CC BY
44
II университета
'ЖУРНАЛ водных / / коммуникации
Список литературы
1. Гиг Дж ван. Прикладная общая теория систем: пер. с англ. / под ред. Б. Г. Сушкова, В. С. Тюхина. — М.: Мир, 1981.
2. Документация по наблюдениям и исследованиям на СГТС ВРГСиС ГБУ «Волго-Балт».
3. Жулин Н. М. Исследование нагрузок в механизмах ворот и затворов: промежуточный отчет. Тема 91-401. — СПб., 1992.
4. Полонский Г. А. Механическое оборудование гидротехнических сооружений: учебник для техникумов. — 3-е изд., перераб. и доп. — М.: Энергия. 1984.
Sanjay Giri,
River Engineering & Moprphology Dept., Deltares/Delft Hydraulics, Delft, The Netherlands
AN OVERVIEW ON RECENT ADVANCES ON COMPUTATIONAL MODELING OF BED FORM EVOLUTION USING DETAILED HYDRODYNAMICS
ОБЗОР ПОСЛЕДНИХ ДОСТИЖЕНИЙ ПО КОМПЬЮТЕРНОМУ МОДЕЛИРОВАНИЮ ИМЕНЕНИЙ РУСЛА С ИСПОЛЬЗОВАНИЕМ
ГИДРОДИНАМИКИ
Within the scope of this report, we basically focus on current state of research regarding physically-based modelling of dune development using detailed hydrodynamics. Though, we also mention herein about those works in which the bedform dynamics have successfully been reproduced without detailed hydrodynamics. This is also of importance as a pragmatic tool, particularly when emphasis is given to the evolution of bed form characteristics, for instance, to evaluate the navigation depth during low water period. Prediction of large scale morphological behaviour of rivers, sediment transport and their influence on water surface variation (or inundation) is significantly associated with the local roughness that is dominated by form drag exerted by bed forms. In order to replicate form drag in a physically-based manner, it is of importance to consider the detailed hydrodynamics. So far, most existing methods are basically relied upon empirically/conceptually parameterized approach. The problem becomes more complicated if consider micro-scale morphological development and associated drag under varying flows. This requires an improved modelling approach that enables to take into account the variability of the bed form features and associated form drag under varying flows with rising and falling stages. Taking into consideration the significance of the problem, there are number of supplementary demands for the furtherance of existing knowledge and development. Particularly, due to significant step forward in computational modelling of fluid and bed form dynamics, we are rather near to a truly predictive tool that can be used to investigate this complicated phenomenon of river engineering practice. At the same time, we must consider that the knowledge being gained from fundamental research should concurrently be implemented to address real-world problems.
В этой статье мы в основном останавливаемся на текущем состоянии исследований, относящихся к физическому моделированию развития дюн, используя гидродинамику. Хотя мы также упоминаем о работах, в которых динамика формирования русла успешно представлена без учета гидродинамики. Это так же важно, как прагматический инструмент, особенно когда акцент делается на эволюции характеристик изменений русла для оценки глубины судоходства в период низкой воды. Прогноз широкомасштабного морфологического поведения рек, транспорт наноса и их влияние на изменение водной поверхности связаны с локальной неровностью. Чтобы повторить изменения физически, необходимо рассмотреть гидродинамику. Пока наиболее успешные методы в основном эмпирически опирались на параметрический подход. Проблема становится более сложной, если рассмотреть морфологическое развитие в микромасштабе и связанное движение в изменяющихся потоках. Это требует улучшенного подхода, который поз-
II университета
[ЖУРНАЛ водных /_/ коммуникации
волит принять во внимание изменчивость черт изменений русла и связанное движение в изменяющихся потоках с возрастающими и снижающимися стадиями. Принимая во внимание важность проблемы, существуют дополнительные требования для поддержания существующих знаний и развития. Благодаря важному шагу вперед в компьютерном моделировании потока и динамики изменения русла, мы подошли к прогностическому инструменту, который может использоваться для исследования этого важного феномена практического строительства русла. В то же время мы должны считать, что знания, полученные из фундаментальных исследований, должны использоваться для решения существующих проблем.
Key words: detailed hydrodynamics, computational modeling, sediment transport, bed form evolution, morphodynamics.
Ключевые слова: гидродинамика, компьютерное моделирование, транспорт наноса, изменение русла, морфодинамика.
