Axisymmetric annulus convection at unit Prandtl number

Abstract

We examine the role played in annulus flows by mechanisms dependent upon the Prandtl number, σ. Solutions are obtained at σ = 1 for both the real annulus system and for the hypothetical “free annulus” system (free slip lateral boundaries). These solutions are compared with previously obtained solutions at σ = 7.

In the free annulus, the solution at σ = 1 differs radically from that at σ = 7. The σ = 1 solution appears to be essentially a finite amplitude mode due to Solberg instability whereas the solution at σ = 7 manifests a flow caused by the diffusive overturning mechanism.

The variation with σ of the real annulus flow is not so fundamental but some differences in the dynamical structures are noted.     

An experimental investigation of blocking by partial barriers in a rotating baroclinic annulus

We present a series of experimental investigations in which a differentially-heated annulus was used to investigate the effects of topography on rotating, stratified flows with similarities to the Earth’s atmospheric or oceanic circulation. In particular, we compare and investigate blocking effects via partial mechanical barriers to previous experiments by the authors utilising azimuthally-periodic topography. The mechanical obstacle used was an isolated ridge, forming a partial barrier, employed to study the difference between partially blocked and fully unblocked flow. The topography was found to lead to the formation of bottom-trapped waves, as well as impacting the circulation at a level much higher than the top of the ridge. This produced a unique flow structure when the drifting flow and the topography interacted in the form of an “interference” regime at low Taylor number, but forming an erratic “irregular” regime at higher Taylor number. The results also showed evidence of resonant wave-triads, similar to those noted with periodic wavenumber-3 topography by Marshall and Read (Geophys. Astrophys. Fluid Dyn., 2015, 109), though the component wavenumbers of the wave-triads and their impact on the flow were found to depend on the topography in question. With periodic topography, wave-triads were found to occur between both the baroclinic and barotropic components of the zonal wavenumber-3 mode and the wavenumber-6 baroclinic component, whereas with the partial barrier two nonlinear resonant wave-triads were noted, each sharing a common wavenumber-1 mode.     

An experimental study of the effects of the upper boundary condition on the thermal convection in a rotating,differentially heated cylindrical annulus of water

Abstract

The effects of the upper boundary condition on the regime diagram and certain characteristics of the convection within a rotating, differentially heated cylindrical anulus of water were studied in the laboratory. It was found that the regime diagram was not substantially affected by the upper boundary condition. However, the thermal amplitude of the baroclinic waves, as a function of parameter space, and, as expected from previous work, the angular drift velocity of those waves were found to be strongly affected by the upper boundary condition. When the upper surface was free, the amplitude changes were explosive and highly non-linear (as discovered earlier by Kaiser, 1970). When the upper surface was rigid, they were smooth and quite linear. The baroclinic wave patterns drifted round the annulus at rates which were in direct response to the imposed “thermal wind”. However, (as previously observed by Koschmieder, 1972), when the upper surface was rigid they drifted approximately ten times more slowly than when it was free.     

An experimental investigation into topographic resonance in a baroclinic rotating annulus

This paper documents an experimental investigation in which a differentially-heated rotating annulus experiment was used to investigate the effects of topography on fluid flow under conditions similar to the atmospheric and oceanic circulation on Earth and other planets. In particular, the relationship between the effects of topographic resonance and the existence and mechanism for generation of low-frequency variability (LFV) were studied, motivated by outstanding questions in works such as Jin and Ghil (J. Atmos. Sci., 1990, 47) and Read and Risch (Geophys. Astrophys. Fluid Dyn., 2011, 105). Whilst employing sinusoidal wavenumber-3 topography a new regime was encountered within a region of stationary wavenumber-3 structural vacillation. Denoted as the “stationary-transition” regime, it featured periodic oscillations between a dominant stationary wavenumber-3 flow and axisymmetric or chaotic flow. Further investigation found that the “stationary-transition” regime appeared to be a near-resonant region where nonlinear topographic resonant instability led to a 23–42 “day” oscillatory behaviour. Within the regime, a Hopf bifurcation sequence was discovered, and the nonlinear instabilities were found to have terms in both wave-zonal flow and wave–wave interactions, including a notable resonant wave-triad. This report summarises the nature of the “stationary-transition” regime, and also makes comparisons with similar regimes of LFV found in other experimental studies, as well as intraseasonal oscillations in the atmosphere.     

