Instabilities in a staircase stratified shear flow

We study stratified shear flow instability where the density profile takes the form of a staircase of interfaces separating uniform layers. Internal gravity waves riding on density interfaces can resonantly interact due to a background shear flow, resulting in the Taylor-Caulfield instability. The many steps of the density profile permit a multitude of interactions between different interfaces, and a rich variety of Taylor-Caulfield instabilities. We analyse the linear instability of a staircase with piecewise-constant density profile embedded in a background linear shear flow, locating all the unstable modes and identifying the strongest. The interaction between nearest-neighbour interfaces leads to the most unstable modes. The nonlinear dynamics of the instabilities are explored in the long-wavelength, weakly stratified limit (the defect approximation). Unstable modes on adjacent interfaces saturate by rolling up the intervening layer into a distinctive billow. These nonlinear structures coexist when stacked vertically and are bordered by the sharp density gradients that are the remnants of the steps of the original staircase. Horizontal averages remain layer-like.     

Effects of wave-wave and wave-mean flow interactions on the evolution of a baroclinic wave

Abstract

The weakly nonlinear evolution of a free baroclinic wave in the presence of slightly supercritical, vertically sheared zonal flow and a forced stationary wave field that consists of a single zonal scale and an arbitrary number of meridional harmonics is examined within the context of the conventional two-layer model. The presence of the (planetary-scale) stationary wave introduces zonal variations in the supercriticality and is shown to alter the growth rate and asymptotic equilibrium of the (synoptic-scale) baroclinic wave via two distinct mechanisms: The first is due to the direct interaction of the stationary wave with the shorter synoptic wave (wave-wave mechanism), and the second is due to the interaction of the synoptic wave with that portion of the mean field that is corrected by the zonally rectified stationary wave fluxes (wave-mean mechanism). These mechanisms can oppose or augment each other depending on the amplitude and spatial structure of the stationary wave field. If the stationary wave field is confined primarily to the upper (lower) layer and consists of only the gravest cross-stream mode, conditions are favorable (unfavorable) for nonzero equilibrium of the free wave.

In addition to the time dependent heat flux generated by baroclinic growth of the free wave, its interaction with a stationary wave field consisting of two or more meridional harmonics generates time dependent heat fluxes that vary with period of the free wave. However, if the stationary wave field contains several meridional harmonics of sufficiently large amplitude, the free baroclinic wave is destroyed.     

The stability of dissipative magnetohydrodynamic shear flow in a parallel magnetic field

Abstract

Strong decay bounds are obtained for linearized perturbations to an unbounded, plane Couette flow in a parallel magnetic field. Finite conductivity and molecular viscosity are found to be stabilizing. Those modes decaying most slowly have the form of rolls aligned with the shear flow. The non-aligned rolls decay at an enhanced rate. Stability bounds at finite amplitude are obtained for flows bounded in one direction using energy methods.     

An experimental study of global instabilities due to the tidal (elliptical) distortion of a rotating elastic cylinder

Abstract

Broad band secondary instability of elliptical vortex motion has been proposed as a principal source of shear-flow turbulence. Here experiments on such instability in an elliptical flow with no shear boundary layer are described. This is made possible by the mechanical distortion in the laboratory frame of a rotating fluid-filled elastic cylinder. One percent ellipticity of a 10 cm diameter cylinder rotating once each second can give rise to an exponentially-growing mode stationary in the laboratory frame. In first order this mode is a sub-harmonic parametric Faraday instability. The finite-amplitude equations represent angular momentum transfer on an inertial time scale due to Reynolds stresses. The growth of this mode is not limited by boundary friction but by detuning and centrifugal stabilization. On average, a generalized Richardson number achieves a marginal value through much of the evolved flow. However, the characteristic flow is intermittent with the cycle: rapid growth, stabilizing momentum transfer from the mean flow, interior re-spin up, and then again. Data is presented in which, at large Reynolds numbers, seven percent ellipticity causes a fifty percent reduction in the kinetic energy of the rotating fluid. In the geophysical setting, this tidal instability in the earth's interior could be inhibited by sub-adiabatic temperature gradients. A near adiabatic region greater than 10 km in height would permit the growth of tidally destabilized modes and the release of energy to three-dimensional disturbances. Such disturbances might play a central role in the geodynamo and add significantly to overall tidal dissipation.     

Application of Proper Orthogonal Decomposition (POD) to inverse problems in saturated groundwater flow

We develop a new Proper Orthogonal Decomposition (POD) reduced order model for saturated groundwater flow, and apply that model to an inverse problem for the hydraulic conductivity field. We use sensitivities as the POD basis. We compare the output when the optimizer uses the reduced order model against results obtained with a full PDE based model. The solutions generated using the POD reduced model are comparable in residual norm to the solutions formed using only the full-scale model. The material parameters are similarly comparable. The time to solution when using the reduced model is reduced by at least an order of magnitude, as are the number of calls to the full model.     

