We review what is known about the convective process in the open ocean, in which the properties of large volumes of water are changed by intermittent, deep-reaching convection, triggered by winter storms. Observational, laboratory, and modeling studies reveal a fascinating and complex interplay of convective and geostrophic scales, the large-scale circulation of the ocean, and the prevailing meteorology. Two aspects make ocean convection interesting from a theoretical point of view. First, the timescales of the convective process in the ocean are sufficiently long that it may be modified by the Earth's rotation; second, the convective process is localized in space so that vertical buoyancy transfer by upright convection can give way to slantwise transfer by baroclinic instability. Moreover, the convective and geostrophic scales are not very disparate from one another. Detailed observations of the process in the Labrador, Greenland, and Mediterranean Seas are described, which were made possible by new observing technology. When interpreted in terms of underlying dynamics and theory and the context provided by laboratory and numerical experiments of rotating convection, great progress in our description and understanding of the processes at work is being made.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98RG02739

Open-ocean convection: Observations, theory, and models

The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales. Its first application was to plumes rising in stably stratified surroundings, and it has been extended to inclined plumes (gravity currents) and related problems by adding the effect of buoyancy forces, which inhibit mixing across a density interface. More recently, the influence of viscosity differences between a turbulent flow and its surroundings has been studied. This paper surveys the background theory and the laboratory experiments that have been used to understand and quantify each of these phenomena, and discusses their applications in the atmosphere, the ocean and various geological contexts.

Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows

Modifications of the widely used K-profile model of the planetary boundary layer (PBL), reported by Troen and Mahrt (TM) in 1986, are proposed and their effects examined by comparison with large eddy simulation (LES) data. The modifications involve three parts. First, the heat flux from the entrainment at the inversion layer is incorporated into the heat and momentum profiles, and it is used to predict the growth of the PBL directly. Second, profiles of the velocity scale and the Prandtl number in the PBL are proposed, in contrast to the constant values used in the TM model. Finally, non-local mixing of momentum was included. The results from the new PBL model and the original TM model are compared with LES data. The TM model was found to give too high PBL heights in the PBL with strong shear, and too low heights for the convection-dominated PBL, which causes unrealistic heat flux profiles. The new PBL model improves the predictability of the PBL height and produces profiles that are more realistic. Moreover, the new PBL model produces more realistic profiles of potential temperature and velocity. We also investigated how each of these three modifications affects the results, and found that explicit representation of the entrainment rate is the most critical.

/pdf/improvement-of-the-k-profile-model-for-the-planetary-kgbgqmcyi8.pdf

Improvement of the K-profile Model for the Planetary Boundary Layer based on Large Eddy Simulation Data

The authors use large-eddy simulation (LES) to investigate entrainment and structure of the inversion layer of a clear convectively driven planetary boundary layer (PBL) over a range of bulk Richardson numbers, Ri. The LES code uses a nested grid technique to achieve fine resolution in all three directions in the inversion layer. Extensive flow visualization is used to examine the structure of the inversion layer and to illustrate the temporal and spatial interaction of a thermal plume and the overlying inversion. It is found that coherent structures in the convective PBL, that is, thermal plumes, are primary instigators of entrainment in the Ri range 13.6 # Ri # 43.8. At Ri 5 13.6, strong horizontal and downward velocities are generated near the inversion layer because of the plume‐interface interaction. This leads to folding of the interface and hence entrainment of warm inversion air at the plume’s edge. At Ri 5 34.5, the inversion’s strong stability prevents folding of the interface but strong horizontal and downward motions near the plume’s edge pull down pockets of warm air below the nominal inversion height. These pockets of warm air are then scoured off by turbulent motions and entrained into the PBL. The structure of the inversion interface from LES is in good visual agreement with lidar measurements in the PBL obtained during the Lidars in Flat Terrain field experiment. A quadrant analysis of the buoyancy flux shows that net entrainment flux (or average minimum buoyancy flux wu min) is identified with quadrant IV w2u1 , 0 motions, that is, warm air moving downward. Plumes generate both large negative quadrant II w1u2 , 0 and positive quadrant III w2u2 . 0 buoyancy fluxes that tend to cancel. The maximum vertical gradient in potential temperature at every (x, y) grid point is used to define a local PBL height, zi(x, y). A statistical analysis of zi shows that skewness of zi depends on the inversion strength. Spectra of zi exhibit a sensitivity to grid resolution. The normalized entrainment rate we/w * , where we and w * are entrainment and convective velocities, varies as ARi21 with A 0.2 in the range 13.6 # Ri # 43.8 and is in good agreement with convection tank measurements. For a clear convective PBL, the authors found that the finite thickness of the inversion layer needs to be considered in an entrainment rate parameterization derived from a jump condition.

/pdf/structure-of-the-entrainment-zone-capping-the-convective-4zc04oj8kz.pdf

Structure of the Entrainment Zone Capping the Convective Atmospheric Boundary Layer

The Paris area is strongly urbanized and is exposed to atmospheric
pollution events. To understand the chemical and physical processes
that are taking place in this area it is necessary to describe
correctly the atmospheric boundary-layer (ABL) dynamics and the ABL
height evolution. During the winter of 1994–1995, within the
framework of the Etude de la Couche Limite Atmospherique en
Agglomeration Parisienne (ECLAP) experiment, the vertical
structure of the ABL over Paris and its immediate suburbs was
extensively documented by means of lidar measurements. We present
methods suited for precise determination of the ABL structure’s
temporal evolution in a dynamic environment as complex as the Paris
area. The purpose is to identify a method that can be used on a
large set of lidar data. We compare commonly used methods that
permit ABL height retrievals from backscatter lidar signals under
different meteorological conditions. Incorrect tracking of the ABL
depth’s diurnal cycle caused by limitations in the methods is
analyzed. The study uses four days of the ECLAP experiment
characterized by different meteorological and synoptic
conditions.

Urban boundary-layer height determination from lidar measurements over the paris area.

In laboratory experiments of simulated atmospheric mixed layers the entrainment zone is investigated from measurements of horizontally averaged temperature and buoyancy flux, and from visual observations of penetrating thermals using a spread laser beam. The region of negative buoyancy flux of entrainment is found to be confined between the outermost height reached by the few most vigorous penetrating parcels, and by the lesser height where mixed-layer fluid occupies, usually, some 90 to 95% of the total area. The height of most negative buoyancy flux of entrainment is found to agree roughly with the level at which mixed-layer fluid occupies half the area.The thickness of the entrainment zone, relative to the depth of the well-mixed layer just beneath, is found to be quite substantial (0·2 to 0·4), and apparently decreases only asymptotically with increasing ‘overall’ Richardson number, Ri*. The thickness is not well predicted by parcel theory.Extensive detrainment is found to occur within the entrainment zone, and adds to the difficulty in defining the position of the local interface between mixed-layer fluid and unmodified fluid.For typical Ri* values occurring in the atmosphere, the dimensionless entrainment rate is found to be given satisfactorily by 0·25(Ri*)−1, although an dependence cannot be ruled out by the present data. Entrainment into a neutral layer in the absence of a capping inversion is found to proceed at the expected rate.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112080001000

B. H. Stockton

Papers

Laboratory studies of the entrainment zone of a convectively mixed layer