Richardson number profiles in laboratory experiments applied to shallow seas

Abstract

A unified analysis is given of the critical conditions for the onset of stratification due to either a vertical or a horizontal buoyancy flux, with tidal or wind stirring.

The critical conditions for the onset of stratification with a horizontal buoyancy flux are found to be of the form of ratios of the tidal slope, or wind setup, to the equivalent surface slope due to the lateral density gradient. These ratios, which are easily determined from sea data, indicate that the profiles of critical flux Richardson Number, averaged over the stirring cycle, are similar to those inferred from the laboratory experiments of Hopfinger and Linden (1982) in which there is zero mean shear turbulence with a stabilising buoyancy flux, and also that the efficiency for the conversion of kinetic energy to potential energy for tidal stirring is similar to that for wind stirring.

The observed much greater efficiency for wind stirring, compared with tidal stirring with a vertical buoyancy flux, is also consistent with the existence of flux Richardson Number profiles in the sea similar to those occurring in the corresponding laboratory experiments. Using the solution of the turbulent kinetic energy equation for the water column, the relative importance of the production of turbulent kinetic energy, and its diffusion by turbulence are assessed, and the critical conditions for the onset of stratification with a vertical buoyancy flux are shown to reduce the classical Simpson—Hunter form.     

Comparing the stream re-aeration coefficient estimated from ANN and empirical models / Comparaison d'estimations par un RNA et par des modèles empiriques du coefficient de réaération en cours d'eau

Abstract

Dissolved oxygen (DO) is one of the most useful indices of river's health and the stream re-aeration coefficient is an important input to computations related to DO. Normally, this coefficient is expressed as a function of several variables, such as mean stream velocity, shear stress velocity, bed slope, flow depth, and Froude number. However, in free surface flows, some of these variables are interrelated, and it is possible to obtain simplified stream re-aeration equations. In recent years, different functional forms have been advanced to represent the re-aeration coefficient for different data sets. In the present study, the artificial neural network (ANN) technique has been applied to estimate the re-aeration coefficient (K ₂) using data sets measured at different reaches of the Kali River in India and values obtained from the literature. Observed stream/channel velocity, bed slope, flow depth, cross-sectional area and re-aeration coefficient data were used for the analysis. Different combinations of variables were tested to obtain the re-aeration coefficient using an ANN. The performance of the ANN was compared with other estimation methods. It was found that the re-aeration coefficient estimated by using an ANN was much closer to the observed values as compared with the other techniques.     

Hydrological characteristics of groundwater in a subtropical coastal plain with large variations in salinity: Pimpama,Queensland, Australia

Abstract

The Pimpama coastal plain is situated in southern Moreton Bay, in subtropical eastern Australia. The plain is low lying and tidal and is situated behind a large sand barrier island. Largely due to recent (30 years) drainage networks within the flood plain, surface water quality has declined. Groundwater hydrographs have enabled the determination of different flow systems: a deeper system responding to seasonal weather patterns and a shallower flow system more responsive to individual rainfall events. Elevated potentiometric heads in semi-confined aquifers reflect upward movement of saline to hypersaline groundwaters. However, interaction of this deeper groundwater with shallower groundwater and the surface drains is yet to be determined. Recharge to the shallower system is by direct infiltration while recharge to the deeper system includes a component from landward ranges or bedrock outcrops within the plain. Discrimination between groundwater bodies is possible using salinity, ionic ratios and stable isotopes. Features of groundwater hydrology, the distribution of salinity and variations in water chemistry all suggest that under current conditions infiltration has increased, plus there is a greater landward migration of groundwaters of marine origin.     

Critical-level crossing of rossby-gravity wave-packets in a linear-shear,stratified flow

Abstract

The propagation of Rossby-gravity waves, which are of astronomical interest near the critical level (or corotation point), is considered in a linear-shear, exponentially stratified flow by means of a ray tracing method. It is shown, using the analytic solutions for the stream function, that for a Richardson number J > 1/4 a wave-packet can cross the critical level in a finite time. In the unstable stratified case (J < 0), it cannot cross the critical level for large |J| (J < 0), but may do so for some intermediate |J| values.

