Joost A. Businger

Bulk Parameterization of Air-Sea Exchanges of Heat and Water Vapor Including the Molecular Constraints at the Interface

Abstract A model is developed for the marine atmospheric surface layer including the interfacial sublayers on both sides of the air-sea interface where molecular constraints on transports are important. Flux-profile relations which are based on the postulation of intermittent renewal of the surface fluid aye matched to the logarithmic profiles and compared with both field and laboratory measurements. These relations enable numerical determination of air-sea exchanges of momentum, heat and water vapor (or bulk transfer coefficients) employing the bulk parameters of mean wind speed, temperature and humidity at a certain height in the atmospheric surface layer, and the water temperature. With increasing wind speed, the flow goes from smooth to rough and the bulk transfer coefficient for momentum also increases. The increase in roughness is associated with increasing wave height which in the present model results in sheltering at the wave troughs. Due to the decrease in turbulent transports, the transfer coef...

The turbulent heat flux from arctic leads

The turbulent transfer of heat from Arctic leads in winter is one of the largest terms in the Arctic heat budget. Results from the AIDJEX Lead Experiment (ALEX) suggest that the sensible component of this turbulent heat flux can be predicted from bulk quantities. Both the exponential relation N = 0.14Rx0.72 and the linear relation N = 1.6 × 10−3Rx+ 1400 fit our data well. In these, N is the Nusselt number formed with the integrated surface heat flux, and Rx is the Reynolds number based on fetch across the lead. Because of the similarity between heat and moisture transfer, these equations also predict the latent heat flux. Over leads in winter, the sensible heat flux is two to four times larger than the latent heat flux.The internal boundary layer (IBL) that develops when cold air encounters the relatively warm lead is most evident in the modified downwind temperature profiles. The height of this boundary layer, δ, depends on the fetch, x, on the surface roughness of the lead, z0 and on both downwind and upwind stability. A tentative, empirical model for boundary layer growth is % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaaiabes% 7aKbqaaiaadQhadaWgaaWcbaGaaGimaaqabaaaaOGaeyypa0JaeqOS% di2aaeWaaeaacqGHsisldaWcaaqaaiaadQhadaWgaaWcbaGaaGimaa% qabaaakeaacaWGmbaaaaGaayjkaiaawMcaamaaCaaaleqabaGaaGim% aiaac6cacaaI4aaaaOWaaeWaaeaadaWcaaqaaiaadIhaaeaacaWG6b% WaaSbaaSqaaiaaicdaaeqaaaaaaOGaayjkaiaawMcaamaaCaaaleqa% baGaaGimaiaac6cacaaI0aaaaaaa!472D!\[\frac{\delta }{{z_0 }} = \beta \left( { - \frac{{z_0 }}{L}} \right)^{0.8} \left( {\frac{x}{{z_0 }}} \right)^{0.4} \] where L is the Obukhov length based on the values of the momentum and sensible heat fluxes at the surface of the lead, and Β is a constant reflecting upwind stability.Velocity profiles over leads are also affected by the surface nonhomogeneity. Besides being warmer than the upwind ice, the surface of the lead is usually somewhat rougher. The velocity profiles therefore tend to decelerate near the surface, accelerate in the mid-region of the IBL because of the intense mixing driven by the upward heat flux, and rejoin the upwind profiles above the boundary layer. The profiles thus have distinctly different shapes for stable and unstable upwind conditions.

A Model for Entrainment into a Cloud-Topped Marine Boundary Layer. Part I: Model Description and Application to a Cold-Air Outbreak Episode

Abstract A model is presented for the growth and evolution of a cloud-topped marine boundary layer. In this model the entrainment rate is determined from the turbulence kinetic energy (TKE) budget. It is assumed that the TKE budget can be partitioned according to whether each process produces TKE or converts it into potential energy, and that dissipation is proportional to production. This leads to an entrainment relationship which is considerably different than used in previous cloud-topped models. This model is used to study an episode of cold-air outbreak over Lake Ontario during the International Field Year for the Great Lakes (IFYGL). The model reproduces changes in potential temperature and dew point as the air crossed the lake and the associated time variation of these parameters at the down-wind shore with an accuracy of better than 1°C. Model and measured soundings closely match, especially with respect to the presence and location of such features as cloud layers. Depth of the mixed layer also w...

Height of the Mixed Layer in the Stably Stratified Planetary Boundary Layer

Publisher Summary Modeling of the stable boundary layer is difficult because usually, a transition from turbulent to laminar flow takes place with increasing height, and steady state is usually not reached in the laminar region but may be approached in the turbulent region. This chapter discusses the formulation of a steady-state stable boundary layer, which, in reality, may occur only after a very long time, possibly during the polar night in the arctic. Under most gravitationally stable conditions in the atmosphere, there is always a good likelihood of a turbulent or mixing layer occurring near the surface. With increasing stability, the length scale of the vertical motion becomes independent of the height above the surface, but proportional to the so-called Obukhov length, and under these conditions, the mean velocity and temperature profiles become linear. The chapter presents two most significant results for the stable boundary layer: (1) the dimensionless boundary layer height varies in inverse proportion to the square-root of the stability parameter and (2) the calculated forms of the stability dependent functions in the geostrophic drag relations are in fair agreement with their empirical estimates from the Wangara data.

