Point-source inertial particle dispersion

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small but finite inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,?v,?t), x and v being the particle position and velocity, respectively. For arbitrary inertia, position and velocity variables are coupled, with the result that p(x,?v,?t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small (but nevertheless finite) inertia, (x,?v)-variables decouple and the determination of p(x,?v,?t) is reduced to solve a system of two standard forced advection–diffusion equations in the space variables x. The latter equations are derived here from first principles, i.e., from the well-known Lagrangian evolution equations for position and particle velocity.     

Bringing groundwater models to LIFE: a new way to assess water resource management options

Abstract

If management of water resources is to fully take into account the requirements of the environment, it will benefit from quantitative predictions of the ecological effects of river flow alterations. A significant relationship between flow reductions caused by groundwater abstraction and ecological conditions (as measured by relevant biotic indices) has been shown in streams in the midlands of England. In this article, we combine this relationship with hydrological indices derived from calibrated regional groundwater models to assess river reaches that are likely to be ecologically impacted by abstraction and might consequently be at risk of failing to meet EC Water Framework Directive standards. We demonstrate the application of this method within the framework of the Ecological Limits of Hydrologic Alteration (ELOHA) approach to making water resource decisions. We provide examples of how this approach can be used to assess the implications of different groundwater abstraction scenarios for river water bodies.

Editor D. Koutsoyiannis; Guest editor M. Acreman

Citation Streetly, M.J., Bradley, D.C., Streetly, H.R., Young, C., Cadman D., and Banham, A., 2014. Bringing groundwater models to LIFE: a new way to assess water resource management options. Hydrological Sciences Journal, 59 (3–4), 578–593.     

Linear and weakly nonlinear internal wave theories applied to “morning glory” waves

Abstract

Detailed comparisons are made between the predictions of Benjamin's weakly nonlinear theory for internal solitary waves in fluids of great depth, with observational data on solitary wave-type disturbances in the lower atmosphere associated with the “morning glory” phenomenon.

It is shown that, while the theory is not wholly unreasonable, neither is it completely satisfactory. In particular, although the calculated wave speeds are generally close to those observed, they are no improvement on those based on linear long wave theory; at the same time the predicted wave half-widths are too large by a factor of two to three. The limitations of the theory appear to be associated with the requirement that wave half-widths are much less than the total fluid depth, a condition not satisfied in the atmospheric case. However, the alternative theory for shallow fluids, based on the Korteweg-de Vries equation is found to be even more unsuitable.

Our analyses highlight some of the problems in comparing theory with observations and bring to the fore some of the present limitations of the data for such purposes.     

The role of the helicity spectrum function in turbulent dynamo theory

Abstract

It is shown that, for general homogeneous turbulence, the anti-symmetric part of the spectrum tensor can be expressed in terms of a single scalar function H(k,ω) (the helicity spectrum function). Under the first-order smoothing approximation, the coefficients α _ij β _ijk in the expansion of the mean electromotive force in terms of the mean magnetic field are determined; α _ij is a weighted integral of H(k,ω), and β _ijk contains a part β(a)ijk which is likewise a weighted integral of H(k, ω). When the turbulence is axisymmetric, β(a)ijk contains Rädler's (1969a) “Ω ∧ J-effect”. It is shown that when the turbulence is statistically symmetric about a plane perpendicular to the axis of symmetry, then βij = O but the Rädler effect is non-zero. Explicit expressions for αij and βijk are given when the velocity field is generated by random forcing in a rotating medium. Finally, it is shown by means of a local analysis that the Rädler effect, in conjunction with uniform mean shear, can give rise to non-oscillatory dynamo action, and it is argued that this effect may be significant in the well-mixed interior of a stellar convection zone, where by symmetry the α-effect may be weak.     

The instability in relativistic,plane parallel,compressible shear flows

Abstract

The growth rates of instabilities in these shear flows are bounded by the rate of shear and the relativistic y factor. It is also shown that (i) the Howard Semi-Circle theorem is still valid, and (ii) the critical layer lies in the flow. Beaming effects are taken into account.     

Alfén waves in a thermally stratified fluid

Abstract

The propagation of Alfvén waves along a uniform horizontal field in a highly conducting incompressible fluid, subject to the convective forces produced by a uniform vertical temperature gradient, is treated in a Boussinesq approximation. It is shown that there are exact solutions with large amplitude but restricted form. Their restricted form means that an arbitrary disturbing force produces other motions as well as Alfvén waves. An arbitrary initial disturbance of small amplitude produces waves whose state of polarization varies along the direction of propagation. For large amplitudes, however, any mixtures of polarization states causes scattering into new modes.     

