Turbulent flow across a natural compound channel

Transcription

1 WATER RESOURCES RESEARCH, VOL. 38, NO. 12, 1270, doi: /2001wr000902, 2002 Turbulent flow across a natural compound channel P. A. Carling and Zhixian Cao Department of Geography, University of Southampton, Highfield, Southampton, UK M. J. Holland Institute of Environmental and Natural Sciences, University of Lancaster, Lancaster, UK D. A. Ervine and K. Babaeyan-Koopaei Department of Civil Engineering, University of Glasgow, Glasgow, UK Received 22 August 2001; revised 23 April 2002; accepted 29 May 2002; published 4 December [1] The measurements and primary analysis of turbulent flow across a compound channel (River Severn, England) are presented. The velocity was measured using a threedimensional acoustic Doppler velocimeter in combination with a directional current meter. The statistical flow structure is examined against existing analytical formulations derived for single channel flows based on laboratory studies. The existence of a vertically twolayer structure around the interface between the main channel and the floodplain is demonstrated, indicating (1) a vertical shear-dominated flow zone near the bed; and (2) away from the bed a transverse shear-dominated flow zone with enhanced turbulent mixing. The temporal spectra clearly reveal the occurrence of anisotropic turbulence both in the main channel and over the floodplain. The present findings necessitate the resolution of both transverse and vertical structures for advanced modeling of compound channel flows. The measured data can be used to assess the performance of mathematical river models. INDEX TERMS: 4568 Oceanography: Physical: Turbulence, diffusion, and mixing processes; 1821 Hydrology: Floods; 1860 Hydrology: Runoff and streamflow; 1719 History of Geophysics: Hydrology; 1794 History of Geophysics: Instruments and techniques; KEYWORDS: compound channel, turbulence, floodplain, anisotropy, ADV, open channel flow, fluvial hydraulics Citation: Carling, P. A., Z. Cao, M. J. Holland, D. A. Ervine, and K. Babaeyan-Koopaei, Turbulent flow across a natural compound channel, Water Resour. Res., 38(12), 1270, doi: /2001wr000902, Introduction [2] Turbulent flow in compound river channels is of increasing interest to fluvial engineers and scientists. The turbulence characteristics are the most influential factors that control channel flood conveyance, sediment movement, river morphological development as well as pollutant transport. Current understanding of compound channel turbulence is far from complete. Previous studies of compound channel flows have been largely limited to laboratory scale experiments [e.g., Knight and Shiono, 1990; Shiono and Knight, 1991; Tominaga and Nezu, 1991; Naot et al., 1993; Knight et al., 1994; Shiono and Muto, 1998] and numerical simulation [e.g., Pezzinga, 1994; Sofialidis and Prinos, 1998, 1999]. In practice, river engineers are still reliant upon traditional one-dimensional (1-D) and depth-averaged 2-D hydraulics approach to estimate the channel discharge capacity [Wormleaton and Merrett, 1990; Ackers, 1992; Ervine et al., 1993; Shiono et al., 1999; Ervine et al., 2000]. One of the basic impediments to enhancing the understanding of compound channel flows is the lack of systematic detailed measured data at the field scale. Existing field measurement studies are limited to single channel Copyright 2002 by the American Geophysical Union /02/2001WR weakly 3-D flows [e.g., Nezu and Nakagawa, 1993; Nikora and Smart, 1997; Sukhodolov et al., 1998). [3] This paper presents, for the first time, the 3-D acoustic Doppler velocimeter (ADV) and directional current meter (DCM) measurements and a basic analysis of the turbulent flow in the near-bank region of a natural compound river channel (River Severn, England). In the earlier sections of the paper the field measurements are described. Then, the mean flow and turbulence characteristics are analyzed in comparison with existing formulations derived for single channel flows. Finally, conclusions are drawn which can aid in the development and testing of mathematical river models. 2. Field Measurement [4] The field measurements were carried out in the River Severn, England, during periods of over-bank flow ( ). The monitored reach consists of a roughly straight and deep channel downstream of a double-meandering channel bend (Figure 1). The true left bank of the river is a river terrace some 1 m higher than the surface on the right bank. The right bank surface is an active floodplain, the width of which is restricted by an artificial embankment. While the terrace is rarely flooded, the active floodplain on the right bank is inundated by discharges in excess of approximately 100 m 3 /s. The main channel has a gravel bed while the steep river banks are predominately grass-

2 6-2 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL Figure 1. Study channel and measurement sites, River Severn: (a) channel reach; (b) ADV probe locations; and (c) DCM probe locations. The solid symbols in Figures 1b and 1c denote that the measured data are shown in subsequent figures.