Introduction
Prediction of the morphologic features of micro-scale bed forms such as ripples and dunes is significant in evaluation of morphological development of river bed, resistance to flow and other characteristics associated with river environments; however this aspect of river engineering practice has been given relatively little attention and there is no existing tool for making physically-based predictions of bed form shape, wavelength and height for arbitrary steady or unsteady flow conditions.
Micro-scale bed forms (dunes) in alluvial streams are usually formed in the lower flow regime under rough turbulent conditions. For bed forms of this type, past observations show strong correlation between turbulence structures induced by flow separation, bed resistance and sediment transport. In other words, the flow, the bed morphology, and the sediment-transport field are tightly coupled and none may be predicted without knowledge of the others. Consequently, all these aspects are equally important for quantitative determination of bed form mor-phodynamics and must be treated in a coupled manner. A comprehensive review of past investigations on river dunes has been presented by Best (2005).
Within a scope of this report, we basically focus on current state of research regarding physically-based modelling of dune development using detailed hydrodynamics. Though, we also mention herein those works, where the bed form dynamics have successfully been reproduced without detailed hydrodynamics. This is also of importance as a pragmatic tool, particularly when emphasis is given to the evolution of bed form characteristics. For an instance to evaluate the navigation depth
during low water period, it is important to predict evolution of bed form characteristics.
On the other hand, prediction of large scale morphological behaviour of rivers, sediment transport and their influence on water surface variation (or inundation) significantly associated with the local roughness that is dominated by form drag exerted by bed forms. In order to replicate form drag in a physically-based manner, it is of importance to consider the detailed hydrodynamics. So far, most existing methods are basically based on an empirically parameterized approach. The problem becomes more complicated if consider morphological development and associated drag under varying flows. This requires an improved modelling approach that enables to take into account the variability of the bed form and the form drag under varying flows.
The recent development of high-performance computers and the associated reduction in computational time has made application of numerical models reliable, particularly for modelling flow and turbulence characteristics over bed forms. These models provide an improved understanding of flow structure over bed forms. However, they do not include bed form dynamics, but treated the bed forms as part of a rigid (non-erod-ible) bed and thus cannot be used to quantify the bed form initiation and evolution process including dynamic form drag exerted by them.
Morphodynamic numerical models have increased both in detail and range of applicability, and being increasingly employed these days solving the sediment transport that depend on local and dynamic flow information. For this purpose, the local flow information is determined from high-resolution hydrodynamic models like DNS, LES or TRANS. Most morphological mod-
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els with the real-world application consider only the large scale and long-term morphological behaviour. They are incapable to predict the evolution of geometric characteristics of micro-scale bed forms as well as associated flow resistance. On the other hand, the advanced models, which are capable to predict the bed form characteristics in a physically based manner cannot be applied to resolve sophisticated real-world problems due to rather intensive computational efforts. Consequently, how to harmonize the theory and practice regarding the physically-based morphodynamic modelling techniques seems to be a challenging problem for modellers and scientists for coming years.
Existing state of the knowledge
Detailed hydrodynamic modelling over bed forms
A number of efforts has been made so far to quantify the flow and turbulence structures over bed forms. Shimizu et al. (2001) developed computational codes for a three-dimensional direct numerical simulation of flow and turbulence over two-dimensional fixed dunes. The numerical model was able to reproduce coherent structures induced by separation at the dune crest. Numerical computations, carried out by Richards and Taylor (1981), Mendoza-Cabrales (1987), Zijlema et al. (1995), Yoon and Patel (1996), Barr et al. (2004) among others also yielded realistic prediction of flow field and turbulence over bed forms. These works along with the laboratory measurements and visualization of flows over bed forms have significantly improved our insight into the physics of those flows. Herein we attempt to describe some recent and advanced models that deal with the detailed hydrodynamic over dunes.