Based on the above results, the possible existence of the regular normal mode with a discrete point eigenvalue in the continuous spectrum is discussed for bounded systems.     

On inviscid stratified parallel flows varying in two directions

Abstract

A stratified parallel flow in a potential force field is investigated. The density, the velocity, and the potential field of the flow are allowed to vary in two directions. Three sufficient conditions are derived for guaranteed stability of the flow. Two are the classical stability conditions in their respective directions. The third, measured by a newly defined Richardson number, is a result of the shear interaction and the pressure balance condition for stability. Like the classical Richardson number which is always positive preceding stability, this new number acts as a constraint on the other two stability conditions. In addition to the above stability criteria, a semi-ellipse theorem is derived for the present flow.     

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.     

Note on the flow of a stratified fluid over a stationary obstacle in a channel

Abstract

A new method is introduced to produce a uniform stratified flow over a stationary obstacle in an open channel. The flow is achieved by discharging the flow from the channel through a sink. The details of the sink are unimportant. The flow speed is limited only by the sink capacity. Selective withdrawal at lower densimetric Froude numbers is effectively eliminated through the use of a contraction. The standing, free-surface, long wave arising from the initiation of the flow is also eliminated by the contraction. Experiments are conducted for flow over a sphere for a range of Reynolds numbers from O(10²) to O(10³) and a range of Richardson numbers from O(10^?1) to O(10). Dye and neutrally buoyant droplets are used for quantitative analysis of the wake structure. The wake is also probed by a hot-film anemometer. The frequency of vortex shedding is obtained. Comparison with data from towed experiments is also presented.     

Simulation and consequences of successive anthropogenic activity in the Agua Amarga coastal aquifer (southeast Spain)

Abstract

The Agua Amarga coastal aquifer has been the object of a succession of anthropogenic interventions over the last 90 years: (a) the operation of saltworks from 1925 to 1975; (b) the withdrawal, since 2003, of groundwater from the aquifer along the coast line; and (c) the programme of pouring seawater over the salt marsh, carried out since 2009, to recover the piezometric levels and the soil moisture conditions. For a better understanding of how these past and present human activities have affected the natural groundwater regime, and to validate certain hypotheses concerning the interpretation of experimental data on temperature depth profiles and piezometric and salinity changes, a numerical fluid flow and solute transport model was designed and applied to the period 1925–2010, using SEAWAT. This model reproduces, in a qualitative and quantitative way, the flow and transport processes that operated during this time, as well as the behaviour of the seawater wedge.

Citation Alhama Manteca, I., 2013. Simulation and consequences of successive anthropogenic activity in the Agua Amarga coastal aquifer (southeast Spain). Hydrological Sciences Journal, 58 (5), 1072–1087.

Editor D. Koutsoyiannis     

Flood simulation using different sources of rainfall in the Huong River,Vietnam / Simulation d'inondation à l'aide de différentes sources d'information pluviométrique dans le bassin de la Rivière Huong,Vietnam

Abstract

The possibility of simulating flooding in the Huong River basin, Vietnam, was examined using quantitative precipitation forecasts at regional and global scales. Raingauge and satellite products were used for observed rainfall. To make maximum use of the spatial heterogeneity of the different types of rainfall data, a distributed hydrological model was set up to represent the hydrological processes. In this way, streamflow simulated using the rainfall data was compared with that observed in situ. The forecast on a global scale showed better performance during normal flow peak simulations than during extreme events. In contrast, it was found that during an extreme flood peak, the use of regional forecasts and satellite data gives results that are in close agreement with results using raingauge data. Using the simulated overflow volumes recorded at the control point downstream, inundation areas were then estimated using topographic characteristics. This study is the first step in developing a future efficient early warning system and evacuation strategy.     