3 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL 6-3 covered gravels and silts. The floodplain surface consists of closely grazed pasture. Because the change in the flow conditions could not be controlled, the flow was, strictly speaking, unsteady. Nevertheless, the data collected correspond to a specific period of time, in which the flow can be considered as quasi steady, with a discharge of 103 m 3 /s. The data presented and analyzed in the following text are of this type. Recognizing the asynchronous nature of the measurements is vital for understanding the evident scatter of data points, as shown later. [5] The 3-D turbulence was measured using a 3-D ADV system (SonTek). Pseudosynoptic velocity profiles were obtained in the vertical by raising the ADV sequentially. The ADV was mounted on a rigid steel scaffolding pole set within a guide rail on a specially constructed scaffold platform. Extending about 7.8 m onto the floodplain and also cantilevered out above the bank line, the platform allowed sampling on the floodplain and in the near-bank region of the channel (Figure 1b). The sampling rate was 25 Hz, and the typical ADV sampling time period was 200 s. The ADV data were processed using the WinADV software, developed at the Water Resources Research Laboratory, U.S. Bureau of Reclamation. Water depths of around 8 m in the main channel precluded deployment of the ADV in a controlled frame of spatial reference. Consequently, mean velocity profiles were measured, using a DCM deployed from a boat, every 2 m across a full cross section (Figure 1c) in the immediate vicinity of the ADV cross section. While it would be ideal to carry out both ADV and DCM measurements in exactly the same cross section, the practical DCM cross section had to be set at a slightly different position due to access reasons. The position in the DCM section was determined from meter markers on a taught rope stretched across the section, and up to 12 readings were obtained in the vertical with more closely spaced readings taken near the bed. Both streamwise and transverse mean velocity components were recorded. 3. Mean Flow [6] To expedite the description, it is necessary to define the coordinate system and notations. The streamwise direction x is defined as perpendicular to the measurement cross section (note in Figure 1a that the ADV and DCM cross sections are slightly different), the transverse direction y is defined as within the cross section and being positive from the left toward the right bank (see Figures 1b and 1c), and the vertical direction z is defined as being the distance from the bed, perpendicular to the xy plane and positive upward. The corresponding mean (time-averaged) velocity components are denoted by U, V, and W, respectively, and the fluctuating velocity components are denoted by u, v, and w. For simplicity, the turbulent correlations between fluctuation velocity components are denoted by, for example, uw and uv, with the commonly used overbar eliminated. For convenient use of the data in potential mathematical river modeling, the data presented in the following are, where applicable, not nondimensionalized. [7] Figures 2 and 3 show the measured mean velocities from both the ADV and the DCM, respectively, on selected verticals corresponding to the solid symbols in Figures 1b and 1c. The 3-D nature of the flow can be seen from the ADV profiles due to the nonzero transverse and vertical velocities. Also included in Figures 2 and 3a are the streamwise mean velocity profiles (solid lines) computed with the conventional log-wake formula [Nezu and Nakagawa, 1993; Sukhodolov et al., 1998] for single channel flows, i.e., U ¼ 1 U * k 1n z þ 2 pz z 0 k sin2 ; ð1þ 2h where U * = bed shear velocity; z 0 = hydrodynamic roughness; h = local flow depth; = 0.2, the wake strength parameter presumed herein because the Reynolds number R e = U m h/n / 10 6 (U m = depth-averaged mean velocity, n = kinematic viscosity of water [see Nezu and Nakagawa, 1993]); and k = von Karman coefficient. [8] For the ADV data, the bed shear velocity in equation p (1) is evaluated using the traditional formula U * ¼ ffiffiffiffiffiffiffiffiffi t 0 =r, where r = water density, and the bed shear stress t 0 is calculated by fitting a linear distribution to the observed shear stress ( uw) data near the bed (shown in Figure 4) and extrapolating to the bed. Afterward the von Karman coefficient and hydrodynamic roughness are estimated, using the method of least squares, by fitting equation (1) to the measured velocity profiles within approximately z/h 0.4. In this regard it is noted that once the bed shear velocity has been calculated from the Reynolds shear stress data, the von Karman coefficient is uniquely determined by the vertical gradient of mean velocity. This is evident from equation (1) when it is applied to the near-bed region where the wake contribution is negligible. This feature has nothing to do with the hydrodynamic roughness or the wake strength parameter. The estimated von Karman coefficient, bed shear velocity, and roughness values are listed in Table 1. Obviously the von Karman coefficient is only slightly larger than the universal value of [9] For the DCM data, the turbulent Reynolds shear stresses are not available. Consequently the bed shear velocity is yet to be determined as are the von Karman coefficient and the hydrodynamic roughness. However, only the mean velocity data are available, which can be used to estimate two of the three unknown variables. Hence the von Karman coefficient is presumed to be equal to the averaged value (= 0.43; see Table 1) estimated from the ADV data. The corresponding bed shear velocity and roughness, estimated by fitting equation (1) to the mean velocity profiles using the least squares method are also given in Table 1. [10] It is recognized from equation (1) that the ratio U * /k of bed shear velocity to the von Karman coefficient is determined by the vertical gradient of mean velocity in the near-bed region, and the roughness indicates a reference height above the bed at which the mean velocity vanishes. After U * /k has been estimated from the vertical velocity gradient, the roughness can be uniquely determined by fitting equation (1) to the measured velocity data. Clearly the large roughness values in Table 1 are entirely reflected by the measured data and thus are justified. It is natural that uncertainty is inevitable when there are only a few measurement points along the flow depth (Figure 3a). This constraint is due to the harsh field measurement conditions under flooding. More discussion on the roughness values is provided in the following text.