The contrasted evolution of high and low flows and precipitation indices in the Duero basin (Spain)

Abstract

Trends in high and low flows are valuable indicators of hydrological change because they highlight changes in various parts of the frequency distribution of streamflow series. This enables improved assessment of water availability in regions with high seasonal and inter-annual variability. There has been a substantial reduction in water resources in the Duero basin (Iberian Peninsula, Spain) and other areas of the Mediterranean region during the last 50 years, and this is likely to continue because of climate change. In this study, we investigated the evolution and trends in high and low flows in the Spanish part of the Duero basin, and in equivalent or closely-related precipitation indices for the period 1961–2005. The results showed a general trend of decrease in the frequency and magnitude of high flows throughout most of the basin. Moreover, the number of days with low flows significantly increased over this period. No clear relationship was evident between the evolution of high/low flows and changes in the distribution frequencies of the precipitation series. In contrast to what was expected, the number of days with heavy precipitation and the mean annual precipitation did not show significant trends across the basin, and the number of days without rainfall decreased slightly. The divergence between precipitation and runoff evolution was more accentuated in spring and summer. In the absence of trends in precipitation, it is possible that reforestation processes in the region, and increasing temperatures in recent decades, could be related to the decreasing frequency of high flows and the increasing frequency of low flows.

Editor Z.W. Kundzewicz; Associate editor S. Grimaldi

Citation Morán-Tejeda, E., López-Moreno, J.I., Vicente-Serrano, S.M., Lorenzo-Lacruz, J. and Ceballos-Barbancho, A., 2012. The contrasted evolution of high and low flows and precipitation indices in the Duero basin (Spain). Hydrological Sciences Journal, 57 (4), 591–611.     

Reflection of hydrostatic mountain waves from spatially nonuniform layers

Abstract

The steady, hydrostatic, inviscid, Boussinesq flow of a stably stratified fluid over a bell-shaped ridge is investigated within the framework of a linear model. The three layer model atmosphere introduced is such that the Brunt-Väisälä frequency is constant in each layer but the interfaces of the middle layer are allowed to vary gently in the cross-ridge direction. In essence, the model can be tuned in both vertical and horizontal directions. These cross-ridge variations can produce significant differences in both the cross-ridge surface wind and the surface drag compared to the response obtained by use of a horizontally uniform reflecting layer. These changes are sensitive to both the vertical location of the middle layer and to the slope of its lower interface at the ridge crest. Many of these features are explained by means of a conventional layered-model analysis.     

Trends in high flows in the central Spanish Pyrenees: response to climatic factors or to land-use change?

Abstract

This paper analyses the evolution of high flows in the central Spanish Pyrenees during the period 1955–1995. The method applied makes it possible to assess whether the contribution of the largest daily discharge and rainfall events to the total annual runoff and precipitation remains stationary or shows any temporal trend. The results show a general negative trend in flood intensity in the last decades, together with an increase in the importance of low flows in the total annual contribution. However, a change in the frequency distribution of precipitation events has not been detected. The different behaviour shown by runoff and precipitation could only be explained as being due to the increase in vegetation cover that is a consequence of the farmland abandonment and reforestation that occurred during the 20th century.     

A large class of non-zonal oceanic flows satisfying the arnold-blumen sufficient condition for stability

Abstract

Recently Andrews has discussed an example of a topographically-forced non-zonal now satisfying the Arnold-Blumen sufficient condition for stability. At large distances from the topographic centre this flow becomes purely zonal and westward. After underlining the richness of solutions of the Andrews model, the present paper goes on to show that Andrews' technique can be applied successfully to a model where the vertical profile of static stability resembles those found in the ocean. In particular we obtain a large class of hydrodynamic stable flows, forced by the bottom topography, for continuously stratified fluids (two layers each with uniform Brunt-Väisälä frequency).     

Amplification of disturbances on a channel flow

Abstract

The stability of a rotating, stationary flow of zero potential vorticity in a slowly varying channel is examined using the method of multiple scales. This technique can be applied when the variations of the basic flow occur on a length scale which is much larger than the one associated with the perturbation. To lowest order the disturbance is described by a propagating part multiplied by a slowly changing amplitude. It is shown that when the phase speed of a disturbance approaches zero, the growth of the amplitude becomes unbounded. This happens when a perturbation superimposed upon a flow which is slightly sub/supercritical, or which alters from a super- to a subcritical state, propagates over a shoaling bottom. If, however, the change of the basic flow is from a sub- to a supercritical state, the phase speed is quite large and the amplitude of the perturbation will just show minor variations along the channel. The same holds true if the steady flow is only moderately affected by the changing topography. The problem has also been analyzed using wave-action formalism, and the outcome of this alternative approach to the stability problem proved to conform to the previously obtained results. Finally, an interpretation of the calculated growth rates is undertaken in terms of “convective” amplification and “absolute” instability.     

