Dynamic mechanism of turbulent flow in meandering channels: considerations for deflection angle

To find turbulent flow structure inside meandering channels, three physical models of river meanders representing strongly curved bend, mild bend and elongated symmetrical meander loop were tested in this paper. Instantaneous velocity data in three dimensions were measured using Micro-ADV at different cross sections of these models. Depth averaged velocity vectors, streamwise velocity, secondary currents, turbulent and mean flow kinetic energy were investigated with respect to the sediment deposition pattern. In order to gain more regarding the force acting the sediment particles, three dimensional velocity fluctuations were analyzed in detailed inside the elongated symmetrical meander loop. Occurrence frequency, transition probability and angle of attack for different events were also computed for the points close to the bed. Of the present results, the importance of sweeps and ejections on sediment deposition can be detected. Further, distribution of bursting events is presented through the water column and compared the results with the previous works. Importantly, occurrence of fluctuating velocities in three dimensions at different locations inside the river meanders in addition to the effect of mean flow and turbulent components is responsible for sediment transport. Streamwise velocity distribution through the depth is also compared with some previous mathematical models. Researchers seeking the better control over the river morphology can apply this method without sacrificing much time and cost. This study is also included some insights to be pursued by future works.     

Spatial growth of gulf stream meanders

Abstract

An attractive explanation for the observed spatial growth of the Gulf Stream meanders is that the meanders are spatially growing unstable waves. The results of a calculation based on a simple two-layer model of baroclinically unstable flow presented here support this idea. The model is a familiar one with the energy for the growth of the meander perturbations coming from the potential energy available in the geostrophic tilt of the interface between the two layers due to their velocity shear. In order to distinguish between spatial and temporal growth, it IS necessary to assume that the meanders are generated in a localized region, or equivalently, that the meanders are upstream disturbances which are amplified as they enter a region of unstable flow. This assumption is implemented mathematically through the use of a Green's function which governs the propagation of the meanders. Analysis of the spatial and temporal characteristics of the Green's function leads to a criterion which must he satisfied if the meanders arc to grow spatially. This criterion is that the mean flow velocity must be sufficiently greater than the velocity shear, U_m > √2 U_s, in order to have spatial growth. This simply means that the growing meanders must be washed downstream faster than they spread upstream, or equivalently the spatial growth is due to downstream advection of growing disturbances. The actual Gulf Stream flow is in fair agreement with this criterion.     

Nonlinearity and unsteadiness in river meandering: a review of progress in theory and modelling

River meandering has been extensively investigated. Two fundamental features to be explored in order to make further progress are nonlinearity and unsteadiness. Linear steady models have played an important role in the development of the subject but suffer from a number of limits. Moreover, rivers are not steady systems; rather their states respond to hydrologic forcing subject to seasonal oscillations, punctuated by the occurrence of flood events. We first derive a classification of river bends based on a systematic assessment of the various physical mechanisms affecting their morphodynamic equilibrium and their evolution in response to variations of hydrodynamic forcing. Using the database by Lagasse et al. ( 2004 ) we also show that natural meanders are typically mildly curved and long, i.e. such that both the centrifugal and the topographic secondary flows are weak, but they are almost invariably nonlinear. We then review some recent developments which allow us to treat analytically the flow and bed topography of mildly curved and long nonlinear bends subject to steady forcing, taking advantage of the fact that flow and bed topography in mildly curved long bends are slowly varying. Results show that nonlinearity has a number of consequences: most notably damping of the morphodynamic response and upstream shifting of the location of the nonlinear peak of the flow speed. Next we extend the latter model to the case of unsteady forcing. Results are found to depend crucially on the ratio between the flood duration and a morphodynamic timescale. It turns out that, in a channel subject to a repeated sequence of floods, the system reaches a dynamic equilibrium. We conclude the paper discussing how the present assessment relates to the debate on meander modelling of the late 1980s and suggesting what we see as promising lines of future developments.     

