Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

Effect of disease-selective predation on prey infected by contact and external sources

We propose and analyze a simple mathematical model for susceptible prey (S)–infected prey (I)–predator (P) interaction, where the susceptible prey population (S) is infected directly from external sources as well as through contact with infected class (I) and the predator completely avoids consuming the infected prey. The model is analyzed to obtain different thresholds of the key parameters under which the system exhibits stability around the biologically feasible equilibria. Through numerical simulations we display the effects of external infection and the infection through contact on the system dynamics in the absence as well as in the presence of the predator. We compare the system dynamics when infection occurs only through contact, with that when it occurs through contact and external sources. Our analysis demonstrates that under a disease-selective predation, stability and oscillations of the system is determined by two key parameters: the external infection rate and the force of infection through contact. Due to the introduction of external infection, the predator and the prey population show limit-cycle oscillations over a range parametric values. We suggest that while predicting the dynamics of such an eco-epidemiological system, the modes of infection and the infection rates might be carefully investigated.

Influence of the Tibetan Plateau uplift on the Asian monsoon-arid environment evolution

As one of the most important geological events in Cenozoic era, the uplift of the Tibetan Plateau (TP) has had profound influences on the Asian and global climate and environment evolution. During the past four decades, many scholars from China and abroad have studied climatic and environmental effects of the TP uplift by using a variety of geological records and paleoclimate numerical simulations. The existing research results enrich our understanding of the mechanisms of Asian monsoon changes and interior aridification, but so far there are still a lot of issues that need to be thought deeply and investigated further. This paper attempts to review the research on the influence of the TP uplift on the Asian monsoon-arid environment, summarize three types of numerical simulations including bulk-plateau uplift, phased uplift and sub-regional uplift, and especially to analyze regional differences in responses of climate and environment to different forms of tectonic uplifts. From previous modeling results, the land-sea distribution and the Himalayan uplift may have a large effect in the establishment and development of the South Asian monsoon. However, the formation and evolution of the monsoon in northern East Asia, the intensified dryness north of the TP and enhanced Asian dust cycle may be more closely related to the uplift of the main body, especially the northern part of the TP. In this review, we also discuss relative roles of the TP uplift and other impact factors, origins of the South Asian monsoon and East Asian monsoon, feedback effects and nonlinear responses of climatic and environmental changes to the plateau uplift. Finally, we make comparisons between numerical simulations and geological records, discuss their uncertainties, and highlight some problems worthy of further studying.

Generation of a buoyancy-driven coastal current by an Antarctic Polynya

Descent and spreading of high salinity water generated by salt rejection during sea ice formation in an Antarctic coastal polynya is studied using a hydrostatic, primitive equation three-dimensional ocean model called the Proudman Oceanographic Laboratory Coastal Ocean Modeling System (POLCOMS). The shape of the polynya is assumed to be a rectangle 100 km long and 30 km wide, and the salinity flux into the polynya at its surface is constant. The model has been run at high horizontal spatial resolution (500 m), and numerical simulations reveal a buoyancy-driven coastal current. The coastal current is a robust feature and appears in a range of simulations designed to investigate the influence of a sloping bottom, variable bottom drag, variable vertical turbulent diffusivities, higher salinity flux, and an offshore position of the polynya. It is shown that bottom drag is the main factor determining the current width. This coastal current has not been produced with other numerical models of polynyas, which may be because these models were run at coarser resolutions. The coastal current becomes unstable upstream of its front when the polynya is adjacent to the coast. When the polynya is situated offshore, an unstable current is produced from its outset owing to the capture of cyclonic eddies. The effect of a coastal protrusion and a canyon on the current motion is investigated. In particular, due to the convex shape of the coastal protrusion, the current sheds a dipolar eddy.

