Barotropic instability of coastal flows as a boundary-value problem: linear and non-linear theory

The barotropic instability is traditionally viewed as an initial-value problem wherein wave perturbations of a laterally sheared flow in a homogeneous uniformly rotating fluid that temporally grows into vortices. The vortices are capable of mixing fluid on the continental shelf with fluid above the continental slope and adjacent deep-sea region. However, the instability can also be viewed as a boundary-value problem. For example, a laterally sheared coastal flow is perturbed at some location, creating perturbations that grow spatially downstream. This process leads to a time periodic flow that exhibits instability in space. This article first examines the linear barotropic instability problem with real frequency and complex wavenumber. It is shown that there exists a frequency band within which a spatially growing wave is present. It is then postulated that far downstream the spatially unstable flow emerges into a chain of identically axisymmetric vortices. Conservation of mass, momentum and energy fluxes are applied to determine the diameter, spacing and the speed of translation of the vortices.     

A theory of convection: Modelling by two buoyant interacting fluids

Abstract

A new model of convection and mixing is presented. The fluid is envisioned as being composed of two buoyant interacting fluids, called thermals and anti-thermals. In the context of the Boussinesq approximation, pairs of governing equations are derived for thermals and anti-thermals. Each pair meets an Invariance Principle as a consequence of the reciprocity in the roles played by thermals and anti-thermals. Each pair is transformed into an average equation for which interaction terms cancel and another very simple equation linking the two fluid properties. An important parameter of the model is the fraction, f, of area occupied by thermals to the total area. A dynamic saturation equilibrium between thermals and antithermals is assumed. This implies a constant values of f throughout the system. The set of equations is written in terms of mean values and root-mean-square fluctuations, in keeping with equations of turbulence theories. The final set consists of four coupled non-linear differential equations. The model neglects dissipation and can be applied to any convective situations where molecular viscosity and diffusivity may be neglected. Applications of the model to mixed-layer deepening and penetrative convection are presented in subsequent papers.     

Can the EU emission trading scheme support CDM forestry?

Abstract

The European Commission is mandated to consider the inclusion of credits from land-use projects under the clean development mechanism (CDM) and joint implementation (JI), beginning with the second period of the European Union's emission trading scheme (ETS) in its report due in July 2006. Temporary credits from afforestation and reforestation under the CDM are seen by many as posing a technical problem for their use under the ETS. This article summarizes three feasible, efficient and environmentally sound alternatives for achieving the integration of such temporary credits in the European emissions trading market starting in 2008. The first proposal integrates tCERs and lCERs (temporary credits) into the EU ETS by allowing for their direct use for compliance purposes. The second proposal builds on the idea of swapping temporary credits for EU allowances (EUAs) by Member States. The third proposal would not require a political decision at the EU level. Instead supportive Member States or private carbon fund operators would agree to swap temporary credits for the CERs or ERUs they hold in their accounts. All three solutions would be linked to a risk-mitigation strategy based on levying a fee or fixing an exchange rate, which would allow governments to hedge the risk of losing temporary credits.     

Facies model of a fine‐grained,tide‐dominated delta: Lower Dir Abu Lifa Member (Eocene), Western Desert,Egypt