Stochastic nature of three dimensional bursting events and sediment entrainment in vortex chamber

In this study, three dimensional quadrant analysis of bursting process was used to recognize the susceptible regions for sediment entrainment and deposition at the bed of a vortex chamber. From the analysis, it was found that two dimensional quadrant analysis in unable to find the turbulent coherent structure of flow near the bed of the vortex chamber. Therefore, a new method based on three dimensional bursting process is introduced in this study to define the turbulent flow structure. Based on the new methodology in this study, the bursting event is divided into eight different cube zones according to three dimensional velocity fluctuations. It was realized that, four cube zones interactions are toward the central orifice of the vortex chamber and four cube zones interactions are toward the wall of the chamber and they are categorized as classes A and B, respectively. The results from the experiments showed that in class A, the internal sweep events (class IV-A) moves the settled sediment particles toward the central orifice of the chamber, whereas in class B the external sweep events (class IV-B) moves the settled sediment particles toward the external region of the chamber. Also the transition probabilities of the bursting events in 64 particular movements were determined. The result showed that stable organizations of each class of the events had highest transition probabilities whereas cross organizations had lowest transition probabilities. Additionally, an effort was made to find the average inclination angle of the three dimensional bursting events in each cube zone. The results showed that near the bed of the vortex chamber by increasing the tangential velocity toward the center of the chamber, the average inclination angle of the events in the cube zones decreased. Also, at the region where the sediment particles were deposited, the inclination angles had higher values.     

Three‐dimensional flow structure and patterns of bed shear stress in an evolving compound meander bend

Compound meander bends with multiple lobes of maximum curvature are common in actively evolving lowland rivers. Interaction among spatial patterns of mean flow, turbulence, bed morphology, bank failures and channel migration in compound bends is poorly understood. In this paper, acoustic Doppler current profiler (ADCP) measurements of the three‐dimensional (3D) flow velocities in a compound bend are examined to evaluate the influence of channel curvature and hydrologic variability on the structure of flow within the bend. Flow structure at various flow stages is related to changes in bed morphology over the study timeframe. Increases in local curvature within the upstream lobe of the bend reduce outer bank velocities at morphologically significant flows, creating a region that protects the bank from high momentum flow and high bed shear stresses. The dimensionless radius of curvature in the upstream lobe is one‐third less than that of the downstream lobe, with average bank erosion rates less than half of the erosion rates for the downstream lobe. Higher bank erosion rates within the downstream lobe correspond to the shift in a core of high velocity and bed shear stresses toward the outer bank as flow moves through the two lobes. These erosion patterns provide a mechanism for continued migration of the downstream lobe in the near future. Bed material size distributions within the bend correspond to spatial patterns of bed shear stress magnitudes, indicating that bed material sorting within the bend is governed by bed shear stress. Results suggest that patterns of flow, sediment entrainment, and planform evolution in compound meander bends are more complex than in simple meander bends. Moreover, interactions among local influences on the flow, such as woody debris, local topographic steering, and locally high curvature, tend to cause compound bends to evolve toward increasing planform complexity over time rather than stable configurations. Copyright © 2016 John Wiley & Sons, Ltd.     

Tidal circulation and energy dissipation in a shallow, sinuous estuary

The tidal dynamics in a pristine, mesotidal (>2 m range), marsh-dominated estuary are examined using moored and moving vessel field observations. Analysis focuses on the structure of the M ₂ tide that accounts for approximately 80% of the observed tidal energy, and indicates a transition in character from a near standing wave on the continental shelf to a more progressive wave within the estuary. A slight maximum in water level (WL) occurs in the estuary 10–20 km from the mouth. M ₂ WL amplitude decreases at 0.015 m/km landward of this point, implying head of tide approximately 75 km from the mouth. In contrast, tidal currents in the main channel 25 km inland are twice those at the estuary mouth. Analysis suggests the tidal character is consistent with a strongly convergent estuarine geometry controlling the tidal response in the estuary. First harmonic (M ₄) current amplitude follows the M ₂ WL distribution, peaking at mid-estuary, whereas M ₄ WL is greatest farther inland. The major axis current amplitude is strongly influenced by local bathymetry and topography. On most bends a momentum core shifts from the inside to outside of the bend moving seaward, similar to that seen in unidirectional river flow but with point bars shifted seaward of the bends. Dissipation rate estimates, based on changes in energy flux, are 0.18–1.65 W m⁻² or 40–175 μW kg^–1. A strong (0.1 m/s), depth-averaged residual flow is produced at the bends, which resembles flow around headlands, forming counter-rotating eddies that meet at the apex of the bends. A large sub-basin in the estuary exhibits remarkably different tidal characteristics and may be resonant at a harmonic of the M ₂ tide.     