The symmetric baroclinic instability of an equatorial current

Abstract

The stability of a baroclinic zonal current to symmetric perturbations on an equatorial β-plane is considered. The fluid is assumed to be Boussinesq, inviseid, adiabatic, hydrostatic, and stably stratified. The solutions exhibit the same stability properties as those on an f-plane: instability occurs whenever Ri < 1/(1 + d), where Ri is the Richardson number and d is a measure of the horizontal shear of the current; the most unstable motions tend to parallel the isotherms of potential temperature; and they have infinitely small scales of variation perpendicular to the isotherms. The variation of Coriolis parameter leads to one important difference in the structure of the eigenfunctions: the rapidly growing modes are concentrated in high latitudes, and the slowly growing ones in low latitudes.

The suggestion that the symmetric cloud bands observed at low latitudes in Jupiter's atmosphere are caused by symmetric instabilities is re-examined in the light of these results. These cloud bands would have to be associated with the slowly-growing, low-latitude modes. These modes consist of small scale motions parallel to the isotherms, with the magnitude of the motions having a large scale modulation as a function of latitude. The time scales of these modes and the latitude scales of their modulation agree qualitatively with the observations of Jupiter's cloud bands, so long as Ri is not very close to zero or to its critical value.     

Soil erosion and overland flow in Japanese cypress plantations: spatio-temporal variations and a sampling strategy

ABSTRACT

Many studies have focused on soil erosion in unmanaged Japanese cypress plantations because the sparse understory vegetation and litter covering the forest ground enhance soil erosion. In this study, soil erosion, litter, and overland flow measurements were conducted over 14 months to identify the spatio-temporal variation and examine the optimal sample size. Fifteen traps (each 0.25 m wide) were installed in line along the bottom of a 15-m-wide slope. Soil erosion and overland flow had large spatial variations as compared to litter. The temporal coefficient of variation of soil erosion and overland flow was highest during dry seasons, while smaller during wet seasons. The random sampling analysis showed that the rate of decrease in spatio-temporal variation became moderate as the sample size increased beyond six. This result indicated that the optimal sample size was five, the total width of which was equivalent to about 8% of the monitored slope width.     

Study of discontinuities in hydrological data using catastrophe theory

Abstract

Modelling and prediction of hydrological processes (e.g. rainfall–runoff) can be influenced by discontinuities in observed data, and one particular case may arise when the time scale (i.e. resolution) is coarse (e.g. monthly). This study investigates the application of catastrophe theory to examine its suitability to identify possible discontinuities in the rainfall–runoff process. A stochastic cusp catastrophe model is used to study possible discontinuities in the monthly rainfall–runoff process at the Aji River basin in Azerbaijan, Iran. Monthly-averaged rainfall and flow data observed over a period of 20 years (1981–2000) are analysed using the Cuspfit program. In this model, rainfall serves as a control variable and runoff as a behavioural variable. The performance of this model is evaluated using four measures: correlation coefficient, log-likelihood, Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results indicate the presence of discontinuities in the rainfall–runoff process, with a significant sudden jump in flow (cusp signal) when rainfall reaches a threshold value. The performance of the model is also found to be better than that of linear and logistic models. The present results, though preliminary, are promising in the sense that catastrophe theory can play a possible role in the study of hydrological systems and processes, especially when the data are noisy.

Citation Ghorbani, M. A., Khatibi, R., Sivakumar, B. & Cobb, L. (2010) Study of discontinuities in hydrological data using catastrophe theory. Hydrol. Sci. J. 55(7), 1137–1151.     

