Vladimir Nikora

FRACTAL STRUCTURES OF RIVER PLAN FORMS

The basis of existing methods for the quantitative description of the plan geometry of rivers is determination of the characteristics of individual meander bends (macroforms). This approach is effective when one is working with a few well-defined macroforms. However, the plan pattern of many rivers is really determined at the next higher geometric level, the morphologically homogeneous river section, which may comprise many tens of macroforms, often with several superimposed scales. At this level, macroform parameters alone do not seem adequate to describe the geometry of the section. New indices are required. The concept of fractals affords a natural way of defining such indices. The presence of hierarchical features (superimposed sinuosity on various scales, braiding with superimposed bars of a range of sizes, etc.) suggests fractal behavior, at least over certain ranges of spatial scale. In this paper we demonstrate fractal behavior for 46 river sections in Moldavia from measurements made from existing topographic maps. We also introduce the notion of internal and external fractal scales that limit the range of fractal behavior; here the internal and external scales are the width of the river channel B and of its valley floor B0, respectively. Using this idea together with elements of fractal geometry, we obtain a relation among the sinuosity, B, B0, and the fractal dimension D of the river bed pattern. We propose the use of D as a new and informative parameter for describing the internal structure of the plan pattern of both single-thread and multithread rivers.

Aquatic interfaces: a hydrodynamic and ecological perspective

ABSTRACT Ecologically-appropriate management of natural and constructed surface water bodies has become increasingly important given the growing anthropogenic pressures, statutory regulations, and climate-change impacts on environmental quality. The development of management strategies requires that a number of knowledge gaps be addressed through interdisciplinary research efforts particularly focusing on the water-biota and water-sediment interfaces where most critical biophysical processes occur. This paper discusses the current state of affairs in this field and highlights potential paths to resolve critical issues, such as hydrodynamically-driven mass transport processes at interfaces and associated responses of organisms through the development of traits. The roles of experimental methods, theoretical modelling, statistical tools, and conceptual upscaling methods in future research are discussed from both engineering and ecological perspectives. The aim is to attract the attention of experienced and emerging hydraulic and environmental researchers to this research area, which is likely to bring new and exciting discoveries at the discipline borders.

River network fractal geometry and its computer simulation

The hierarchical ordinal and statistical models of river networks are proposed. Their investigation has been carried out on the basis of river networks computer simulation as well as on empirical data analysis. The simulated river networks display self-similar behavior on small scales (the fractal dimension D ≈ 1.52 and Hursts exponent H = 1.0) and self-affine behavior on large scales (the lacunary dimension DG ≈ 1.71, H ≈ 0.58). Similar behavior is also qualitatively characteristic for natural river networks (for catchment areas from 142 to 63,700 km2 we obtained DG ≈ 1.87 and H ≈ 0.73). Thus in both cases one finds a region of scales with self-affine behavior (H < 1) and with DG < 2. Proceeding from fractal properties of the river networks, the theoretical basis of scaling relationships L ∼ Aβ and ℒ ∼ Ae, widely used in hydrology, are given (L, ℒ and A denote the main river length, the total length of the river network, and catchment area, respectively); β = 1/(1+H) and e=DG/2.

Turbulence structure of open channel flows over permeable and impermeable beds: a comparative study

The behavior of turbulent open channel flows over permeable surfaces is not well understood. In particular, it is not clear how the surface and the subsurface flow within the permeable bed interact and influence each other. In order to clarify this issue we carried out two sets of experiments, one involving velocity measurements in open channel flows over an impermeable bed composed of a single layer of spheres, and another one where velocities were measured over and within a permeable bed made of five such layers. Comparison of surface flow velocity statistics between the two sets of experiments confirmed that bed permeability can significantly affect flow resistance. It was also confirmed that even in the hydraulically rough regime, the friction factors for the permeable bed increase with increasing Reynolds number. Such an increase in flow resistance implies a different distribution of normal form-induced stress between the permeable and impermeable bed cases. Subsurface flow measurements performed within the permeable bed revealed that there is an intense transport of turbulent kinetic energy (TKE) occurring from the surface to the subsurface flow. We provide evidence that the transport of TKE toward the lower bed levels is driven mainly by pressure fluctuations, whereas TKE transport due to turbulent velocity fluctuations is limited to a thinner layer placed in the upper part of the bed. It was also confirmed that the turbulence imposed by the surface flow gradually dissipates while penetrating within the porous medium. Dissipation occurs faster for the small scales than for the large ones, which instead are persistent, although weak, even at the lowest bed levels

Biomechanical properties of aquatic plants and their effects on plant-flow interactions in streams and rivers

We analysed the biomechanical properties of aquatic plant stems of four common submerged river macrophyte species with bending, tension and cyclic loading/unloading tests and related these properties to the hydraulic habitats of the plants. The studied species included Glyceria fluitans, Ranunculus penicillatus, Myriophyllum alterniflorum and Fontinalis antipyretica. Habitat assessment shows that these species occur in a range from low to high flow velocities, respectively. G. fluitans is a semi-aquatic species with stems of a high flexural rigidity and high breaking force and breaking stress that enable them to carry their own weight and balance gravity when growing upright in slow flowing rivers. G. fluitans may also grow horizontally often producing emerged terrestrial stems. In contrast, F. antipyretica grows in fierce water flow. Its stems have the highest flexibility, a significantly higher ‘tension’ Young’s modulus, breaking stress and work of fracture and a lower plastic deformation compared to M. alterniflorum and R. penicillatus. These traits enable F. antipyretica to survive even in swift flowing streams and constrict the growth of M. alterniflorum and R. penicillatus to the river reaches with moderate flow velocities. R. penicillatus has a weak bottom part with a low breaking force and breaking stress acting as a predetermined breaking point and enabling seasonal regrowth from root parts.