The changing role of ecohydrological science in guiding environmental flows

Abstract

The term “environmental flows” is now widely used to reflect the hydrological regime required to sustain freshwater and estuarine ecosystems, and the human livelihoods and well-being that depend on them. The definition suggests a central role for ecohydrological science to help determine a required flow regime for a target ecosystem condition. Indeed, many countries have established laws and policies to implement environmental flows with the expectation that science can deliver the answers. This article provides an overview of recent developments and applications of environmental flows on six continents to explore the changing role of ecohydrological sciences, recognizing its limitations and the emerging needs of society, water resource managers and policy makers. Science has responded with new methods to link hydrology to ecosystem status, but these have also raised fundamental questions that go beyond ecohydrology, such as who decides on the target condition of the ecosystem? Some environmental flow methods are based on the natural flow paradigm, which assumes the desired regime is the natural “unmodified” condition. However, this may be unrealistic where flow regimes have been altered for many centuries and are likely to change with future climate change. Ecosystems are dynamic, so the adoption of environmental flows needs to have a similar dynamic basis. Furthermore, methodological developments have been made in two directions: first, broad-scale hydrological analysis of flow regimes (assuming ecological relevance of hydrograph components) and, second, analysis of ecological impacts of more than one stressor (e.g. flow, morphology, water quality). All methods retain a degree of uncertainty, which translates into risks, and raises questions regarding trust between scientists and the public. Communication between scientists, social scientists, practitioners, policy makers and the public is thus becoming as important as the quality of the science.

Editor Z.W. Kundzewicz

Citation Acreman, M.C., Overton, I.C., King, J., Wood, P., Cowx, I.G., Dunbar, M.J., Kendy, E., and Young, W., 2014. The changing role of ecohydrological science in guiding environmental flows. Hydrological Sciences Journal, 59 (3–4), 433–450     

Nonlinear internal waves in the upper atmosphere

To investigate the mechanism of mixing in oscillatory doubly diffusive (ODD) convection, we truncate the horizontal modal expansion of the Boussinesq equations to obtain a simplified model of the process. In the astrophysically interesting case with low Prandtl number (traditionally called semiconvection), large-scale shears are generated as in ordinary thermal convection. The interplay between the shear and the oscillatory convection produces intermittent overturning of the fluid with significant mixing. By contrast, in the parameter regime appropriate to sea water, large-scale flows are not generated by the convection. However, if such flows are imposed externally, intermittent overturning with enhanced mixing is observed.     

Laboratory experiments in a baroclinic annulus with heating and cooling on the horizontal boundaries

Abstract

Experiments have been performed in a cylindrical annulus with horizontal temperature gradients imposed upon the horizontal boundaries and in which the vertical depth was smaller than the width of the annulus. Qualitative observations were made by the use of small, suspended, reflective flakes in the liquid (water).

Four basic regimes of flow were observed: (1) axisymmetric flow, (2) deep cellular convection, (3) boundary layer convective rolls, and (4) baroclinic waves. In some cases there was a mix of baroclinic and convective instabilities present. As a “mean” interior Richardson number was decreased from a value greater than unity to one less than zero, axisymmetric baroclinic instability of the Solberg type was never observed. Rather, the transition was from non-axisymmetric baroclinic waves, to a mix of baroclinic and convective instability, to irregular cellular convection.     

