement between the simulated stratification and the observed one, but details of their parameterization might not be too critical. The ACC transport is shown to have a contribution forced by the local wind stress as well as another contribution relating to the nonlocal forcing by wind stress and density flux over the entire Antarctic zone.

scholarly journals Similarity Theory in the Surface Layer of Large-Eddy Simulations of the Wind-, Wave-, and Buoyancy-Forced Southern Ocean

2019 ◽  
Vol 49 (8) ◽  
pp. 2165-2187 ◽  
Author(s):  
William G. Large ◽  
Edward G. Patton ◽  
Alice K. DuVivier ◽  
Peter P. Sullivan ◽  
Leonel Romero
Keyword(s):  
Surface Layer ◽  
Southern Ocean ◽  
Wind Wave ◽  
Similarity Theory ◽  
Large Eddy Simulations ◽  
Stokes Drift ◽  
Total Production ◽  
Similarity Functions ◽  
Wide Range ◽  
Large Eddy

AbstractMonin–Obukhov similarity theory is applied to the surface layer of large-eddy simulations (LES) of deep Southern Ocean boundary layers. Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes drift) forcing. Two No-Stokes LES are used to determine the extent of the ocean surface layer and to adapt the nondimensional momentum and buoyancy gradients, as functions of the stability parameter. Stokes-forced LES are used to modify this parameter for wave effects, then to formulate dependencies of Stokes similarity functions on a Stokes parameter ξ. To account for wind-wave misalignment, the dimensional analysis is extended with two independent variables, namely, the production of turbulent kinetic energy in the surface layer due to Stokes shear and the total production, so that their ratio gives ξ. Stokes forcing is shown to reduce vertical shear more than stratification, and to enhance viscosity and diffusivity by factors up to 5.8 and 4.0, respectively, such that the Prandtl number can exceed unity. A practical parameterization is developed for ξ in terms of the meteorological forcing plus a Stokes drift profile, so that the Stokes and stability similarity functions can be combined to give turbulent velocity scales. These scales for both viscosity and diffusivity are evaluated against the LES, and the correlations are nearly 0.97. The benefit of calculating Stokes drift profiles from directional wave spectra is demonstrated by similarly evaluating three alternatives.

Temperature fluctuations in the atmospheric boundary layer

1960 ◽  
Vol 7 (3) ◽  
pp. 375-384 ◽  
Author(s):  
C. H. B. Priestley
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Thermal Stratification ◽  
Similarity Theory ◽  
Temperature Fluctuations ◽  
Vertical Temperature Gradient ◽  
Vertical Temperature ◽  
Systematic Analysis ◽  
Wide Range ◽  
Regression Relations

A systematic analysis is made of published measurements of the magnitude of temperature fluctuations in the atmospheric boundary layer. These cover a wide range of height, wind speed, and thermal stratification. Within appropriate ranges of the variables, there is evidence for the existence of a dominantly forced convection régime, and also one wherein the predictions of the similarity theory of free convection are fairly closely approached. Subject to the limitations set by the recording systems used, regression relations are obtained for the magnitude of the fluctuations in terms of height and vertical temperature gradient or heat flux.

scholarly journals Nondimensionalization of the Atmospheric Boundary-Layer System: Obukhov Length and Monin–Obukhov Similarity Theory

2021 ◽  
Author(s):  
Jun–Ichi Yano ◽  
Marta Wacławczyk
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Similarity Theory ◽  
Stable Stratification ◽  
Governing Equations ◽  
Layer Depth ◽  
Layer System ◽  
Obukhov Length ◽  
Layer Flow ◽  
Dimensional Argument

AbstractThe Obukhov length, although often adopted as a characteristic scale of the atmospheric boundary layer, has been introduced purely based on a dimensional argument without a deductive derivation from the governing equations. Here, its derivation is pursued by the nondimensionalization method in the same manner as for the Rossby deformation radius and the Ekman-layer depth. Physical implications of the Obukhov length are inferred by nondimensionalizing the turbulence-kinetic-energy equation for the horizontally homogeneous boundary layer. A nondimensionalization length scale for a full set of equations for boundary-layer flow formally reduces to the Obukhov length by dividing this scale by a rescaling factor. This rescaling factor increases with increasing stable stratification of the boundary layer, in which flows tend to be more horizontal and gentler; thus the Obukhov length increasingly loses its relevance. A heuristic, but deductive, derivation of Monin–Obukhov similarity theory is also outlined based on the obtained nondimensionalization results.

On the Growth of Layers of Nonprecipitating Cumulus Convection

2007 ◽  
Vol 64 (8) ◽  
pp. 2916-2931 ◽  
Author(s):  
Bjorn Stevens
Keyword(s):  
Boundary Layer ◽  
Inversion Layer ◽  
Bowen Ratio ◽  
Cloud Layer ◽  
Buoyancy Flux ◽  
Cloud Base ◽  
Moist Convection ◽  
Wide Range ◽  
Surface Buoyancy ◽  
Convective Layer

A prototype problem of a nonprecipitating convective layer growing into a layer of uniform stratification and exponentially decreasing humidity is introduced to study the mechanism by which the cumulus-topped boundary layer grows. The problem naturally admits the surface buoyancy flux, outer layer stratification, and moisture scale as governing parameters. Large-eddy simulations show that many of the well-known properties of the cumulus-topped boundary layer (including a well-mixed subcloud layer, a cloud-base transition layer, a conditionally unstable cloud layer, and an inversion layer) emerge naturally in the simulations. The simulations also quantify the differences between nonprecipitating moist convection and its dry counterpart. Whereas dry penetrative convective layers grow proportionally to the square root of time (diffusively) the cumulus layers grow proportionally to time (ballistically). The associated downward transport of warm, dry air results in a significant decrease in the surface Bowen ratio. The linear-in-time growth of the cloud layer is shown to result from the transport and subsequent evaporation of liquid water into the inversion layer. This process acts as a sink of buoyancy, which acts to imbue the free troposphere with the properties of the cloud layer. A simple model, based on this mechanism, and formulated in terms of an effective dry buoyancy flux (which is constrained by the subcloud layer’s similarity to a dry convective layer), is shown to provide good predictions of the growth of the layer across a wide range of governing parameters.

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