There are number of works being carried out pointing out the importance of detailed modelling of flow and turbulence over micro-scale bed forms. An interesting work was conducted by Chang and Scotti (2004) regarding modelling unsteady turbulent flows over ripples. The basic point of interest in this work is that they attempted to analyze the performance of RANS model and LES with dynamic eddy viscosity model. They came to the conclusion that RANS and LES agree well with regard to the streamwise component of the flow velocity; however RANS is found to
severely underpredict the turbulent characteristics and overpredict the vertical velocity profiles. They concluded that RANS model is not appropriate to employ in case of small-scale sediment transport, for an instance suspended sediment transport in a ripple scale level, due to the low values of the Reynolds stress that translate to low values of estimated eddy diffusivity. Moreover, they argued that sediments are ejected into the flow above the ripples primarily by the instabilities in the Shear layer, which remove sediments from the cloud that forms in the ripples, precisely where the largest discrepancy in the prediction of the Reynolds stress occurs between RANS and LES. This requires the correct modelling of the entire turbulent flow. These arguments might be correct in case of small- scale sediment transport with suspension, particularly in coastal region, but might be not valid for the case of bed form evolution with predominantly bedload transport.
Nelson et al. (2005) tested two computational codes with a direct numerical simulation (DNS) model with and without sub-grid scale closures to compute the flow and pressure fields over two- and three-dimensional bed forms. They also examined model prediction capabilities on flow and pressure fields in the wake region of backward-facing steps. They found that despite good performance of LES and DNS flow models, these models are prohibitively computationally intensive due to the necessity of computing a three-dimensional flow field even for two-dimensional topography, as can be seen from inspection of the Reynolds stress equations. Therefore, these models are not efficient enough to be applied in mor-phodynamic simulation, which require iterative application of the flow model over many small time steps as the bed morphology changes. Due to this difficulty, and for the sake of comparison, they used a vertical two-dimensional TRANS model (to be described below) and preliminarily examined the model capabilities. That model used a rigid-lid condition for the water-surface boundary. They concluded that the model predicts mean velocities at least as well as if not better than the LES model despite some significant quantitative discrepancies in Reynolds stress estimation in the wake region. In addition, the rigid-lid two-dimensional model predicted turbulence characteristic fairly well in the near-bed region.
Fig. 2. Simulation of flow and turbulent characteristics (solid lines) simulated by a DNS model (developed at Hokkaido University) and comparison with experiments (dots). Also, results are presented to show the effect of near-bed grid resolution
1.2 x/h=2 1.2 x/h=4
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steadiness and non-hydrostatic effects. Non-equilibrium bedload sediment transport is treated using an Eulerian stochastic formulation of the sediment exchange process in terms of pick up and deposition functions proposed by Nakagawa and Tsuji-moto (1980). The proposed approach for sediment transport explicitly considers the local flow variability during morphodynamic computation.
The pick up rate is expressed as follows:
pAd! (p./ P- i) g = °-03t •(! - °-035/ x *)3, (i)
where: ps =sediment pick up rate;
p and ps = fluid and sediment density respectively;
t*= dimensionless local bed shear stress. The sediment deposition rate reads as:
Pd = Pf (s), (2)
where: pd = sediment deposition rate;
fs(s) = distribution function of step
length.
The distribution function of the mean step-length is assumed to be exponential as follows:
1 (
L (s) = — exp
Л
s Л
(3)
where: A = the mean step length;
s = the distance of sediment motion from pick up point.
The bed shear stress is computed from a logarithmic bottom boundary condition as:
■ = iln ^
к Уо
(4)
where: up — velocity at grid point closest to the bed (in the middle of the grid cell);
yp — the distance from the bed to this
^ p
velocity point;
u* — local bed shear velocity;
K — Karman constant;
yo = ks 30;
ks = 2.5d , in which ks is roughness height and d is particle diameter.
As described in Nelson et al. (2008), the boundary shear stress is neither a time-averaged nor an instantaneous, but some surrogate developed from an instantaneous velocity. Since the computational time step is rather small, this allows for variation in flow structure to alter the sediment pick up at each time step. For instance, two time series of near-bed velocity with the
same mean but different variances yield significantly different sediment entrainment. Based on experiments on flow and sediment transport over bed forms and downstream of backward-facing steps, capturing this variability appears to be important for understanding bed form behaviour (Nelson et al., 2005). Thus, despite the relatively simple model for bedload entrainment and deposition, it appears to capture the important physical processes necessary for modelling bed form initiation and evolution.