The variation of cosmogenic Kr and Xe in a core from Estherville mesosiderite: direct evidence that the lunar131Xe anomaly is a depth effect

Kr and Xe were measured by a stepwise heating technique in three samples of a drill core in the “Minnesota” fragment of the Estherville mesosiderite. The cosmogenic⁷⁸Kr/⁸³Kr decreased from the “top” sample to the “bottom” sample(“top” = 0.163 ± 0.005, “bottom” = 0.151 ± 0.005) while the cosmogenic¹³¹Xe/¹²⁶Xe ratio increased(“top” = 5.58 ± 0.35, “bottom” = 6.92 ± 0.17). Cosmic-ray track studies have shown that the “top” sample was indeed closer to the preatmospheric surface than the “bottom” sample by ～ 10 cm. This is the first direct evidence, in a sample of known geometry, that the cosmogenic¹³¹Xe/¹²⁶Xe ratio increases as a function of depth, and as such, confirms the hypothesis that the lunar¹³¹Xe anomaly is a bona fide depth effect due to resonance neutron capture in¹³⁰Ba.     

Diffusive destabilisation of the baroclinic circular vortex

Abstract

It is shown that, even for vanishingly small diffusivities of momentum and heat, a rotating stratified zonal shear flow is more unstable to zonally symmetric disturbances than would be indicated by the classical inviscid adiabatic criterion, unless σ, the Prandtl number, = 1. Both monotonic instability, and growing oscillations ("overstability") are involved, the former determining the stability criterion and having the higher growth rates. The more σ differs from 1, the larger the region in parameter space for which the flow is stable by the classical criterion, but actually unstable.

If the baroclinity is sufficiently great for the classical criterion also to indicate instability, the corresponding inviscid adiabatic modes usually have the numerically highest growth rates. An exception is the case of small isotherm slope and small σ.

A single normal mode of the linearized theory is also, formally, a finite amplitude solution; however, no theoretical attempt is made to assess the effect of finite amplitude in general. But, in a following paper, viscous overturning (the mechanism giving rise to the sub‐classical monotonic instability when σ > 1) is shown to play an important role at finite amplitude in certain examples of nonlinear steady thermally‐driven axisymmetric flow of water in a rotating annulus. Irrespective of whether analogous mechanisms turn out to be identifiable and important in large‐scale nature, it appears then that a Prandtl‐type parameter should enter the discussion of any attempt to make laboratory or numerical models of zonally‐symmetric baroclinic geophysical or astrophysical flows.     

A nonlinear dynamo driven by rapidly rotating convection

In Kim et al. (Kim, E., Hughes, D.W. and Soward, A.M., “An investigation into high conductivity dynamo action driven by rotating convection”, Geophys. Astrophys. Fluid Dynam. 91, 303–332 ().) we investigated kinematic dynamo action driven by rapidly rotating convection in a cylindrical annulus. Here we extend this work to consider self-consistent nonlinear dynamo action in which the back-reaction of the Lorentz force on the flow is taken into account. In particular, we investigate, as a function of magnetic Prandtl number, the evolution of an initially weak magnetic field in two different types of convective flow – one chaotic and the other integrable. On saturation, the latter shows a systematic dependence on the magnetic Prandtl number whereas the former appears not to. In addition, we show how, in keeping with the findings of Cattaneo et al. (Cattaneo, F., Hughes, D.W. and Kim, E., “Suppression of chaos in a simplified nonlinear dynamo model”, Phys. Rev. Lett. 76, 2057–2060 ().), saturation of the growth of the magnetic field is brought about, for the originally chaotic flow, by a strong suppression of chaos.     

Cyclonic-anticyclonic asymmetry and a new soliton concept for rossby vortices in the laboratory,oceans and the atmospheres of giant planets

Abstract

It is demonstrated in laboratory experiments with rotating shallow water that large scale Rossby vortices, greater than the Rossby-Obukhov radius in size, have dispersive and non-linear properties that are fundamentally different for the two possible polarities. We call this “cyclonic-anticyclonic asymmetry”. This asymmetry manifests itself in the following way: first, anticylones, unlike cyclones, do not undergo the dispersive spreading inherent in a linear wave packet. and therefore, having a considerably longer natural lifetime, are obvious candidates for Rossby solitons; second, dipolar vortices are, because of the comparatively rapid decay of a cyclone, transformed into anticyclonic solitons; third, anticyclones are much more readily generated by zonal flows of the type existing in planetary atmospheres. The evident dominance of anticyclones amongst the long-lived vortices in the atmospheres of giant planets strongly suggests that the cyclonic-anticyclonic symmetry plays a decisive role in the atmospheric cyclogenesis of large planets.