Circulation cells topology and their effect on migration pattern of different multi-bend meandering rivers

In meandering rivers, a cross-stream flow, referred to as a secondary current, has important effects on broad spectra of hydraulic/environmental characteristics, running the gamut from river hydrodynamics and geomorphology to stream ecology. The transport equation for vorticity and kinetic energy transfer should be analyzed to specify terms involved in generation of secondary currents. However, there is limited research on scrutinizing these terms in meandering rivers. On the other hand, while rivers are mostly multi-bend, previous studies have been limited to single bends. In the current paper, three physical multi-bend channels representing a strongly curved bend, a mild bend and an elongated symmetrical meander loop are designed in order to unravel mechanisms responsible for forming circulation cells in cross sections. Experiments are carried out in the middle bend of these models. Cross-stream turbulence anisotropy considerably strengthens almost all near bank cells. Moreover, contrary to single sharp bends, multi bend effects hinder the transfer of the kinetic energy in both directions in the entrance section of the strongly curved bend.     

Flow fields in tightly curving meander bends of low width‐depth ratio

Upland swamp channels with low width/depth ratios (w/d), armoured beds, minimal sediment loads, tightly curving bends and an absence of point bars provide a striking contrast to the flow characteristics of larger channels with higher w/d ratios. Two subsets of these bends were examined in relation to their patterns of cross‐stream flow relative to the channel boundary. The first, with mean w/d = 2·0 and gentle barforms, exhibited even velocity distributions at bend entrances but developed vertically stacked pairs of maximum velocity filaments (MVFs). Cross‐stream circulation increased with decreasing curvature before essentially ceasing in the tightest bend due to the conservation of angular momentum and reduced vertical velocity differentials; bed friction has more limited influence in narrow deep channels relative to bank friction. In the second subset of bends, with larger w/d (mean 4·8) and much steeper barforms, the MVFs were laterally paired and strongly helical flow was partly driven by the vertical confinement of flow due to large, stable barforms at the bend entrances. In one bend, the velocity profile became inverted immediately past the apex and caused helical flow to abruptly reverse. Point bars in relatively wide bedload channels appear to greatly distort secondary flow patterns. In narrow, deep, sediment‐starved channels, separation zones against the convex and/or the concave bank deliver the flow confinement that would otherwise be provided by point bars or concave‐bank benches. In these channels, separation zones are important for protecting both the channel bed and banks from scour. Three‐dimensional near bankfull flow fields are presented for one bend with a meander pool; inward shifting of the MVF and limited sediment supply are proposed as mechanisms for the development and maintenance of these features. These flow data in narrow and deep peatland channels demonstrate very different flow patterns and morphological characteristics relative to the more commonly studied wide, shallow channels with more abundant sediment. Copyright © 2009 John Wiley & Sons, Ltd.     

Analytical solutions to runoff on hillslopes with curvature: numerical and laboratory verification

Predicting the behavior of overland flow with analytical solutions to the kinematic wave equation is appealing due to its relative ease of implementation. Such simple solutions, however, have largely been constrained to applications on simple planar hillslopes. This study presents analytical solutions to the kinematic wave equation for hillslopes with modest topographic curvature that causes divergence or convergence of runoff flowpaths. The solution averages flow depths along changing hillslope contours whose lengths vary according hillslope width function, and results in a one-dimensional approximation to the two-dimensional flow field. The solutions are tested against both two-dimensional numerical solutions to the kinematic wave equation (in ParFlow) and against experiments that use rainfall simulation on machined hillslopes with defined curvature properties. Excellent agreement between numerical, experimental and analytical solutions is found for hillslopes with mild to moderate curvature. The solutions show that curvature drives large changes in maximum flow rate q_peak and time of concentration t_c , predictions frequently used in engineering hydrologic design and analysis.     