This model study revealed that vertical grid spacing patterns have a significant impact on model performance, particularly for the mor-phodynamic simulations. Bed form evolution was poorly simulated by the model for the case when vertical grid was distributed uniformly. On the other hand, when same number of grid was stretched exponentially in the vertical direction with fine spacing near the bed, the result was found to be dramatically improved. Bed form evolution and geometric characteristics appeared to be more realistic and sustainable. Simulation of bed form evolution showed that computation with stretched grid spacing can realistically replicate some key physical features observed in natural rivers during bed form evolution, namely amalgamation, asymmetric dune shapes and celerity variation. A typical example of some selected instantaneous bed form evolution pattern simulated by the proposed model is depicted in Fig. 4. The simulation results clearly show qualitatively improved bed form features for the case with the non-uniform vertical grid. This fact leads us to the conclusion that the improved flow variability near the bed is rather important for replicating bed form initiation and evolution.
Fig. 4. A typical example of Instantaneous bed form characteristics a — experiment; b — model simulation using uniform grid and; c — model simulation using non-uniform grid with fine spacing near the bed
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b
c
Jerolmack and Mohrig (2005] proposed a nonlinear stochastic surface evolution model to simulate bed form growth. They hypothesize that the detailed flow structure is not important for determining temporal and spatial scaling, referred to as 'local growth model' for the evolution of the sediment-fluid interface. They argued that the sediment-fluid interface has an internal dynamic that is independent of the details of the system, and allows for a geometric description of its evolution.
Their model incorporates three major components (1) a relationship between sediment flux and local bed elevation (i.e., mass conservation); (2) the dependence of sediment flux on local flow strength (i. e., relation between sediment flux and boundary shear stress); and (3) the dependence of flow strength on local topography (i. e., the relation between shear stress, bed elevation and bed slope). In such a manner, they succeeded in simulating the qualitative features of bed form evolution, where fluid enters only through a small, interpretable set of coefficient that, as they proposed, may be related to measured quantities. They came to the conclusion that the presence of turbulence is important in terms of a perturbation source, but the structure of turbulence may be less important in terms of transport and bed form dynamics.
Paarlberg et al. (2006, 2007) used a 2D vertical shallow water equation coupled with sediment transport model. Since the model could not reproduce physically the flow separation induced by bed forms, an empirical approach is adapted to parameterize flow separation.
Bed form morphodynamics and hydraulic resistance (form roughness exerted by bed forms) under varying flows
The total flow resistance for flows over bed forms is associated with skin friction of sediment particles and form drag exerted by bed forms on the flow (Einstein and Barbarossa, 1952). In the case of a flat bed, the effective shear stress is equivalent to the grain shear stress, but the contribution of form drag becomes significant with the presence of bed forms due to spatial pressure variation over them. An adequate determination of bed form-induced resistance to flow, including its role in flows with temporal variation, is essential from a practical engineering point of view, because the relation of stage to discharge in
temporally varying flows with bed forms depends critically on the total drag. Furthermore, accurate predictions of form drag and total drag are key to the prediction of local and spatially averaged value of skin friction stress, as used in many sediment transport relations.
Many attempts have been made to improve both understanding and predictive capability of bed form evolution, transition and associated resistance under varying flow conditions. Most, if not all. of the approaches are empirical or semi-empirical. There is still no prediction method that can treat these phenomena in a coupled manner based on a first-principles physical formulation, i. e. a model which explicitly treats the physics of flow, morphodynamics of bed forms, non-equilibrium sediment transport, drag effect due to the pressure variation in the presence of bed forms and associated flow-field modification, effects on water surface and flow-depth variation. The interactions among the flow-field, bed geometry and sediment transport are quite complex and difficult to capture in simple models. The bed forms are created and altered by the flow and, conversely, the flow is acted upon by the bed forms through the production of form drag and significant variation in local mean flow and turbulent fields (Nelson et.al, 1993).