According to our concept, the Rossby soliton is a “real” vortex; unlike a wave, it retains some fluid particles within it throughout its lifetime. Two similar solitons can merge by mutual collisions. This picture of a “vortical” soliton differs in an essential way from the earlier idea due to Maxworthy and Redekopp (1976) of purely “wave-like” Rossby solitons that can freely pass through one another.

Laboratory experiments were performed by us to simulate the new Rossby solition, with special reference to naturally-occurring vortices of the same general type as Jupiter's great red spot. The experimental data presented contradict the idea of “pure wave solitons” but confirm our concept of “vortical solutions”.     

Rocking instability of free-standing statues atop slender cantilevers under ground motion

This paper deals with the dynamic response of free-standing statues on the top surface of slender elastically supported cantilevers subjected to horizontal ground motion. Given that there is no link between the base of the statue and the top surface of the monolithic cantilever the statue is in equilibrium in the vertical direction under its own weight. Attention is focused on the determination of the minimum amplitude ground acceleration which leads to the rocking (overturning) instability of the statue whose mass and rotatory inertia are a priory known. It is assumed that the friction between the base of the statue and the top surface of the cantilever is sufficiently large to prevent sliding so that rocking prevails. After simulating the statue by a rigid block freely supported on the top surface of the elastically restrained monolithic cantilever, a theoretical dynamic analysis of the cantilever–rigid block system under horizontal ground motion is comprehensively presented. Two modes of overturning instability of the free standing rigid block are discussed: instability without or with impact. Criteria for overturning instability of the rigid block associated with the minimum amplitude ground acceleration which leads through the vanishing of the angular velocity to an escaped motion in the phase-plane portrait, are properly assessed.     

On the inadequacies of Long's model for steady two-dimensional stratified flows

Nonlinear analysis of two-dimensional steady flows with density stratification in the presence of gravity is considered. Inadequacies of Long's model for steady stratified flow over topography are explored. These include occurrence of closed streamline regions and waves propagating upstream. The usual requirements in Long's model of constant dynamic pressure and constant vertical density gradient in the upstream condition are believed to be the cause of these inadequacies. In this article, we consider a relaxation of these requirements, and also provide a systematic framework to accomplish this. As illustrations of this generalized formulation, exact solutions are given for the following two special flow configurations: the stratified flow over a barrier in an infinite channel; the stratified flow due to a line sink in an infinite channel. These solutions exhibit again closed-streamline regions as well as waves propagating upstream. The persistence of these inadequacies in the generalized Long's model appears to indicate that they are not quite consequences of the assumptions of constant dynamic pressure and constant vertical density gradient in Long's model, contrary to previous belief.

On the other hand, solutions admitted by the generalized Long's model show that departures from Long's model become small as the flow becomes more and more supercritical. They provide a nonlinear mechanism for the generation of columnar disturbances upstream of the obstacle and lead in subcritical flows to qualitatively different streamline topological patterns involving saddle points, which may describe the lee-wave-breaking process in subcritical flows and could serve as seats of turbulence in real flows. The occurrences of upstream disturbances in the presence of lee-wave-breaking activity described by the present solution are in accord with the experiments of Long (Long, R.R., “Some aspects of the flow of stratified fluids, Part 3. Continuous density gradients”, Tellus 7, 341--357 (1955)) and Davis (Davis, R.E., “The two-dimensional flow of a stratified fluid over an obstacle”, J. Fluid Mech. 36, 127–143 ()).     