A numerical study of the string function using a primitive equation ocean model

Abstract

We use results from a primitive-equation ocean numerical model (SCRUM) to test a theoretical 'string function' formulation put forward by Tyler and Käse in another article in this issue. The string function acts as a stream function for the large-scale potential energy flow under the combined beta and topographic effects. The model results verify that large-scale anomalies propagate along the string function contours with a speed correctly given by the cross-string gradient. For anomalies having a scale similar to the Rossby radius, material rates of change in the layer mass following the string velocity are balanced by material rates of change in relative vorticity following the flow velocity. It is shown that large-amplitude anomalies can be generated when wind stress is resonant with the string function configuration.     

Radial expansion of the magnetohydrodynamic equations for axially symmetric configurations

Abstract

We introduce a general expansion approach to obtain a fully consistent closed set of magnetohydrodynamic equations in two independent variables, which is particularly useful to describe axially symmetric, time-dependent problems with weak variation of all quantities in the radial direction. This is done by considering the hierarchy of expanded magnetofluid equations in cylindrical coordinates and equating terms with equal powers in the radial coordinate r. From geometrical considerations it is shown that the radial expansions of the pertaining physical quantities are either even series or odd series in r; this introduces a significant reduction in the number of variables and equations. The closure of the system is provided by appropriate boundary conditions. Among other possible applications, the method is relevant for the analysis of structure and dynamics of magnetic field concentrations in stellar atmospheres.     

The natural radiochemical and growth records in contemporary hermatypic corals from the Atlantic and Caribbean

The skeletal banding observed in vertical cross-sections of two species of coral,Montastrea annularis from Jamaica andDiploria labrynthiformis from Bermuda, has been confirmed to be annual by ingrowth of²²⁸Th towards radioactive equilibrium with²²⁸Ra taken up from seawater. In addition the Bermuda coral is shown to have incorporated²¹⁰Pb at essentially constant specific activity over at least the last thirty years.The individual annual patterns of growth banding in a suite of specimens ofD. Labrynthiformis from Bermuda are shown to be correlative. The mass of CaCO₃ accumulated each year is positively correlated with the band width for the corresponding year.     

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     

Froude number effects on flow over topography

Abstract

The response or a depth independent two layer flow to an underlying topographic irregularity is studied for flows in which the square of the internal Froude number exceeds the Rossby number. Irrespective of the magnitude of the Rossby number, rotation is important for such flows. The flow generally adjusts so that the thickness of the lower layer is nearly constant. However small anomalies from the constant thickness are found to extend to very large distances from the topography when the Rossby number exceeds unity.     

Asymptotic aspects of the Boussinesq approximation for gases and liquids

Abstract

The asymptotic formulation of the Boussinesq approximation relates the pressure of the fluid to a thermodynamical quantity involving the heat capacity c_Po . In this paper we examine the implications of such a scaling, in particular: (i) the singular degeneracy of the equation of state ρ = ρ* (1 ?α* (T?;T*)) of a liquid: this equation of state is valid only for small values of the coefficient α T*; (ii) in which manner the scaling introduces the Mach number of the flow as a small parameter e for a compressible fluid. The equations at order zero with respect to ? are the same equations for gases and for liquids only if the thermodynamics of the medium is described by using the Brunt-Väisälä frequency instead of the temperature.     

Non-linear hydrodynamic stability of oceanic flows

Abstract

In this paper an analytical method to study the hydrodynamic stability of simple barotropic, non-divergent flows is discussed. The method is based on the variational approach introduced by Arnold and derived from the Lyapunov stability criteria. In this context, the sufficient condition for the stability of a steady barotropic flow ψ(x,y) is obtained when dP(ψ)/dP_{ψ = ψ}, the derivative of the absolute vorticity P(ψ), is positive definite. In this case, we discuss the effect of higher derivatives dⁿP(ψ)/dψⁿψ_{ψ = ψ} on the non-linear stability. Then we show that some classical examples of oceanic non-divergent flows (i.e. lee waves downstream an Island, steady flows through a Strait, the Fofonoff gyre) are stable to finite-amplitude perturbations.     

Three-dimensional primary instabilities of a stratified,dissipative, parallel flow

Abstract

We demonstrate the existence of a class of dissipative, stratified, parallel shear flows which, as a consequence of linear supercritical instability, evolve directly into three-dimensional flows without the requirement for an intermediate two-dimensional finite-amplitude state. This represents a counter-example to a common misinterpretation of Squire's theorm, namely that the fastest-growing unstable mode of a dissipative parallel shear flow must be two-dimensional.