A mixed-phase bulk orographic precipitation model with embedded convection

A novel analytical model for mixed-phase, unblocked and unseeded orographic precipitation with embedded convection is developed and evaluated. The model takes an idealised background flow and terrain geometry, and calculates the area-averaged precipitation rate and other microphysical quantities. The results provide insight into key physical processes, including cloud condensation, vapour deposition, evaporation, sublimation, as well as precipitation formation and sedimentation (fallout). To account for embedded convection in nominally stratiform clouds, diagnostics for purely convective and purely stratiform clouds are calculated independently and combined using weighting functions based on relevant dynamical and microphysical time scales. An in-depth description of the model is presented, as well as a quantitative assessment of its performance against idealised, convection-permitting numerical simulations with a sophisticated microphysics parameterisation. The model is found to accurately reproduce the simulation diagnostics over most of the parameter space considered.

Multiple stationary solutions of an irradiated slab

A mathematical model describing the heat budget of an irradiated medium is introduced. The one-dimensional form of the equations and boundary conditions are presented and analysed. Heat transport at one face of the slab occurs by absorption (and reflection) of an incoming beam of short-wave radiation with a fraction of this radiation penetrating into the body of the slab, a diffusive heat flux in the slab and a prescribed incoming heat flux term. The other face of the slab is immersed in its own melt and is considered to be a free surface. Here, temperature continuity is prescribed and evolution of the surface is determined by a Stefan condition. These boundary conditions are flexible enough to describe a range of situations such as a laser shining on an opaque medium, or the natural environment of polar sea ice or lake ice. A two-stream radiation model is used which replaces the simple Beer’s law of radiation attenuation frequently used for semi-infinite domains. The stationary solutions of the governing equations are sought and it is found that there exists two possible stationary solutions for a given set of boundary conditions and a range of parameter choices. It is found that the existence of two stationary solutions is a direct result of the model of radiation absorption, due to its effect on the albedo of the medium. A linear stability analysis and numerical calculations indicate that where two stationary solutions exist, the solution corresponding to a larger thickness is always stable and the solution corresponding to a smaller thickness is unstable. Numerical simulations reveal that when there are two solutions, if the slab is thinner than the smaller stationary thickness it will melt completely, whereas if the slab is thicker than the smaller stationary thickness it will evolve toward the larger stationary thickness. These results indicate that other mechanisms (e.g. wave-induced agglomeration of crystals) are necessary to grow a slab from zero initial thickness in the parameter regime that yields two stationary solutions.

A model of melt pond evolution on sea ice

A one-dimensional, thermodynamic, and radiative model of a melt pond on sea ice is presented that explicitly treats the melt pond as an extra phase. A two-stream radiation model, which allows albedo to be determined from bulk optical properties, and a parameterization of the summertime evolution of optical properties, is used. Heat transport within the sea ice is described using an equation describing heat transport in a mushy layer of a binary alloy (salt water). The model is tested by comparison of numerical simulations with SHEBA data and previous modeling. The presence of melt ponds on the sea ice surface is demonstrated to have a significant effect on the heat and mass balance. Sensitivity tests indicate that the maximum melt pond depth is highly sensitive to optical parameters and drainage. INDEX TERMS: 4207 Oceanography: General: Arctic and Antarctic oceanography; 4255 Oceanography: General: Numerical modeling; 4299 Oceanography: General: General or miscellaneous; KEYWORDS: sea ice, melt pond, albedo, Arctic Ocean, radiation model, thermodynamic

Analytical solutions of a minimal model of species migration in a bounded domain

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally.

Flow structure and near-field dispersion in arrays of building-like obstacles

Dispersion in the near-field region of localised releases in urban areas is difficult to predict because of the strong influence of individual buildings. Effects include upstream dispersion, trapping of material into building wakes and enhanced concentration fluctuations. As a result, concentration patterns are highly variable in time and mean profiles in the near field are strongly non-Gaussian. These aspects of near-field dispersion are documented by analysing data from direct numerical simulations in arrays of building-like obstacles and are related to the underlying flow structure. The mean flow structure around the buildings is found to exert a strong influence over the dispersion of material in the near field. Diverging streamlines around buildings enhance lateral dispersion. Entrainment of material into building wakes in the very near field gives rise to secondary sources, which then affect the subsequent dispersion pattern. High levels of concentration fluctuations are also found in this very near field; the fluctuation intensity is of order 2 to 5.