Engelund (1966), Engelund and Fredsoe (1982), and van Rijn (1982, 1984) were among those who developed empirical or semi-empirical methods for predicting bed form-induced resistance to flow and sediment transport considering form drag. Brownlie (1983) proposed methods to predict stage-discharge relations induced by bed forms. Karim (1995) developed a relation for the Manning coefficient that incorporates the role of bed configuration in determining bed resistance. Nelson et al. (1993) proposed a drag coefficient closure to provide a mechanism for determining the skin friction component of boundary shear stress. Bennett (1995, 1997) proposed an algorithm to determine stage-discharge relations as well as bedload and suspended-sediment transport for the entire range of bed forms. His proposed method is also useful for predicting equilibrium geometry of lower regime bed forms. In his algorithm, skin friction and form resistance are differentiated using a drag coefficient closure and a two-segment logarithmic velocity profile, as
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proposed by Smith and McLean (1977). Fedele et al. (2000) proposed a methodology to compute the components of the total shear stress (grain shear stress and form drag) for a steady, two-dimensional flow over fully developed dunes. The method is based on a simple energy balance with an analysis of spatially-averaged shear stress profile. Wright and Parker (2004) proposed a relationship between total shear stress and skin friction which is similar to one proposed by Engelund and Hansen (1967). In their relationship, the Froude number is incorporated which is known to be an important parameter affecting the stability of dunes. This relation seems to be appropriate only for lower-regime conditions, which is usually encountered in large, low-slope sand-bed streams.
Most of previously proposed methods require prior knowledge of bed form dimensions or determine only the equilibrium state of bed configuration based on known flow conditions. These approaches do not deal with the dynamics of bed forms and temporal evolution of form drag in temporally varying flows. Moreover, none of the above-mentioned approaches do consider the hysteresis effect that is readily apparent in many time-varying flows, despite the fact that predicting the form drag due to bed forms is often critically important for predicting stage variations during flood events. Few attempts have been made to analyze the hysteresis characteristics observed during bed form transition under temporally varying flow conditions during the rising and falling limbs of flood waves. However, strong hysteresis between time varying flow discharge and bed resistance has been observed in several studies. The discharge-roughness relationship is usually found to be in the form of a loop (Simons and Richardson, 1961; Izumi et al., 2003). This phenomenon is attributed to the distinctive characteristics of bed form evolution/transition and, in turn, differences in resistance to flow during rising and falling stages of flows, even under the similar hydraulic conditions. Yamagu-chi and Izumi (2002, 2003) provided a physical explanation of such a hysteresis using a weakly nonlinear stability analysis. They verified their predictions against a laboratory observation on the transition process of the bed form configuration under unsteady discharge conditions (Izumi et al., 2003).
Some field and laboratory studies have been performed to analyze dynamic behavior of sediment motion under unsteady flow. Some of them was performed to observe the development of bed forms during different flood events in the Dutch Rhine branches (Wilbers & Brinke, 2003; Sieben, 2006). These studies have provided a valuable insight into the behaviour of dune mor-phodynamics under varying flows in the Rhine branches. Wilbers & Brinke (2003) found different characteristics of dune growth and decay for the various sections during different flood events. They attributed those differences to grain size as well as the distribution of discharge over the main channel and the floodplain. They concluded that the growth and migration rate of dunes as well as bedload trans-port rates during the rising stage of a flood wave can be predicted from the mobility of the bed material with simple power relations. Sieben (2006) observed a lag between the discharge and bed form amplitude during flood event of 1997 and 1998 in the Waal. Analyzing bed form evolution data for 1998 flood event, he found that bed form length becomes lowest during maximum flood discharge and subsequently increases during falling stage. Earlier, Julien et al. (2002) also conducted detailed field measurement in the Rhine River during flooding events and found noticeable hysteresis in the relation between bed form height and discharge.
Itakura et al. (1986) carried out observations to characterize bed evolution in Ishikari River during a flood event. They identified the distinctive bed evolution that depended upon the time-varying hydraulic properties of the flow, including a transition from flat bed to dunes during low but increasing flow, a transition from dunes to a flat bed at the maximum flow rate, and reappearance of dunes during falling stage. Kuhnle (1992) investigated bedload transport during rising and falling stages in two natural streams. Sutter et al. (2001) and Lee et al. (2004) performed some laboratory experiments on the bedload transport process under unsteady flow conditions and showed the hysteresis between bedload transport and water level. However, the nature of the hysteresis curve in this work is different than that found for bed form characteristics, as the difference in bedload transport during rising and falling stages is found to depend on the local (instantaneous) flow condition.