An Observational Case for the Prevalence of Roll Vortices in the Hurricane Boundary Layer

Abstract Doppler velocity data from Weather Surveillance Radar-1988 Doppler (WSR-88D) radars during four hurricane landfalls are analyzed to investigate the presence of organized vortices in the hurricane boundary layer (HBL). The wavelength, depth, magnitude, and track of velocity anomalies were compiled through analysis of Doppler velocity data. The analysis reveals alternating bands of enhanced and reduced azimuthal winds closely aligned with the mean wind direction. Resulting statistics provide compelling evidence for the presence of organized secondary circulations or boundary layer rolls across significant areas during four hurricane landfalls. The results confirm previous observations of the presence of rolls in the HBL. A potential limitation of the study presented here is the resolution of the WSR-88D data. In particular, analysis of higher-resolution data (e.g., from the Doppler on Wheels) is needed to confirm that data aliasing has not unduly impacted the statistics reported here. Momentum flux...

Transition of Stratus into Fog along the California Coast: Observations and Modeling

A case of fog formation along the California coast is examined with the aid of a one-dimensional, higherorder, turbulence-closure model in conjunction with a set of myriad observations. The event is characterized by persistent along-coast winds in the marine layer, and this pattern justifies a Lagrangian approach to the study. A slab of marine layer air is tracked from the waters near the California‐Oregon border to the California bight over a 2-day period. Observations indicate that the marine layer is covered by stratus cloud and comes under the influence of large-scale subsidence and progressively increasing sea surface temperature along the southbound trajectory. It is hypothesized that cloud-top cooling and large-scale subsidence are paramount to the fog formation process. The one-dimensional model, evaluated with various observations along the Lagrangian path, is used to test the hypothesis. The principal findings of the study are 1) fog forms in response to relatively long preconditioning of the marine layer, 2) radiative cooling at the cloud top is the primary mechanism for cooling and mixing the cloud-topped marine layer, and 3) subsidence acts to strengthen the inversion above the cloud top and forces lowering of the cloud. Although the positive fluxes of sensible and latent heat at the air‐sea interface are the factors that govern the onset of fog, sensitivity studies with the one-dimensional model indicate that these sensible and latent heat fluxes are of secondary importance as compared to subsidence and cloud-top cooling. Sensitivity tests also suggest that there is an optimal inversion strength favorable to fog formation and that the moisture conditions above the inversion influence fog evolution.

A note on free convection

The limiting condition of µ*, →0 in the unstable atmospheric boundary layer is usually referred to as ‘free convection’. Some of the similarity laws that are proposed for this condition do not agree with experiment. A mechanism is proposed in this paper to show why the asymptotic free convection condition is never completely reached near the surface. It is shown that local turbulent shear production plays an important role in shaping the temperature profile even when the average velocity is zero.

A study of convective elements in the atmospheric surface layer

A statistical model, based on a method of Vulfson, is used to examine some of the plume-like temperature structures formed in the unstable boundary layer. The model assumes that the plume diameter changes slowly with height so that a cylindrical approximation may be made. Measurements of the vertical velocity and temperature were used to determine the temperature dependent portion of the vertical velocity field. Temperature data were collected from sensors on a tower and from aircraft; velocity data were collected only from the tower.Using this model for analysis of the data indicates that: (1) the average isotherm diameter and the population of isotherms are a function ofz/L; (2) the distribution of core temperatures is approximately a uniform distribution.Independent of the model, a convective velocity was determined and found to have approximately the same profile as the temperature; from this the average velocity of the plumes was found to be a linear function ofz/L, fromz/L ∼- 0.1 toz/L ∼- 1.0. As a consequence of this functional dependence, the entrainment into the plumes is approximately constant over this range. The cumulative temperature distribution function was found to be an asymmetric function ofz/L. A simple relation which is independent ofu* is given to determine the heat flux.

A Model for Entrainment into a Cloud-Topped Marine Boundary Layer. Pad II: Discussion of Model Behavior and Comparison with Other Models

Abstract The model for the cloud-topped marine boundary layer presented by Stage and Businger (1981) is discussed and compared with previous models. Our model gives a considerably different interpretation of the energetics of the layer and indicates that a much higher fraction (20%) of the layer turbulence kinetic energy production is available to drive entrainment than previously supposed. In a test case, the Lilly (1968) minimum entrainment model gives entrainment rates similar to ours; however, this model is based on physically unrealistic assumptions about layer energetics. It is noted that two soundings from the International Field Year for the Great Lakes (IFYGL) exhibit behavior not allowed by Deardorff’s (1976) model. In these cases our model gives a good fit to the data and Deardorff’s model predicted a boundary layer much deeper than observed. The depth of the layer of radiative cooling at cloud top is shown to be important only if it is a significant fraction of the mixed-layer depth zB. Layer ...

The drag coefficient as determined by the dissipation method and its relation to intermittent convection in the surface layer

The influence of intermittent convection on surface-layer stress estimates during the GARP Atlantic Tropical Experiment (GATE) is described. A negative correlation between the drag coefficient (CD) and the wind speed (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]) is found when short averaging periods are used. Well-defined, discrete events produce this negative correlation, and these events are shown to correspond to the passage of convective plumes. Constraints on averaging times necessary to obtain reasonable stress estimates using the bulk method are discussed.Conditional sampling is used to produce average values of dissipation (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbae% baaaa!37AB!\[\bar \varepsilon \]), wind speed (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]), and virtual temperature (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmivayaara% WaaSbaaSqaaiaaiw8aaeqaaaaa!385B!\[\bar T_\upsilon \]) for each high turbulent intensity event, and for the quiescent periods in between. Such statistics indicate that the highly turbulent states coincide with the presence of plumes and account for the negative correlation between CD and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]. Some of these statistics are also stability dependent.The probability distributions of the dissipation rate are bimodally log-normal which suggests that turbulence generated at two different heights is being sampled. This, along with other results of this paper, support a picture of a boundary layer which is dominated by vertical exchange.