Quasigeostrophic Turbulence in a Three-Layer Model: Effects of Vertical Structure in the Mean Shear

1992 ◽  
Vol 49 (19) ◽  
pp. 1861-1870 ◽  
Author(s):  
Isaac M. Held ◽  
Enda O'Brien
2013 ◽  
Vol 70 (5) ◽  
pp. 1505-1511 ◽  
Author(s):  
Noboru Nakamura ◽  
Lei Wang

Abstract It is shown that the classical quasigeostrophic two-layer model of baroclinic instability possesses an optimal ratio of layer thicknesses that maximizes the growth rate, given the basic-state shear (thermal wind), beta, and the mean Rossby radius. This ratio is interpreted as the vertical structure of the most unstable mode. For positive shear and beta, the optimal thickness of the lower layer approaches the midheight of the model in the limit of strong criticality (shear/beta) but it is proportional to criticality in the opposite limit. For a set of parameters typical of the earth’s midlatitudes, the growth rate maximizes at a lower-layer thickness substantially less than the midheight and at a correspondingly larger zonal wavenumber. It is demonstrated that a turbulent baroclinic jet whose statistical steady state is marginally critical when run with equal layer thicknesses can remain highly supercritical when run with a nearly optimal thickness ratio.


2019 ◽  
Vol 49 (10) ◽  
pp. 2553-2570 ◽  
Author(s):  
Mads B. Poulsen ◽  
Markus Jochum ◽  
James R. Maddison ◽  
David P. Marshall ◽  
Roman Nuterman

AbstractAn interpretation of eddy form stress via the geometry described by the Eliassen–Palm flux tensor is explored. Complimentary to previous works on eddy Reynolds stress geometry, this study shows that eddy form stress is fully described by a vertical ellipse, whose size, shape, and orientation with respect to the mean flow shear determine the strength and direction of vertical momentum transfers. Following a recent proposal, this geometric framework is here used to form a Gent–McWilliams eddy transfer coefficient that depends on eddy energy and a nondimensional geometric parameter α, bounded in magnitude by unity. The parameter α expresses the efficiency by which eddies exchange energy with baroclinic mean flow via along-gradient eddy buoyancy flux—a flux equivalent to eddy form stress along mean buoyancy contours. An eddy-resolving ocean general circulation model is used to estimate the spatial structure of α in the Southern Ocean and assess its potential to form a basis for parameterization. The eddy efficiency α averages to a low but positive value of 0.043 within the Antarctic Circumpolar Current, consistent with an inefficient eddy field extracting energy from the mean flow. It is found that the low eddy efficiency is mainly the result of that eddy buoyancy fluxes are weakly anisotropic on average. The eddy efficiency is subject to pronounced vertical structure and is maximum at ~3-km depth, where eddy buoyancy fluxes tend to be directed most downgradient. Since α partly sets the eddy form stress in the Southern Ocean, a parameterization for α must reproduce its vertical structure to provide a faithful representation of vertical stress divergence and eddy forcing.


2015 ◽  
Vol 25 (13) ◽  
pp. 2439-2475 ◽  
Author(s):  
Pierre Degond ◽  
Laurent Navoret

We present an individual-based model describing disk-like self-propelled particles moving inside parallel planes. The disk directions of motion follow alignment rules inside each layer. Additionally, the disks are subject to interactions with those of the neighboring layers arising from volume exclusion constraints. These interactions affect the disk inclinations with respect to the plane of motion. We formally derive a macroscopic model composed of planar self-organized hydrodynamic (SOH) models describing the transport of mass and evolution of mean direction of motion of the disks in each plane, supplemented with transport equations for the mean disk inclination. These planar models are coupled due to the interactions with the neighboring planes. Numerical comparisons between the individual-based and macroscopic models are carried out. These models could be applicable, for instance, to describe sperm-cell collective dynamics.


Forests ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 1164
Author(s):  
Seok Hwan Yun ◽  
Chae Yeon Park ◽  
Eun Sub Kim ◽  
Dong Kun Lee

As the intensity of the urban heat island effect increases, the cooling effect of urban trees has become important. Urban trees cool surfaces during the day via shading, increasing albedo and transpiration. Many studies are being conducted to calculate the transpiration rate; however, most approaches are not suitable for urban trees and oversimplify plant physiological processes. We propose a multi-layer model for the transpiration of urban trees, accounting for plant physiological processes and considering the vertical structure of trees and buildings. It has been expanded from an urban canopy model to accurately simulate the photosynthetically active radiation and leaf surface temperature. To evaluate how tree and surrounding building conditions affect transpiration, we simulated the transpiration of trees in different scenarios such as building height (i.e., 1H, 2H and 3H, H = 12 m), tree location (i.e., south tree and north tree in a E-W street), and vertical leaf area density (LAD) (i.e., constant density, high density with few layers, high density in middle layers, and high density in lower layers). The transpiration rate was estimated to be more sensitive to the building height and tree location than the LAD distribution. Transpiration-efficient trees differed depending on the surrounding condition and plant location. This model is a useful tool that provides guidelines on the planting of thermo-efficient trees depending on the structure or environment of the city.