In the recent work of Giri et al. (2007), the previously proposed morphodynamic model (Giri and Shimizu, 2006, 2007) has been extended, which can replicate the bed shear stress variation in accordance with the variation of form drag exerted by the temporal growth or decay of bed forms under temporally varying flows. The model is shown to reproduce dune evolution, transition to flat bed, and the reappearance of bed forms in the falling stage of time-varying flow (Fig. 1). In order to accurately simulate this phenomenon, an assumption is made in the form of the particle step-length parameter used in the non-equilibri-
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um sediment transport formulation. This parameter, which is usually treated as a linear function of particle size, is also varied as a function of boundary shear stress in the approach presented here-this more general formulation appears to produce better results for the treatment of bed form evolution in time varying flows, and is also consistent with most theoretical formulations of sediment motion. In their numerical experiments they revealed that stage-discharge relationships significantly depend on the pattern of discharge variation with time, shape of falling and rising limbs, magnitude of peak flow, flow intensity, sediment
transport mechanism and so on. They revealed that the hysteresis loop in stage-discharge relations might occur or not occur depending on these characteristics (Fig. 6). The knowledge gained from their analysis has offered an incentive to investigate the influence of local flow variability and bed configuration on mean step-length, thereby exploring and expanding the existing understanding of non-equilibrium sediment transport more comprehensively.
Recently, Nelson et al. (2008) explored performance of model mentioned above based on their laboratory experiment on bed form response under varying discharge with sharp rise and sharp decrease. They comprehensively analyzed the experimental and simulation results. As they described, the model appeared to perform reasonably for the ini-
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tiation of bed forms on a flat bed and predicts the general evolution of increasing wavelength and height from an initial stage, but the response to a rapid flow change is muted relative to measurements. The model results showed a more rapid increase in wavelength during the high-flow period relative to a constant low flow, but the rapid increase and subsequent decrease were not correctly predicted. These discrepancies were attributed to the fact that a constant step length was used in the model. Giri and Shimizu (2007) also found that the value of step length has a significant effect on the wave-length selection. While a constant step length appears to be adequate for constant flow, it is likely that the shortcomings of the morphologic evolution model for time-varying flows are associated with this assumption. As Nelson et al. (2008) found in their result that the initial response to the sudden increase in flow is roughly double the average skin friction, it seems clear that the average step length of particles moving as bedload should also increase in response. In these works, for the first time, sediment-transport models for bed forms are taking direct consideration of the effects of variability in predicting sediment motion and the subtle feedback between the flow and topographically induced accelerations that govern the local turbulence fields and, thereby, the transport of sediment. This is a significant step forward on modelling bed form dynamics and resistance to flow with the use of detailed hydrodynamics.
Future direction
As it was mentioned above, the works on developing models with direct consideration of the flow variability and associated sediment motion are being actively conducted by several group of researchers. This would definitely lead scientist and engineers to a physically-based predictive tool for bed form dynamics, thereby enables to dramatically improve our understanding of these physical processes. As pointed out by some researchers (Jim Best, 2005), some additional focus on future research is of importance in present context. Likewise, an important aspect is the effect of these bed form evolution to the water surface, particularly under varying discharge during flood event.
On the other hand, we argue that there must be a parallel efforts that should be made to seek
for the practical implementation of the knowledge gained.
Fundamental research needs
— Detailed knowledge of bed form evolution under varying flows. Investigation on appearance of superimposed small bed forms over large dunes during falling stage and low flows. Even under the steady flow condition, the process of superimposition/amalgamation takes place during bed form development. Many researchers have been pointed out this fact, though a comprehensive investigation has yet to be done. The laboratory investigation conducted by Fernandez et al. (2006) has thrown some light on the mean and turbulent structure of flow across the ripple-dune transition. They examined a triangular, fixed bed form of ripple-size which amalgamates with a smaller, triangular, bed form to generate a final bed form approximately the size of a dune. Fig. 7 shows an example of distribution of Reynolds stress over some individual and superimposed bed forms with different shapes. This work describes the effect superimposition during ripple-dune transition on mean flow and turbulent field. However, some field investigation revealed the fact of appearance of small scale bed forms over the large ones, particularly during falling stage of flood event. The development and interaction between bed forms and their overall contribution to the flow resistance should be explored in a comprehensive way. The advanced numerical models might be capable to replicate this phenomenon, which is rather complicated to quantify properly in a laboratory or field situations.