Deformation patterns in a high-viscosity lava flow inferred from the crystal preferred orientation and imbrication structures: an example from Salina (Aeolian Islands,southern Tyrrhenian Sea,Italy)

Shape-preferred orientation and imbrication structures of crystals have been measured on samples representative of the base, centre and top of a highly viscous lava flow on Salina (Aeolian Islands, southern Tyrrhenian Sea). The data allow zones with different deformation patterns to be identified. In the base and top of the flow, deformation leads to the development of discrete preferred orientation and imbrication of the elongate crystals. The sense of shear is right-lateral at the base and left-lateral at the top of the flow. Shear strain can be estimated by the analysis of crystal preferred orientation. Deformation increases from the flow centre to the outer, more viscous boundary layers. Random orientation of crystals in the inner zone supports the presence of plug flow in a pseudoplastic lava. The textural features of the studied lava may be related to different mechanisms (i.e. lateral expansion). We conclude that the observed crystal alignments and imbrication structures may be related to a plug flow moving between two non-deforming walls. The walls are represented by the solidified, broken upper and basal crust of the flow. The low shear strain values calculated in the outer margins of the flow are indicative of the last deformation event. Crystal preferred orientation and imbrication structures may be related to the occurrence of velocity gradients existing between the inner zone of the flow and its solidus or near-solidus outer margins.     

Development of a remotely controlled debris flow monitoring system in the Dolomites (Acquabona,Italy)

Direct measurements of the hydrological conditions for the occurrence of debris flows and of flow behaviour are of the outmost importance for developing effective flow prevention techniques. An automated and remotely controlled monitoring system was installed in Acquabona Creek in the Dolomites, Italian Eastern Alps, where debris flows occur every year. Its present configuration consists of three on‐site stations, located in the debris‐flow initiation area, in the lower channel and in the retention basin. The monitoring system is equipped with sensors for measuring rainfall, pore‐water pressure in the mobile channel bottom, ground vibrations, debris flow depth, total normal stress and fluid pore‐pressure at the base of the flow. Three video cameras take motion pictures of the events at the initiation zone, in the lower channel and in the deposition area. Data from the on‐site stations are radio‐transmitted to an off‐site station and stored in a host PC, from where they are telemetrically downloaded and used by the Padova University for the study of debris flows. The efficiency of the sensors and of the whole monitoring system has been verified by the analysis of data collected so far. Examples of these data are presented and briefly discussed. If implemented at the numerous debris‐flow sites in the Dolomitic Region, the technology used, derived from the development of this system, will provide civil defence and warn residents of impending debris flows. Copyright © 2003 John Wiley & Sons, Ltd.     

River flow regime and snow cover of the Pamir Alay (Central Asia) in a changing climate

Abstract

The Vakhsh and Pyandj rivers, main tributaries of the Amu Darya River in the mountainous region of the Pamir Alay, play an important role in the water resources of the Aral Sea basin (Central Asia). In this region, the glaciers and snow cover significantly influence the water cycle and flow regime, which could be strongly modified by climate change. The present study, part of a project funded by the European Commission, analyses the hydrological situation in six benchmark basins covering areas of between 1800 and 8400 km², essentially located in Tajikistan, with a variety of topographical situations, precipitation amounts and glacierized areas. Four types of parameter are discussed: temperature, glaciation, snow cover and river flows. The study is based mainly on a long-time series that ended in the 1990s (with the collapse of the Soviet Union) and on field observations and data collection. In addition, a short, more recent period (May 2000 to May 2002) was examined to better understand the role of snow cover, using scarce monitored data and satellite information. The results confirm the overall homogeneous trend of temperature increase in the mountain range and its impacts on the surface water regime. Concerning the snow cover, significant differences are noted in the location, elevation, orientation and morphology of snow cover in the respective basins. The changes in the river flow regime are regulated by the combination of the snow cover dynamics and the increasing trend of the air temperature.

Editor Z.W. Kundzewicz     

Crystal-rich mass flow deposits related to the eruption of a sublacustrine silicic cryptodome (Early Permian Collio Basin, Italian Alps)

Sedimentological, granulometric and petrographic data are presented from a detailed study on a crystal-rich mass flow deposit, which is presumably related to the eruption of a sublacustrine cryptodome. The deposit forms a prominent intercalation in the Lower Permian Collio Formation in the Italian Alps north of Brescia. Outcrops of the 10–20-m-thick volcaniclastic deposit (Dasdana I Beds, DB) can be traced over 12 km from east to west. The DB consists of a thick, crystal-rich, sandy–gravelly lower subunit representing a sequence of amalgamated Bouma-a(b) divisions overlain by a thin, well-bedded, sandy–muddy subunit that is rich in outsize porphyritic silicic fragments. Modal and computer-aided image analyses reveal that the crystal-rich lower subunit contains up to 80% of volcanogenic crystals. Some samples contain up to 60% of porphyritic fragments, which have a phenocryst content of about 20%. The wide textural range from cryptocrystalline, poikilomosaic, to rarer medium-grained granophyric groundmass, the irregular to lensoid shapes of the porphyritic fragments, and the presence of basement and sedimentary clasts suggest that the DB originated from a sublacustrine eruption of a partially extrusive cryptodome (ca. 1.6 km³). Two other porphyritic felsic cryptodomes (Dosso dei Lupi, Dosso del Bue), described briefly here, emplaced into the Collio Formation sometime after the DB event, and expose flat bases and tilted sediments at their sides. Textures observed in these domes are comparable to those found in the DB porphyritic fragments.     