Morphed block-crack preferential sedimentation in a reservoir bed: a smart design and evolution in nature

Abstract

A pedological study of the reservoir bed of Al-Khoud Dam, Oman, revealed an unusual sedimentation pattern which evolved into an intricate composition of silt blocks surrounded by vertical cracks and horizontal layers filled with a “proppant” sand. The discovered soil morphology reflects the complex topology of water motion (infiltration–seepage–evaporation) through the sand-filled cracks/layers and blocks during both the rare flood events and ensuing periods of ponding, and the long, intervening dry periods. These naturally formed soils demonstrate an ability to preserve a large quantity of water inside the silty blocks at depths of 0.5 to 1.5 m, despite the high temperature and dryness of the topsoil. The hydrological optimality and “smartness” of these soils is attributed to the unique block-crack system. Natural, lush vegetation was found in adjacent zones of the reservoir bed, and acted as a footprint of the shallow “fractured perched aquifer”. Planted “ivy” (Convolvulaceae) in the vertical face of one pedon showed intensive growth without irrigation. Soil moisture content data confirmed the hydrological immobility of water in the blocks if not depleted by transpiration. The novel phenomena reported unveil the possible alteration of soil heterogeneity for optimization of the soil–water system in arid zone soils.

Editor D. Koutsoyiannis; Associate editor F.F. Hattermann

Citation Al-Ismaily, S.S., Al-Maktoumi, A.K., Kacimov, A.R., Al-Saqri, S.M., Al-Busaidi, H.A., and Al-Haddabi, M.H., 2013. Morphed block-crack preferential sedimentation in a reservoir bed: a smart design and evolution in nature. Hydrological Sciences Journal, 58 (8), 1779–1788.     

Hydrological controls of erosion and sediment transport in volcanic torrents

Abstract

Sediment is transported in the form of debris flows in major gullies dissecting permeable volcanic slopes as exemplified by the Kami-kamihori Valley in the northern Japan Alps. Four years of hydrological observations in the headwater area of the gully showed that the surface runoff which triggers debris flows is related to peak 10- to 20-minute rainfall. Sediment production in such a short time is not sufficient to prepare a debris flow. Therefore, debris must have been accumulated at a particular section by repeated sediment discharge due to minor rainstorms. The volume of the debris produced in the headwaters was evaluated and correlated to an effective rainfall. The quantity of sediment transport at seven sections along the gully by debris flows in three periods was evaluated through the measurement of the topographic changes. It was compared with the total effective rainfall for the pertinent period, and the mean “sediment concentration” in the debris flow was calculated for each section and for each period. It was shown that the change in the sediment concentration along the gully reflects the entrainment of debris from the gully floor in the acceleration zone and the deposition in the deceleration zone. It was also demonstrated that the sediment delivery of a debris flow depends on the time distribution of rainfall, because rainfall time bases appropriate to prediction of the sediment transport at different reaches vary.     

A quasi-geostrophic numerical model of a rotating internally heated fluid

Abstract

A quasi-geostrophic numerical model of flow in a rotating channel is integrated under conditions typical of laboratory experiments with an internally heated annulus system. Compared to a laboratory experiment, or a full Navier-Stokes simulation, the quasi geostrophic numerical model is a simple system. It includes nonlinear interactions, dissipation via conventional parameterizations of Ekman layers and internal diffusion, and a steady forcing term which represents heating near the centre of the channel and cooling near both sides. Explicit boundary layers, cylindrical geometry effects, horizontal variations in static stability and variations in conductivity and diffusivity with temperature are all absent, and ageostrophic advection is incompletely represented. Nevertheless, over a range of parameters, flows are produced which strongly resemble those seen in the laboratory thus suggesting that the most important physical processes are represented. The numerical model is used to map out a regime diagram which includes examples of steady flows, flows with periodic time dependence (wavenumber vacillations) and flows which are irregularly time dependent.     

The structure of separated flow past a circular cylinder in a rotating frame

Abstract

This paper examines the detailed E ^1/4-layer structure of separated flow past a circular cylinder in a low-Rossby-number rotating fluid as the Ekman number E tends to zero. This structure is based on an initial proposal by Page (1987) but with some modifications in response to further evidence, outlined both in this paper and elsewhere, on the behaviour of E ^1/4-layer flows in this context. Numerical calculations for flow in an E ^1/4 shear layer along the separated free streamline are described and the mass flux from this layer is then used to calculate the higher-order flow within the separation bubble. The flow structure is found to have two forms, depending on the value of the O(1) parameter λ, and these are compared with results from published “Navier-Stokes” type calculations for the flow at small but finite values of E.     