Equilibrium hydrodynamics concept for developing dunes

Experiments utilizing two-dimensional fixed dune profiles and varying flow depth (dune regime flows) highlight the equilibrium (self-similar) nature of the near-bed boundary layer over developing dunes with flow separation in the dune lee. The negligible variation in roughness layer (comprising the interfacial and form-induced layers) flow structure for developing dunes was confirmed in terms of spatial fields of time-averaged velocities and stresses; and vertical distributions of: (a) double-averaged (in time and space) longitudinal velocity, (b) double-averaged normal stresses, and (c) the components of the momentum balance for the flow. The finding of an equilibrium nature for the near-bed flow over developing dunes is significant in its centrality to understanding the feedback loop between flow, bed morphology, and sediment transport that controls erodible-bed development. Further research is required into the form of the distribution of double-averaged velocity in the form-induced layer above roughne...

Fractal geometry of individual river channels and its computer simulation

A new method for analyzing the self-similarity and self-affinity of single-thread channels is proposed. It permits the determination of the fractal scaling exponents, of the characteristic scales, and the evaluation of the degree of anisotropy for self-similar fractal lines. Based upon the application of this method to the Dniester and Pruth rivers we established the self-similarity of the river pattern on small scales and the self-affinity on large scales. For these rivers we obtained the fractal scaling exponents, the characteristic scales, and the anisotropy parameters. A computer model has been developed which simulates river patterns whose fractal properties are close to the properties of natural objects. A generalized model of fractal behavior of natural rivers is proposed. On the basis of self-affinity of natural and simulated rivers on large scales, a hypothesis has been formulated which explains the violation of the dimension principle in the well-known relation between the river length and the catchment area.

Structure of the internal boundary layer over a patch of pinnid bivalves ( Atrina zelandica ) in an estuary

Measurements of tidal-current boundary-layer flow over an experimental 2-m by 2-m patch of pinnid bivalves (Atrina zelandica) in a northern New Zealand estuary are presented. Previous work demonstrated a link between mesoscale (order 100 m) patchiness of the benthic biota and time-averaged boundary-layer dynamics. The aim in this new experiment was to describe the three-dimensional structure of turbulence at the patch scale (order 1 m). Flow over three densities of Atrina was investigated: 340 individuals per 4 m 2 , 50 individuals per 4 m 2 and zero individuals. An internal boundary layer (IBL) grows downstream from the leading edge of the patch at the base of the ambient boundary layer. One meter in from the leading edge, the top of the IBL was ∼12 cm above the bed for the high-density patch and ∼6 cm for the low-density patch. Flow in the IBL was three-dimensional in that vertical and transverse mean velocities were nonzero, secondary Reynolds stresses were nonzero and comparable with the primary stress, and velocity spectra deviated from scaling relationships for two-dimensional flow. Thus, the observed IBL was still in its infancy, i.e., it consisted of a roughness sublayer only as the distance from the leading edge of the patch was not enough for development of a second, overlying logarithmic layer. In summary, the IBL that envelops the Atrina patch is a region of lower mean longitudinal velocities but more energetic turbulence relative to the ambient boundary layer. The former translates into shelter, which some organisms might take advantage of, and the latter translates into increased vertical exchange across the top of the IBL, which might enhance fluxes of nutrients, colonists and suspended sediments, and might have implications for deposition and resuspension of organically rich biodeposits. The results extend our knowledge of turbulence over patches of suspension feeders at the 1-m scale and therefore provide information needed to improve depiction of flow in models of suspension-feeder-flow interactions.

Flow–plant interactions at leaf, stem and shoot scales: drag, turbulence, and biomechanics

Flow–plant interactions are experimentally investigated at leaf, stem, and shoot scales in an open-channel flume at a range of Reynolds numbers. The experiments included measurements of instantaneous drag forces acting on leaves, stems, and shoots of the common freshwater plant species Glyceria fluitans, complemented with velocity measurements, high-resolution video recordings, and biomechanical tests of leaf and stem properties. The analyses of bulk statistics, power spectral densities, transfer functions, and cross-correlations of measured velocities and drag forces revealed that flow characteristics, drag force, and plant biomechanical and morphological properties are strongly interconnected and scale-dependent. The plant element–flow interactions can be subdivided into two classes: (I) passive interactions when the drag variability is due to the time variability of the wetted and frontal areas and squared approach velocity (due to the large-scale turbulence); and (II) active interactions representing a range of element-specific instabilities that depend on the element flexural rigidity and morphology. Implications of experimental findings for plant biophysics and ecology are briefly discussed.

Spatially Averaged Flows over Mobile Rough Beds: Definitions, Averaging Theorems, and Conservation Equations

AbstractThis paper reports the double-averaged (in space and in time) hydrodynamic equations for mobile-boundary conditions that are derived based on the refined double-averaging theorems, modified Reynolds decomposition, and improved definitions of the spatial and time bed porosities. The obtained double-averaged conservation equations provide a mathematical framework for studying mobile-boundary flows such as gravel bed rivers during flood events or flows over vegetated beds. These equations will help in designing measurement campaigns for obtaining mobile bed data and their interpretation and parameterization, eventually leading to improved and more robust predictive models.