Numerical simulations of thermal convection in a rapidly rotating spherical shell cooled inhomogeneously from above

Abstract

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell with and without inhomogeneous temperature anomalies on the top boundary have been carried out using a three-dimensional, time-dependent, spectral-transform code. The spherical shell of Boussinesq fluid has inner and outer radii the same as those of the Earth's liquid outer core. The Taylor number is 10⁷, the Prandtl number is 1, and the Rayleigh number R is 5R_c (R_c is the critical value of R for the onset of convection when the top boundary is isothermal and R is based on the spherically averaged temperature difference across the shell). The shell is heated from below and cooled from above; there is no internal heating. The lower boundary of the shell is isothermal and both boundaries are rigid and impermeable. Three cases are considered. In one, the upper boundary is isothermal while in the others, temperature anomalies with (l,m) = (3,2) and (6,4) are imposed on the top boundary. The spherically averaged temperature difference across the shell is the same in all three cases. The amplitudes of the imposed temperature anomalies are equal to one-half of the spherically averaged temperature difference across the shell. Convective structures are strongly controlled by both rotation and the imposed temperature anomalies suggesting that thermal inhomogeneities imposed by the mantle on the core have a significant influence on the motions inside the core. The imposed temperature anomaly locks the thermal perturbation structure in the outer part of the spherical shell onto the upper boundary and significantly modifies the velocity structure in the same region. However, the radial velocity structure in the outer part of the shell is different from the temperature perturbation structure. The influence of the imposed temperature anomaly decreases with depth in the shell. Thermal structure and velocity structure are similar and convective rolls are more columnar in the inner part of the shell where the effects of rotation are most dominant.     

A model of equilibrium bed topography for meander bends with erodible banks

Channel curvature produces secondary currents and a transverse sloping channel bed, along which the depth increases towards the outer bank. As a result deep pools tend to form adjacent to the outer bank, promoting bank collapse. The interaction of sediment grains with the primary and secondary flow and the transverse sloping bed also causes meanders to move different grain sizes in different proportions and directions, resulting in a consistent sorting pattern. Several models have been developed to describe this process, but they all have the potential to over‐predict pool depth because they cannot account for the influence of erodible banks. In reality, bank collapse might lead to the development of a wider, shallower cross‐section and any resulting flow depth discrepancy can bias associated predictions of flow, sediment transport, and grain‐size sorting. While bed topography, sediment transport and grain sorting in bends will partly be controlled by the sedimentary characteristics of the bank materials, the magnitude of this effect has not previously been explored. This paper reports the development of a model of flow, sediment transport, grain‐size sorting, and bed topography for river bends with erodible banks. The model is tested via intercomparison of predicted and observed bed topography in one low‐energy (5·3 W m^?2 specific stream power) and one high‐energy (43·4 W m^?2) study reach, namely the River South Esk in Scotland and Goodwin Creek in Mississippi, respectively. Model predictions of bed topography are found to be satisfactory, at least close to the apices of bends. Finally, the model is used in sensitivity analyses that provide insight into the influence of bank erodibility on equilibrium meander morphology and associated patterns of grain‐size sorting. The sensitivity of meander response to bank cohesion is found to increase as a function of the available stream power within the two study bends. Copyright © 2002 John Wiley & Sons, Ltd.     