Some interactions between small numbers of baroclinic,geostrophic vortices

Abstract

Various interactions between small numbers (two and four) of baroclinic, geostrophic point vortices in a two-layer system are studied with attention to the qualitative changes in behavior which occur as size of the deformation radius is varied.

A particularly interesting interaction, which illustrates the richness of baroclinic vortex dynamics, is a collision between two hetons. (A heton is a vortex pair in which the constituent vortices have opposite signs and are in opposite layers. The “breadth” of a heton is the distance between its constituent vortices. A translating heton transports heat.) When two hetons, which initially have different breadths, collide, the result is either an exchange of partners, or a “slip-through” collision in which the initial structures are preserved. It is shown here that the outcome is always an exchange, provided the deformation radius is sufficiently small. This strongly contrasts with a collision between pairs of classical, one-layer vortices in which no exchange occurs if the initial ratio of the breadths is sufficiently extreme.

Finally the transport of passive fluid by a translating baroclinic pair is investigated. A pair of vortices in the top layer transports no lower layer fluid if the distance between the vortices is less than 1.72 deformation radii. By contrast, the size of the region trapped by a heton increases without bound as the spacing between the vortices increases.     

Unusual types of degassing from melts of peripheral magma chambers of “dormant” El’brus volcano, Russia: Geochemical and mineralogical features

In addition to traditional degassing of the melt in the subsurface magma chambers of the “dormant” El’brus volcano, alsodegassing through pores and microcracks that occur in the top of magma chambers has also been detected. It is proven by studies of compactness, porosity, and permeability of the rocks. The speeds at which gases (H, He, H₂S, CO₂, F, and Cl) pass through gneiss and volcanic rocks were estimated. Magma chambers on the ground surface are expressed in stable thermal anomalies revealed by night-time thermal sounding from an NOAA satellite. The presence of magma chambers at depths of 2–12 km was proven by magnetotelluric sounding [Sobisevich et al., 2003] and gravity studies. In addition to occasional “columns” of bright-white fluorescence above the thermal anomalies, aerosol “clouds” and hydrogen flows were detected by lidar and hydrogen surveying [Alekseev et al., 2007, 2009]. Observation at the same sites detected steam outbursts occurring periodically, the snow-ice cover thaws and the smell of hydrogen sulfide is felt. Geochemical characteristics of degassing were studied by snow sampling from up to 1 m deep pits. They were taken within contours of the thermal anomalies, above active fault zones, in the sites of bright-white fluorescence “columns,” and on a new fumarole locality. It is shown that the degassing of melt was accompanied by the gas transporting many elements (Li, B, Si, P, S, Ca, Zn, Pb, Mo, Ba, W, Hg, Ag, U, Th, I, Au, and Pt) in a fine-grained state (a few microns or possibly nanometers) with an active participation of F and Cl. Native platinum, chalcopyrite, halite, sylvite, barite, gypsum, zircon, opal, chlorinated organics, etc. were for the first time discovered in the Mt. El’brus area using electron microscope studies of solid residue from dehydrated snow samples. “Hidden” ore mineralization genetically related to degassing of melts enriched in ore elements may be supposedly found in paleo- and present-day areas of volcanic activity.     

Sustainable groundwater management of the stressed Coastal aquifer in the Gaza region

Abstract

This study proposes an empirical approach that can lead to the sustainable management of groundwater resources. This approach enables a comprehensive understanding of an aquifer, delineates distinct hydrological scenarios, and recommends a set of operational activities for each sub-region of the aquifer. The paper focuses on the Coastal aquifer of the Gaza Strip region which has been divided into three sub-regions. The southern sub-region (WSW) is classified as scenario “+a2”, which indicates that it can be used as a multi-annual groundwater reservoir. The northern sub-region (NW-E) is designated scenario “-a2”, where the recommended operational measures include injection of freshwater in wells and cleaning of the surface environment. The third sub-region (CSE), is classified as scenario “-b2”, which requires severe management measures to correct both a negative hydrological and environmental situation. The approach also involves on-going monitoring of the aquifer, and can be considered as an empirical tool to provide preliminary guidelines for long-term groundwater management.