Trends in runoff and erosion processes over an arid limestone hillside,northern Negev,Israel / Tendances d'écoulement et des processus d'érosion sur une pente de colline aride calcaire,Negev du nord,Israel

Abstract

The study describes an experimental site installed in an arid region for the study of spatial variations in rainfall, runoff and erosion processes along slopes. Data obtained indicate that despite the frequent development of universal overland flow, due to excess rainfall, runoff generated at the upper part of slopes, 60–70m in length, has little or no chance of reaching the slope base during most rainstorms and thus does not contribute to channel flow. The spatial distribution of areas contributing to channel storm flow was found to be similar to that observed in the humid regions. In both cases the contributing area is limited to a belt extending at the base of the slope area. An analysis of the factors affecting the spatial pattern of runoff development in the arid zone is presented. Suspended sediment data collected indicate that no correlation exists between observed sediment concentrations and runoff rates.     

Precipitation patterns and associated hydrological extremes in the Yangtze River basin,China, using TRMM/PR data and EOF analysis

Abstract

A decadal-scale study to retrieve the spatio-temporal precipitation patterns of the Yangtze River basin, China, using the Tropical Rain Mapping Mission, Precipitation Radar (TRMM/PR) data is presented. The empirical orthogonal function (EOF) based on monthly TRMM/PR data extracts several leading precipitation patterns, which are largely connected with physical implications at the basin scale. With the aid of gauge station data, the amplitudes of major principal components (PCs) were used to examine the generic relationships between precipitation variations and hydrological extremes (e.g. floods and droughts) during summer seasons over the past decade. The emergence of such major precipitation patterns clearly reveals the possible linkages with hydrological processes, and the oscillations in relation to the amplitude of major PCs are consistent with these observed hydrological extremes. Although the floods in some sections of the Yangtze River were, to some extent, tied to human activities, such as the removal of wetlands, the variations in major precipitation patterns are recognized as the primary driving force of the flow extremes associated with floods and droughts. The research findings indicate that long-distance hydro-meteorological signals of large-scale precipitation variations over such a large river basin can be successfully identified with the aid of EOF analysis. The retrieved precipitation patterns and their low-frequency jumps of amplitude in relation to PCs are valuable tools to help understand the association between the precipitation variations and the occurrence of hydrological extremes. Such a study can certainly aid in disaster mitigation and decision-making in water resource management.

Editor Z.W. Kundzewicz; Associate editor A. Montanari

Citation Sun, Z., Chang, N.-B., Huang, Q., and Opp, C., 2013. Precipitation patterns and associated hydrological extremes in the Yangtze River basin, China, using TRMM/PR data and EOF analysis. Hydrological Sciences Journal, 57 (7), 1315–1324.     

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.     

A) A. I. H. S. / A) I. A. S. H.

SUMMARY

Basing their studies on an extended Reynolds principle of similarity, the authors present in this paper a thorough theoretical investigation of the turbulent flow in pipes.

Making appropriate assumptions regarding the distribution of the turbulent apparent viscosity over the entire pipe diameter, the well-known discharge formulas, i. e. the resistance laws, of Prandtl-V. Kármán for the hydraulically smooth and the hydraulically rough region, and of Colebrook for the transition region—the accuracy of these being well established by measurements—can be clearly shown to be correct.

Thus it is also possible to determine the velocity distribution in the region near the wall for the hydraulically smooth region and the transition region, as well as for the hydraulically rough region.

The concept, that the flow with a fully developed roughness effect begins when the laminar boundary layer at the wall disappears can be seen to be in close agreement with the asssumptions made. The limits which were established for the hydraulically rough region and the transition region correspond well with the curve plotted by PRANDTL and the boundary curve of Rouse.     

UTILIZATION OF THE RESULTS FROM REPRESENTATIVE AND EXPERIMENTAL BASINS WITH A VIEW TO THE MANAGEMENT OF WATER RESOURCES / Utilisation des résultats obtenus sur les bassins représentatifs et expérimentaux en vue de l'aménagement des ressources en eau

Abstract

The management of water resources requires knowledge of the spatial and temporal distribution of surface and groundwater resources, and an assessment of the influence of man on the hydrological regime.

For small water courses regional estimates can be made from representative basins which offer guidelines (1) for the computation of mean annual flow and in some cases for the determination of the statistical distribution of the annual flow; (2) for the computation of the 10-year flood maximum discharge and volume.