— Transition between 2D and 3D dunes. Investigation on effect of dune dimensionality (two and three) on the mean flow and turbulent field, and primarily their effect on form drag or resistance to flow. Sirovich and Karlsson (1997) conducted series of wind tunnel experiments on flow over "riblets" in order to determine what sort of patterns would effectively reduce drag on airplane surfaces. They demonstrated that a strictly 2-D aligned pattern (Fig. 8, right plot) produced a larger drag than a smooth surface while an out-of-phase random pattern (Fig. 8, left plot) produced a lower drag than a smooth surface. This appeared to occur because random orientations of riblets effectively alter the burst-sweep cycle, reducing boundary shear stress. Sirovich and Karlsson
(1997) found that hydraulic drag was reduced by up to 20 % by changing the arrangement of perturbations. The transition between 2-D and 3-D bed forms is analogous to a change from an aligned to a random pattern of roughness elements, with the complication that the 3-D bed forms induce secondary flow circulations. Venditti (2007) has described these facts in his recent study and attempted to explore in laboratory condition the turbulence and drag over 2D and 3D dunes. Earlier, Maddux et al. (2003a, 2003b) performed a detailed laboratory study on flow and turbulence over three-dimensional dunes. Also, a field study on flow field and morphology over three dimensional dune was conducted by Parsons et al. (2005), and found some similarities as well as differences with the laboratory experiments. All these physical observations provide some additional insight in to the said problem. However, it would be efficient and reliable if we can use a numerical model with detailed hydrodynamics to understand these behaviours in more comprehensive manner.
Interpretation of dynamic behaviour of bed forms to the roughness description. Make use of numerical models with detailed hydrodynamics to evaluate all above mentioned phenomena and derive some quantitative relationships. Few existing models are already capable to do these kind of studies.
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Fig. 7. Distribution of Reynolds stress over some individual and superimposed bed forms with different shapes (After Fernandez et al., 2006)
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Random panera Aligned pattern
Fig. 8. Plan view of strictly two-dimensional aligned pattern (right plot) and out-of-phase random pattern (left plot) of riblets (After Sirovich and Karlsson, 1997)
Fig. 9. Friction coefficient (Cf = 2u*2/Uo2 ) against Reynolds number for the channel bed with different pattern (After Sirovich and Karlsson, 1997)
Practical implementation
As it has been pointed out in previous section, there are number of supplementary demands for the furtherance of existing knowledge and development. Particularly, due to significant step forward in computational modelling of fluid and bed form dynamics, we are rather near to a truly predictive tool that can be used to investigate aforesaid phenomenon. At the same time, we must consider that the knowledge being gained from fundamental research should concurrently be implemented to solve real-world problems.
In the present state, an advanced model cannot be used to resolve big scale phenomenon in a straightforward way due to rather intensive computational efforts. However, it appears to be possible to draw some quantitative relationships from the knowledge and understanding that can be gained by means of sophisticated models.
BO o-
Ii университета 'ЖУРНАЛ водных / I коммуникации
Here are some important issues to be addressed in more comprehensive manner:
— Description of form drag exerted by bed forms using hydrodynamic models with non-hydrostatic pressure distribution.
— Evolution of form drag to be quantified for arbitrary steady and unsteady flow using detailed hydrodynamic models coupled with sediment transport model (the morphodynamic model).
— Bed form evolution and transition under varying flows.
— Water surface variation induced by bed forms under steady and varying flows.
— Interpretation of bed form evolution to dynamic roughness and flow resistance.
— Prediction of stage-discharge relationship with hysteresis effect induced by bed form evolution and transition.
We are not far from resolving the problem that would at least be able to provide an improved parameterization of roughness behaviour to be implemented in real-world application, if we keep continuing research and development efforts in this direction keeping closed collaborations with various research and academic institution around the world.
References
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TWO-PHASE BOUNDARY LAYER MODEL TESTED AGAINST COUETTE FLOW
MEASUREMENTS
ДВУХФАЗНАЯ МОДЕЛЬ ПОГРАНИЧНОГО СЛОЯ, ПРОТЕСТИРОВАННАЯ ^69
С ПОМОЩЬЮ ПОТОКА КУЭТТА
Arno Talmon,
Delft University of Technology
In the hydraulic pipeline transport of concentrated solid-liquid mixtures there is a need for improved physics-based friction laws. For flow velocities higher than the deposit-limit-velocity the equivalent liquid hypothesis, or variations on it, are often applied. For these conditions, and for the suspension flow above deposits, a boundary