Physical explanations of variations in river meander migration rates from model comparison

In meandering rivers, the local channel migration rate increases with increasing bend sharpness until it reaches a maximum at a certain critical value of the bend sharpness. Beyond this critical value, the migration rate decreases if bend sharpness increases. Similarly, reach‐averaged migration rates attain a maximum at a certain river sinuosity. This work investigates the physics of these phenomena by comparing the results of two physics‐based models of different complexity, in which the migration rates are proportional to the near‐bank flow velocity excess. In the computational tests the river was allowed to meander progressively, starting from an almost straight planimetry. Both models reproduced the observed peak in the curve describing the local migration rate as a function of the ratio radius of curvature‐channel width (R/B), with a rising limb at lower R/B values and a falling limb at higher R/B values. The rising limb can be explained by the decrease in relative lag distance between near‐bank flow velocity and forcing curvature as R/B increases. The falling limb results from the decrease in local channel curvature and near‐bank flow velocity excess. Since the models do not include flow separation, the results indicate that this phenomenon is not needed to explain the decrease of channel migration rates in sharp bends. The models reproduced also the peak in the curve describing the reach‐averaged migration rates as a function of river sinuosity The increase and then decrease of reach‐averaged migration rates as sinuosity increases appears to be mainly caused by the variation of the reach‐averaged value of the ratio R/B. Copyright © 2009 John Wiley & Sons, Ltd.     

An analysis of the characteristics of rough bed turbulent shear stresses in an open channel

Entrainment of sediment particles from channel beds into the channel flow is influenced by the characteristics of the flow turbulence which produces stochastic shear stress fluctuations at the bed. Recent studies of the structure of turbulent flow has recognized the importance of bursting processes as important mechanisms for the transfer of momentum into the laminar boundary layer. Of these processes, the sweep event has been recognized as the most important bursting event for entrainment of sediment particles as it imposes forces in the direction of the flow resulting in movement of particles by rolling, sliding and occasionally saltating. Similarly, the ejection event has been recognized as important for sediment transport since these events maintain the sediment particles in suspension. In this study, the characteristics of bursting processes and, in particular, the sweep event were investigated in a flume with a rough bed. The instantaneous velocity fluctuations of the flow were measured in two-dimensions using a small electromagnetic velocity meter and the turbulent shear stresses were determined from these velocity fluctuations. It was found that the shear stress applied to the sediment particles on the bed resulting from sweep events depends on the magnitude of the turbulent shear stress and its probability distribution. A statistical analysis of the experimental data was undertaken and it was found necessary to apply a Box-Cox transformation to transform the data into a normally distributed sample. This enabled determination of the mean shear stress, angle of action and standard error of estimate for sweep and ejection events. These instantaneous shear stresses were found to be greater than the mean flow shear stress and for the sweep event to be approximately 40 percent greater near the channel bed. Results from this analysis suggest that the critical shear stress determined from Shield's diagram is not sufficient to predict the initiation of motion due to its use of the temporal mean shear stress. It is suggested that initiation of particle motion, but not continuous motion, can occur earlier than suggested by Shield's diagram due to the higher shear stresses imposed on the particles by the stochastic shear stresses resulting from turbulence within the flow.     

Temporal and spatial adjustments of channel migration and planform geometry: responses to ENSO driven climate anomalies on the tropical freely‐meandering Aguapeí River,São Paulo,Brazil

Two reaches of Aguapeí River, a left‐bank tributary of the Paraná River in western São Paulo state, Brazil, were studied with the objective of assessing the role of bend curvature on channel migration in this wet‐tropical system and examining if land‐use changes or ENSO (El Niño Southern Oscillation) driven climate anomalies over nearly half a century have changed migration behaviour and planform geometry. Meander‐bend migration rates and morphometric parameters including meander‐bend curvature, sinuosity, meander wavelength and channel width, were measured and the frequency of bend cutoffs was analysed in order to determine the rate of change of channel adjustment over a 48 year period to 2010. Results show that maximum average channel migration rates occur in bends with curvatures of about 2–3 r_c/w, similar to other previously studied temperate and subarctic freely meandering rivers although not as pronounced and with a tendency to favour tighter curvature. From 1962 to 2010 the Aguapeí River has undergone a significant reduction in sinuosity, a shift from tightly curving to more open bends, an overall decline in channel migration rates, an associated decrease in the frequency of neck‐cutoffs and an overall increase in channel width. As the majority of the drainage basin (96%) was already deforested in 1962, channel form and process changes were, unlike an interpretation for an adjacent river system, not attributed to altered land‐use but rather to a sharp ENSO‐driven increase in the magnitude of peak flow‐discharges of some 32% since 1972. In summary, this research revealed that recent climate and associated flow regime changes are having a pronounced effect on river channel behaviour in the Aguapeí River investigated here. Copyright © 2018 John Wiley & Sons, Ltd.     