Phytoplankton–zooplankton dynamics in the ‘presence’ or ‘absence’ of toxic phytoplankton

The inhibitory effects of toxin-producing phytoplankton (TPP) on zooplankton modulate the dynamics of marine plankton. In this article, we employ simple mathematical models to compare theoretically the dynamics of phytoplankton–zooplankton interaction in situations where the TPP are present with those where TPP are absent. We consider two sets of three-component interaction models: one that does not include the effect of TPP and the other that does. The negative effects of TPP on zooplankton is described by a non-linear interaction term. Extensive theoretical analyses of the models have been performed to understand the qualitative behaviour of the model systems around every possible equilibria. The results of local-stability analysis and numerical simulations demonstrate that the two model-systems differ qualitatively with regard to oscillations and stability. The model system that does not include TPP is asymptotically stable around the coexisting equilibria, whereas, the system that includes TPP oscillates for a range of parametric values associated with toxin-inhibition rate and competition coefficients. Our analysis suggests that the qualitative dynamics of the plankton–zooplankton interactions are very likely to alter due to the presence of TPP species, and therefore the effects of TPP should be considered carefully while modelling plankton dynamics.

Coalescence of particles by differential sedimentation

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.

Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

Effect of "Pollutants" on the functionality of breathable roofing membranes in a bat roost

The performance of breathable roofing membranes (BRM’s) in buildings where bats roost have been investigated using experimental measurements and numerical simulations. Measurement techniques as outlined in BS EN ISO 12572 of membranes from manufacturers in its pure state and those that have been contaminated with bat urine, faeces and natural oils transmitted via fur because they were found in bat roost have been tested for their permeability functions. The findings from this shows that there are significant differences between the functionality of the pure samples compared to the contaminated samples, with an average of about 20-30% reduction in functionality. This paper integrates modelling techniques using a heat, air and mass software with a simulink interface on a Matlab platform to investigate the moisture transfer properties of the BRMs. The simulation results demonstrate high level of condensation formation when the BRM is contaminated as compared to when it is not.

The physics of orographic gravity wave drag

The drag and momentum fluxes produced by gravity waves generated in flow over orography are reviewed, focusing on adiabatic conditions without phase transitions or radiation effects, and steady mean incoming flow. The orographic gravity wave drag is first introduced in its simplest possible form, for inviscid, linearized, non-rotating flow with the Boussinesq and hydrostatic approximations, and constant wind and static stability. Subsequently, the contributions made by previous authors (primarily using theory and numerical simulations) to elucidate how the drag is affected by additional physical processes are surveyed. These include the effect of orography anisotropy, vertical wind shear, total and partial critical levels, vertical wave reflection and resonance, non-hydrostatic effects and trapped lee waves, rotation and nonlinearity. Frictional and boundary layer effects are also briefly mentioned. A better understanding of all of these aspects is important for guiding the improvement of drag parametrization schemes.

Urban microclimates and urban heat island in Chongqing, China

Chongqing is the largest directly-controlled municipality in China, which is now undergoing a rapid urbanization. The urbanization rate increased from 35.6% in 2000 to 48.3% in 2007, and it is estimated to reach at least 70% by 2020. The question remains open: What are the consequences of such rapid urbanization in Chongqing in terms of urban microclimate? Furthermore, Chongqing is located within the Three Gorges Reservoir (TGR) region and the upper Yangtze River, where the Three Gorges Reservoir (TGR) project started in 1993 and was completed in 2010. As one of the biggest construction projects in the world with a rising water level of 175m and water storage capacity of about 39.3 billion m3, it would be interesting to investigate how such a gigantic project impacts the surrounding micro-environment, especially in Chongqing. Different research approaches are adopted in the study. Our literature review indicates present studies on the urban climate in Chongqing are mainly confined within the historical trend analysis of several weather stations operated by the Chongqing government, little is known about the spatial distribution of urban air temperature and how the local land cover influences the air temperature, especially when there are rivers running through the Chongqing urban area. To contribute to the present knowledge, a series of field measurement campaigns and numerical simulations were carried out. Two complementary types of field measurements are included: fixed weather stations and mobile transverse measurement. Numerical simulations using a house-developed program are able to predict the urban air temperature in Chongqing.