Existing facies models of tide‐dominated deltas largely omit fine‐grained, mud‐rich successions. Sedimentary facies and sequence stratigraphic analysis of the exceptionally well‐preserved Late Eocene Dir Abu Lifa Member (Western Desert, Egypt) aims to bridge this gap. The succession was deposited in a structurally controlled, shallow, macrotidal embayment and deposition was supplemented by fluvial processes but lacked wave influence. The succession contains two stacked, progradational parasequence sets bounded by regionally extensive flooding surfaces. Within this succession two main genetic elements are identified: non‐channelized tidal bars and tidal channels. Non‐channelized tidal bars comprise coarsening‐upward sandbodies, including large, downcurrent‐dipping accretion surfaces, sometimes capped by palaeosols indicating emergence. Tidal channels are preserved as single‐storey and multilateral bodies filled by: (i) laterally migrating, elongate tidal bars (inclined heterolithic strata, 5 to 25 m thick); (ii) forward‐facing lobate bars (sigmoidal heterolithic strata, up to 10 m thick); (iii) side bars displaying oblique to vertical accretion (4 to 7 m thick); or (iv) vertically‐accreting mud (1 to 4 m thick). Palaeocurrent data show that channels were swept by bidirectional tidal currents and typically were mutually evasive. Along‐strike variability defines a similar large‐scale architecture in both parasequence sets: a deeply scoured channel belt characterized by widespread inclined heterolithic strata is eroded from the parasequence‐set top, and flanked by stacked, non‐channelized tidal bars and smaller channelized bodies. The tide‐dominated delta is characterized by: (i) the regressive stratigraphic context; (ii) net‐progradational stratigraphic architecture within the succession; (iii) the absence of upward deepening trends and tidal ravinement surfaces; and (iv) architectural relations that demonstrate contemporaneous tidal distributary channel infill and tidal bar accretion at the delta front. The detailed facies analysis of this fine‐grained, tide‐dominated deltaic succession expands the range of depositional models available for the evaluation of ancient tidal successions, which are currently biased towards transgressive, valley‐confined estuarine and coarser grained deltaic depositional systems.     

Variably saturated groundwater modelling for optimizing managed aquifer recharge using trench infiltration

Spreading‐basin methods have resulted in more than 130 million cubic metres of recharge to the unconfined Navajo Sandstone of southern Utah in the past decade, but infiltration rates have slowed in recent years because of reduced hydraulic gradients and (or) clogging. Trench infiltration is a promising alternative technique for increasing recharge and minimizing evaporation. This paper uses a variably saturated flow model to further investigate the relative importance of the following variables on rates of trench infiltration to unconfined aquifers: saturated hydraulic conductivity, trench spacing and dimensions, initial water‐table depth, alternate wet/dry periods, and number of parallel trenches. Modelling results showed (1) increased infiltration with higher hydraulic conductivity, deeper initial water tables, and larger spacing between parallel trenches, (2) deeper or wider trenches do not substantially increase infiltration, (3) alternating wet/dry periods result in less overall infiltration than keeping the trenches continuously full, and (4) larger numbers of parallel trenches within a fixed area increases infiltration but with a diminishing effect as trench spacing becomes tighter. An empirical equation for estimating expected trench infiltration rates as a function of hydraulic conductivity and initial water‐table depth was derived and can be used for evaluating feasibility of trench infiltration in other hydrogeologic settings. Copyright © 2014 John Wiley & Sons, Ltd.     

Hydrous partial melting in the sheeted dike complex at fast spreading ridges: experimental and natural observations

In ophiolites and in present-day oceanic crust formed at fast spreading ridges, oceanic plagiogranites are commonly observed at, or close to the base of the sheeted dike complex. They can be produced either by differentiation of mafic melts, or by hydrous partial melting of the hydrothermally altered sheeted dikes. In addition, the hydrothermally altered base of the sheeted dike complex, which is often infiltrated by plagiogranitic veins, is usually recrystallized into granoblastic dikes that are commonly interpreted as a result of prograde granulitic metamorphism. To test the anatectic origin of oceanic plagiogranites, we performed melting experiments on a natural hydrothermally altered dike, under conditions that match those prevailing at the base of the sheeted dike complex. All generated melts are water saturated, transitional between tholeiitic and calc-alkaline, and match the compositions of oceanic plagiogranites observed close to the base of the sheeted dike complex. Newly crystallized clinopyroxene and plagioclase have compositions that are characteristic of the same minerals in granoblastic dikes. Published silicic melt compositions obtained in classical MORB fractionation experiments also broadly match the compositions of oceanic plagiogranites; however, the compositions of the coexisting experimental minerals significantly deviate from those of the granoblastic dikes. Our results demonstrate that hydrous partial melting is a likely common process in the root zone of the sheeted dike complex, starting at temperatures exceeding 850°C. The newly formed melt can either crystallize to form oceanic plagiogranites or may be recycled within the melt lens resulting in hybridized and contaminated MORB melts. It represents the main MORB crustal contamination process. The residue after the partial melting event is represented by the granoblastic dikes. Our results support a model with a dynamic melt lens that has the potential to trigger hydrous partial melting reactions in the previously hydrothermally altered sheeted dikes. A new thermometer using the Al content of clinopyroxene is also elaborated.