Role of interchange instability in flux transfer event origin

It is shown that the interaction of the interplanetary magnetic field (IMF), when it has southward component, with the geomagnetic field leads to the formation of an enhanced pressure layer (EPL) near the magnetopause. Currents flowing on the boundary between the EPL and the magnetosheath prevent the IMF from penetrating the magnetosphere. However, the outward boundary of the EPL is unstable. The interchange instability permanently destroys the EPL. Separate filaments of the EPL move away from the Earth. New colder plasma of the magnetosheath with a frozen magnetic field replaces the hotter EPL plasma, and the process of EPL formation and destruction repeats itself.The instability increment is calculated for various magnitudes of the azimuthal wave number, k_y, and curvature radius of the magnetic field lines, R_c. The disturbances with R⁻¹_e\leqk_y\leq4R⁻¹_e (where R_e is the Earth’s radius) and R_c\simeqR_e are the most unstable.A possible result of the interchange instability of the EPL may be patchy reconnection, displayed as flux transfer events (FTEs) near the magnetopause.     

Assessment of detachment and sediment transport capacity of runoff by field experiments on a silt loam soil

The detachment capacity (D_c) and transport capacity (T_c) of overland flow are important variables in the assessment of soil erosion. They determine respectively the lower and upper limit of sediment transport by runoff and therefore control detachment and deposition pro‐cesses. In this study, the detachment and transport capacity of runoff was investigated by rainfall simulations and overland flow experiments on small field plots. On the bare field plots, it was found that T_c was strongly related to total runoff discharge. This was also observed for the plots covered by maize residues, but T_c was less due to the lower runoff velocity. A simple regression equation was derived to estimate T_c for both bare and covered soil. Comparing our observations with T_c equations mentioned in the literature revealed that T_c equations based on laboratory experiments overestimated, on average, our measurements. Although T_c can be assessed more easily in laboratory experiments, the applicability of the results to field conditions remains questionable. Detachment by runoff was also related to total runoff discharge. The D_c values were, however, 4–50 times smaller than the T_c at corresponding high and low runoff discharge. This indicates that detachment by runoff constitutes only part of the transported sediment. Interrill erosion supplies an important additional amount of sediment. In this study, however, only sealed soils were considered. In the case of freshly tilled, loose soils, the D_c of runoff may be larger, resulting in a larger contribution to the total soil loss. Copyright © 2008 John Wiley & Sons, Ltd.     

Secondary circulation induced by flow curvature and Coriolis effects around headlands and islands

Previous studies have shown that flow curvature in river bends generates a secondary circulation in the plane normal to the mean flow direction. A similar circulation pattern is shown to exist in oceanic situations when flows are subject to curvature, mainly due to interaction with topographic features. However, it is shown that, due to differences between oceanic conditions and river bends, theory and prediction methods based on the assumptions for river bends are invalid for oceanic flows. Via scaling arguments based on the equations of motion, that include both the effects of flow curvature and the Coriolis force, parameters that govern the different flow regimes are identified. The maximum strength of the secondary flow is derived for each flow regime and is verified using a three-dimensional (3-D) numerical model applied to an idealized island. It is also shown that upwelling, due to the generation of secondary flow, occurs off the tips of the headland or island, and its influence can extend far downstream.Responsible Editor: Richard Signell     

Kinematic stationary geodynamo models with separated toroidal and poloidal motions