The effect of low‐permeability fault zones on groundwater flow in a compartmentalized system. Experimental evidence from a carbonate aquifer (Southern Italy)

The hydrogeological behaviour of fault zones in carbonate aquifers is often neglected in conceptual and numerical models. Furthermore, no information is available regarding the relationships between piezometric levels when significant compartmentalization occurs due to the occurrence of low‐flow fault zones. The aim of this study was to refine the conceptualization of subsurface flow in faulted carbonate aquifers and to analyse relationships between sub‐basins within a compartmentalized aquifer system in Southern Italy. The interactions between compartments that straddle low‐flow faults were investigated over four hydrologic years using a statistical approach to compare (i) the hydraulic heads within two wells located up‐ and down‐gradient of tectonic discontinuities as well as (ii) the rainfall and piezometric levels. The results of this study suggest that a set of barriers exists between the wells, and, therefore, the total head loss observed between the wells (approximately 80 m) should be distributed across several aquitards, with one aquitard exhibiting a relatively high permeability or low degree of integrity. Due to slight differences in permeability, transient conditions in aquitards can occur over relatively short periods, which is in agreement with the results of the statistical data analysis. Consequently, rather than being caused by pure aquitards, aquifer system compartmentalization likely results from slight differences in the permeability between lower‐permeability fault zones and adjacent higher‐permeability protoliths. Copyright © 2014 John Wiley & Sons, Ltd.     

The influence of preferential flow on hillslope hydrology in a semi‐arid watershed (in the Spanish Dehesas)

Preferential flow is known to influence hillslope hydrology in many areas around the world. Most research on preferential flow has been performed in temperate regions. Preferential infiltration has also been found in semi‐arid regions, but its impact on the hydrology of these regions is poorly known. The aim of this study is to describe and quantify the influence of preferential flow on the hillslope hydrology from small scale (infiltration) to large scale (subsurface stormflow) in a semi‐arid Dehesa landscape. Precipitation, soil moisture content, piezometric water level and discharge data were used to analyse the hydrological functioning of a catchment in Spain. Variability of soil moisture content during the transition from dry to wet season (September to November) within horizontal soil layers leads to the conclusion that there is preferential infiltration into the soils. When the rainfall intensity is high, a water level rapidly builds up in the piezometer pipes in the area, sometimes even reaching soil surface. This water level also drops back to bedrock within a few hours (under dry catchment conditions) to days (under wet catchment conditions). As the soil matrix is not necessarily wet while this water layer is built up, it is thought to be a transient water table in large connected pores which drain partly to the matrix, partly fill up bedrock irregularities and partly drain through subsurface flow to the channels. When the soil matrix becomes wetter the loss of water from macropores to the matrix and bedrock decreases and subsurface stormflow increases. It may be concluded that the hillslope hydrological system consists of a fine matrix domain and a macropore domain, which have their own flow characteristics but which also interact, depending on the soil matrix and macropore moisture contents. The macropore flow can result in subsurface flow, ranging from 13% contribution to total discharge for a large event of high intensity rainfall or high discharge to 80% of total discharge for a small event with low intensity rainfall or low discharge. During large events the fraction of subsurface stormflow in the discharge is suppressed by the large amount of surface runoff. Copyright © 2008 John Wiley & Sons, Ltd.     

The relationship between sap flow of intercropped young poplar trees (Populus×euramericana cv. N3016) and environmental factors in a semiarid region of northeastern China

Estimating transpiration of the trees in agroforestry system is important in water management of the site. Sap flow of intercropped fast‐growing young poplar trees and microclimate factors in semiarid northeastern China was measured in two growing seasons (2008 and 2009). Sapwood growth and water storage of wood and leaf increment during the growing season were involved in the calculation of sap flow. The results showed that diurnal variation of sap flow followed to that of short wave solar radiation. Sap flows both in 10 min mean and daily gross values mainly depended on solar radiation and vapor pressure deficit, and the relations well fit hyperbolic function. The regression coefficients of monthly window data indicated that the seasonal variation of sap flow capacities decreased gradually from June to September. Moderate soil water stress of upper soil layer (0–50 cm) did not constrain the sap flow because the trees could use the water at deeper soil layer. The daily sap flow per tree ranged 0.8 to 18.1 and 3.7 to 23.8 kg d^?1 tree^?1, with averages of 8.7 and 14.3 kg d^?1 tree^?1 in 2008 and 2009 respectively. An empirical model was established to estimate the sap flow of the poplar trees by solar radiation, vapor pressure deficit, leaf area index and Julian days. Copyright © 2011 John Wiley & Sons, Ltd.