2008 ◽  
Vol 38 (9) ◽  
pp. 1992-2002 ◽  
Author(s):  
Annalisa Bracco ◽  
Joseph Pedlosky ◽  
Robert S. Pickart

Abstract This paper extends A. Bracco and J. Pedlosky’s investigation of the eddy-formation mechanism in the eastern Labrador Sea by including a more realistic depiction of the boundary current. The quasigeostrophic model consists of a meridional, coastally trapped current with three vertical layers. The current configuration and topographic domain are chosen to match, as closely as possible, the observations of the boundary current and the varying topographic slope along the West Greenland coast. The role played by the bottom-intensified component of the boundary current on the formation of the Labrador Sea Irminger Rings is explored. Consistent with the earlier study, a short, localized bottom-trapped wave is responsible for most of the perturbation energy growth. However, for the instability to occur in the three-layer model, the deepest component of the boundary current must be sufficiently strong, highlighting the importance of the near-bottom flow. The model is able to reproduce important features of the observed vortices in the eastern Labrador Sea, including the polarity, radius, rate of formation, and vertical structure. At the time of formation, the eddies have a surface signature as well as a strong circulation at depth, possibly allowing for the transport of both surface and near-bottom water from the boundary current into the interior basin. This work also supports the idea that changes in the current structure could be responsible for the observed interannual variability in the number of Irminger Rings formed.


2005 ◽  
Vol 44 (9) ◽  
pp. 1324-1345 ◽  
Author(s):  
Rob K. Newsom ◽  
David Ligon ◽  
Ron Calhoun ◽  
Rob Heap ◽  
Edward Cregan ◽  
...  

Abstract Dual-Doppler lidar observations are used to assess the accuracy of single-Doppler retrievals of microscale wind and temperature fields in a shear-driven convective boundary layer. The retrieval algorithm, which is based on four-dimensional variational data assimilation, is applied by using dual- and single-Doppler lidar data that are acquired during the Joint Urban 2003 field experiment. The velocity field that was retrieved using single-Doppler data is compared directly with radial velocities that were measured by a second noncollocated lidar. Dual-Doppler retrievals are also performed and then compared with the single-Doppler retrieval. The linear correlation coefficient and rms deviation between the single-Doppler retrieval and the observations from the second lidar are found to be 0.94 and 1.2 m s−1, respectively. The high correlation is mainly the result of good agreement in the mean vertical structure as observed by the two lidars. Comparisons between the single- and dual-Doppler retrieval indicate that the single-Doppler retrieval underestimates the magnitude of fluctuations in the crossbeam direction. Vertical profiles of horizontally averaged correlations between the single- and dual-Doppler retrievals also show a marginal correlation (0.4–0.8) between one of the horizontal velocity components. Again, this suggests that the retrieval algorithm has difficulty estimating the crossbeam component from single-Doppler data.


2016 ◽  
Author(s):  
Sonaljit Mukherjee ◽  
Amit Tandon

Abstract. Atmospheric fluxes influence the momentum and scalar properties in the upper-cean. Buoyancy fluxes result in a diurnal variability in the sea-surface temperature (SST), whereas the wind stress forms near-inertial currents in the mixed layer (ML). In this study, we investigate the contrasts between the simulated SST and the vertical structure of the temperature and shear by three different mixing models: the PWP bulk mixed-layer model, the KPP non-local boundary layer model and the κ−ϵ local mixing model. We choose two upper-ocean datasets for our studies, namely the SWAPP (1990) and the MLML (1991). The SWAPP dataset shows the presence of strong near-inertial shear below the ML and negligible near-inertial shear within the ML. The MLML dataset shows a negligible rise in the SST during the first 22 day mixing phase, which is followed by a steep rise by 6 °C during the subsequent 75 day restratification phase. Comparison with the SWAPP dataset shows that the KPP and κ−ϵ models form strong shear near the surface due to weak eddy viscosities, thus producing a thin shear layer over the entire range of frequencies in the wind stress. At the ML base, the models form an inertial and a diurnal maximum. The inertial maximum extends over a substantial range of depths, and is continuous for the κ−ϵ model but discontinuous for the KPP and PWP models. Comparison with the MLML dataset reveals that the KPP yields the largest SST amplitude over a 24-hour diurnal cycle, and is followed by the κ−ϵ and PWP. However, the net warming of SST at the end of the diurnal cycle is stronger for the PWP compared to κ−ϵ and KPP. The PWP also forms stronger temperature gradients at the ML base compared to κ−ϵ and KPP. Over multiple diurnal cycles, the shallowing and deepening of the mixed layer results in multiple sharp temperature gradients in PWP, thus forming a serrated vertical profile that remains unaffected during the restratification phase of the MLML dataset.