Abstract

This paper is concerned with a three-dimensional spherical model of a stationary dynamo that consists of a convective layer with a simple poloidal flow of the S^2c ₂ kind between a rotating inner body core and solid outer shell. The rotation of the inner core and the outer shell means that there are regions of concentrated shear or differential rotation at the convective layer boundaries. The induction equation for the inside of the convective layer was solved numerically by the Bullard-Gellman method, the eigenvalue of the problem being the magnetic Reynolds number of the poloidal flow (R _M2) and it was assumed that the magnetic Reynolds number of the core (R _M1) and of the shell (R _M3) were prescribed parameters. Hence R _M2 was studied as a function of R _M1 and R _M3, along with the orientation of the rotation axis, the radial dependence of the poloidal velocity and the relative thickness of the layers for the three different situations, (i) the core alone rotating, (ii) the shell alone rotating and (iii) the core and the shell rotating together. In all three cases it was found that, at definite orientations of the rotation axis, there is a good convergence of both the eigenvalues and the eigenfunctions of the problem as the number of spherical harmonics used to represent the problem increases. For R _M1 =R _M3= 10³, corresponding to the westward drift velocity and the parameters of the Earth's core, the critical values of R _M2 are found to be three orders of magnitude lower than R _M1, R _M3 so that the poloidal flow velocity sufficient for maintaining the dynamo process is 10-20 m/yr. With only the core or the shell rotating, the velocity field generally differs little from the axially symmetric case. However, for R _M2 (or R _M3) lying in the range 10² to 10⁵, the self-excitation condition is found to be of the form R _M2˙R ^½ _M1=constant (or R _M2˙R^½ _M3=constant) and the solution does not possess the properties of the Braginsky near-axisymmetric dynamo. We should expect this, in particular, in the Braginsky limit R _M2˙R^?½; _M1=constant.

An analysis of known three-dimensional dynamo models indicates the importance of the absence of mirror symmetry planes for the efficient generation of magnetic fields.     

The influence of meander bend evolution on the formation of multiple cutoffs: findings inferred from floodplain architecture and bend geometry

The evolution of meander bends and formation of cutoffs, including a series of cutoffs developed simultaneously in a number of bends, have been investigated by many researchers. However, relatively little is known about factors that lead to the development of multiple cutoffs that are formed subsequently at one location. The present study aims to determine the influence of meander bend development on multiple chute cutoff formation in a single bend. The research is based on the sedimentary record of meander migration and cutoffs preserved in a lowland river floodplain (the lower Obra River, Poland). Analysis of changes in meander geometry was conducted to describe the influence of their migration on cutoff formation and in other rivers where multiple cutoffs occurred. The results showed that multiple cutoffs in the lower Obra River have occurred during the last 3000 years, owing to the interaction of upstream and downstream controls: migration of meander bends in opposing directions accompanied by an increase of flood frequency and sediment supply. The flow and sediment supply has been further altered since the nineteenth century due to anthropogenic impacts: an artificial cutoff of the downstream bend and elevation of channel levées. Similar mechanisms driving the formation of multiple cutoff have been found in other river courses, despite significantly higher energy of the compared rivers. Moreover, development of a confined‐shape bend (caused by artificial barrier or autogenic bend behaviour) may also favour the formation of multiple cutoffs. However, counter migration of meanders enhanced by increased flood frequency and sediment supply are primary triggers for such events. Copyright © 2015 John Wiley & Sons, Ltd.     

Spatio-temporal variation of transition probability of bursting events over the ripples at the bed of open channel

In this study, the turbulent flow structure over the ripples at the bed of open channel was investigated experimentally. An analysis of bursting process was used to recognize the susceptible regions for sediment entrainment and deposition over the ripples. Two artificial ripples were built according to the ripples, formed by nature. Three different configurations of ripples were used by changing the wavelength. According to analysis of bursting event it was found that at the stoss side of ripples, quadrants (II) and (IV) were dominant to the quadrants (I) and (III) and at the lee side of the ripple it was vice versa. Also the transition probabilities of the bursting events were determined. The results showed that stable organizations of each class of the events had highest transition probabilities whereas cross organizations had lowest transition probabilities. Additionally, an effort was made to find the average inclination angle of the bursting events in quadrants (II) and (IV). The results showed that the mean angle of events in quadrants (II) and (IV) increases at the downstream of stoss side to the crest in each experimental test. Also, at the lee side where the sediment particles were deposited, the inclination angles had the highest values.