An example concerning the tropical African Sahel is given. From a general study of the daily precipitation, a simple rainfall/runoff model used on a daily basis and calibrated on data from representative basins, and also the direct comparison of results from 55 representative basins, statistical distribution curves were established for annual runoff based on mean annual precipitation and the geomorphological characteristics of the basins.

Another example concerning tropical Africa west of Congo presents a methodology for the computation of the 10-year flood (maximum discharge and volume).

The systematic study of 60 representative basins makes it possible to plot the runoff coefficient R/P as a function of basin climate, mean slope and soil permeability. Other curves are used to determine the time of rise and the base time of the hydrograph as a function of the basin area and the mean slope.

The experimental basin is a good tool for the assessment of the influence of man on hydrological parameters. An example shows the influence of land use on the regression between annual precipitation and annual runoff.     

Magnetic Helicity in fast dynamos

The behaviour of magnetic helicity in kinematic dynamos at large magnetic Reynolds number is considered. Hughes, et al . [ Phys. Lett. A 223 , 167-172 (1996)] observe that the relative helicity tends to zero in the limit of large magnetic Reynolds number. This paper gives upper bounds on the helicity, by relating the helicity spectrum to the energy spectrum. These bounds are confirmed by numerical simulation and the distribution of helicity over scales is considered. Although it is found that the total helicity becomes small in the limit of high conductivity, there can remain significant, but cancelling, helicity at large and small scales of the field. This is illustrated by considering the evolution of helicity in the stretch-twist-fold dynamo picture.     

Flow of a double-diffusive stratified fluid in a differentially-rotating cylinder

Abstract

A study has been made of a basic state of axisymmetric flow, at large rotational Reynolds numbers, in a double-diffusive stratified fluid contained in a vertically-mounted, differentially-rotating cylindrical cavity. The aim is to describe the qualitative characteristics of the flow of a fluid, the density of which is stratified by two diffusive effects, i.e., temperature and salinity gradients. Attention is confined to situations in which the temperature and salinity gradients make opposing contributions to the overall density profile, the undisturbed stratification being gravitationally stable. Finite difference numerical solutions of the governing Navier-Stokes equations have been obtained using the Boussinesq approximation. The results are presented in a way that illustrates the explicit effects of double-diffusivity when the cavity aspect ratio, height/radius, is O(1). The principal non-dimensional parameters characterizing the flow field are identified. In the interior core, the primary dynamic balance is between the horizontal density gradient and the vertical shear of the prevailing azimuthal velocity. The effective stratification is seen to decrease as the double-diffusivity increases, even if the overall stratification parameter, St, is held constant. The solute field contains a very thin boundary layer structure at large Lewis numbers. The effective stratification increases with the Prandtl number. Results have been derived for extreme values of the cavity aspect ratio. For small cavity aspect ratios, the dominant dynamic ingredients are viscous diffusion and rotation. For large aspect ratios, the bulk of the flow field is determined by the rotating sidewall. In this case, the direct influence of the double-diffusivity is minor.     

Mixing efficiency in stably-stratified decaying turbulence

Abstract

The behavior of the flux Richardson number R _f, as a function of the overall Richardson number Ri ₀, was investigated for a stably stratified, grid-generated, turbulent flow evolving in a closed-loop water channel. The turbulent dissipation rate ε, the buoyancy or vertical mass flux p wbar; and the rms density fluctuation ρ′ were obtained from simultaneous single-point measurements of the horizontal and vertical velocity components and density fluctuations. From these, R _f and Ri ₀ were calculated at each point in the spatially evolving flow. The resulting curves of R _f vs. Ri ₀ exhibit the full range of behavior found in the very different case studied by Linden (1980). The length scale arguments of Gibson (1980) and Stillinger et al. (1983b) provide an underlying mechanism which successfully accounts for the shape of the R _f vs. Ri ₀ curve.