2006 ◽  
Vol 7 (5) ◽  
pp. 868-879 ◽  
Author(s):  
Aihui Wang ◽  
Xubin Zeng ◽  
Samuel S. P. Shen ◽  
Qing-Cun Zeng ◽  
Robert E. Dickinson

Abstract This paper intends to investigate the time scales of land surface hydrology and enhance the understanding of the hydrological cycle between the atmosphere, vegetation, and soil. A three-layer model for land surface hydrology is developed to study the temporal variation and vertical structure of water reservoirs in the vegetation–soil system in response to precipitation forcing. The model is an extension of the existing one-layer bucket model. A new time scale is derived, and it better represents the response time scale of soil moisture in the root zone than the previously derived inherent time scale (i.e., the ratio of the field capacity to the potential evaporation). It is found that different water reservoirs of the vegetation–soil system have different time scales. Precipitation forcing is mainly concentrated on short time scales with small low-frequency components, but it can cause long time-scale disturbances in the soil moisture of root zone. This time scale increases with soil depth, but it can be reduced significantly under wetter conditions. Although the time scale of total water content in the vertical column in the three-layer model is similar to that of the one-layer bucket model, the time scale of evapotranspiration is very different. This suggests the need to consider the vertical structure in land surface hydrology reservoirs and in climate study.


2014 ◽  
Vol 71 (10) ◽  
pp. 3788-3800 ◽  
Author(s):  
Pablo Zurita-Gotor

Abstract Friction is an important parameter in atmospheric modeling that may affect internal variability in a number of ways. It directly damps the annular-mode variability, but it also helps to maintain it through baroclinic feedbacks. Also, by determining the mean strength and position of the midlatitude jet, friction affects the internal dynamics that drive this variability. This work investigates the relevance of all of these factors for the sensitivity of the persistence of annular variability to changes in the zonal-mean friction using an idealized quasigeostrophic two-layer model. This model produces realistic variability, yet it is so simple that one can cleanly separate the different effects. It is found that the sensitivity of persistence to friction is dominated by the direct damping effect, while changes in the eddy momentum forcing and in the mean jet are not as important. As in more complex models, the persistence of the jet anomalies in this model decreases at all lags with increasing friction, but the long-time decorrelation decay rate of these anomalies is remarkably insensitive to friction. Although this implies that the eddy feedback must increase with friction to maintain the anomalies against the enhanced damping, it is shown that this is not due to baroclinic effects. A model that assumes that the eddy forcing does not change with friction can reproduce reasonably well the numerical results. The crucial factor that determines the model’s sensitivity to friction is the spectral structure of the eddy momentum forcing.


2010 ◽  
Vol 40 (5) ◽  
pp. 1075-1086
Author(s):  
Joseph Pedlosky

Abstract A quasigeostrophic, two-layer model is used to study the baroclinic circulation around a thin, meridionally elongated island. The flow is driven by either buoyancy forcing or wind stress, each of whose structure would produce an antisymmetric double-gyre flow. The ocean bottom is flat. When the island partially straddles the intergyre boundary, fluid from one gyre is forced to flow into the other. The amount of the intergyre flow depends on the island constant, that is, the value of the geostrophic streamfunction on the island in each layer. That constant is calculated in a manner similar to earlier studies and is determined by the average, along the meridional length of the island, of the interior Sverdrup solution just to the east of the island. Explicit solutions are given for both buoyancy and wind-driven flows. The presence of an island of nonzero width requires the determination of the baroclinic streamfunction on the basin’s eastern boundary. The value of the boundary term is proportional to the island’s area. This adds a generally small additional baroclinic intergyre flow. In all cases, the intergyre flow produced by the island is not related to topographic steering of the flow but rather the pressure anomaly on the island as manifested by the barotropic and baroclinic island constants. The vertical structure of the flow around the island is a function of the parameterization of the vertical mixing in the problem and, in particular, the degree to which long baroclinic Rossby waves can traverse the basin before becoming thermally damped.


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