4 6-4 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL Figure 2. ADV (symbols) and computed (lines) mean velocities: (a) y = m; (b) y = 25.0 m; and (c) y = 27.0 m. The solid lines correspond to 0.2, and for dashed lines is given in Table 1. [11] It is appreciated that there are other methods for evaluating the bed shear velocity [Nezu and Nakagawa, 1993]. Lyn [1991] compared several methods for his flume experiments and found that the Reynolds shear stress extrapolation-based method, the log law-based approach, and an independent empirical correlation accord well with p each other, whereas the estimation using U * ¼ ffiffiffiffiffiffiffiffi p grj or U * ¼ ffiffiffiffiffiffiffiffi ghj shows considerable discrepancy (R = hydraulic radius, J = bed, water surface or energy slope). As is well known, the bed or water surface slope is a rather elusive quantity and difficult to determine accurately for natural channel flows. Thus the bed shear velocity values computed from the Reynolds shear stress extrapolation and log law fitting are more reliable than the slope-based estimation. The following analysis will be confined to the bed shear velocity due to the former methods (i.e., excluding the slope-based estimation). For reference, the water surface slope is estimated to be equal to from a detailed water surface survey, and the bed slope averaged across the main channel is approximately (±15%) from a topography survey. Accordingly the bed shear velocity is about 5.3 cm/s due to hydraulic radius (R 2.9 m) and ranges between 3.64 and 8.65 cm/s due to local flow depth for the verticals shown in Table 1. Generally the bed shear velocity due to slope estimation is smaller than those derived from the Reynolds shear stress extrapolation and the log law. Given an elusive slope quantity, deriving bed shear velocity from reach-average slope values is overly simplistic for plainly compound channel flows. [12] It is found in Figures 2 and 3a that near the bed, there exists a log velocity zone in both the main channel and the floodplain, as is the case in single channel flows (note that the wake component is negligible near the bed). This result is related to the linear distribution of the Reynolds shear stress ( uw; see Figure 4) near the bed. Approaching the floodplain, the log velocity zone extends gradually toward the water surface (where the wake component becomes

5 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL 6-5 Figure 3. DCM (symbols) and computed (lines) mean velocities: (a) on selected verticals; and (b) isovels of DCM streamwise velocity (m/s). The solid lines correspond to 0.2, and for dashed lines is given in Table 1.

6 6-6 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL Figure 4. Reynolds shear stress from ADV data: (a) y = m; (b) y = 25.0 m; and (c) y = 27.0 m. The dashed lines indicate the vertically two-layer flow structure, and the solid lines correspond to linear distributions valid for single channel flows. appreciable), as shown in Figures 2 and 3a. Within the main channel, the streamwise velocity near the free surface deviates considerably from the log wake law, resulting from the strong transverse momentum exchange. Specifically, the transverse momentum exchange serves to slow down the water flow near the free surface so that the streamwise velocity is lower than what would otherwise be anticipated in single channel flows. This phenomenon has been found to exist close to channel banks in single channel flows [Nezu and Nakagawa, 1993; Knight et al., 1994]. The effect Table 1. Parameters for Streamwise Mean Velocity Profiles Under Log Wake Law Location of Verticals Bed Shear Velocity U *, cm/s Source y, m uv Extrapolation (ADV) or Log Law p Fitting (DCM) U * ¼ ffiffiffiffiffiffiffiffi ghj z 0,m h, m k ADV ± ± ± DCM

7 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL 6-7 Figure 5. Turbulent intensities from ADV data and analytical formulations: (a) y = m; (b) y = 25.0 m; and (c) y = 27.0 m. of the hindered streamwise flow near the free surface must not be ignored. This retardation may give rise to increased flow shearing near the bed, which subsequently results in the large values of hydrodynamic roughness z 0 in, and close to, the main channel (see Figure 1 and Table 1). Such large values of hydrodynamic roughness are not commonly seen in single natural channel flows [Nikora and Smart, 1997; Sukhodolov et al., 1998]. Plausibly the large roughness encompasses contributions from the complicated channel geometry (Figure 1) in terms of form resistance (e.g., residual effect from the upstream meandering and an irregular bank line topography), etc. This observation seems to be a rather telling case supporting the perspective that natural flows are worthy of further thorough investigation, due to their much more complex and realistic nature, in contrast to laboratory flows. [13] As far as the isovels of the streamwise velocity are concerned (Figure 3b), the overall flow pattern is more complicated than that seen in laboratory symmetrical compound channels [Knight et al., 1994]. Specifically, the flow pattern in the left-hand side of the cross section (y < 16.0 m) is qualitatively similar to what would be seen close to a side bank in a single channel [see Nezu and Nakagawa, 1993, Figure 6.10]. The hindered velocity near the free surface immediately to the left of the cross section center (say, 8.0 < y < 16.0 m) is typical of straight prismatic channels of small (width-to-depth) aspect ratio [Flintham and Carling, 1988] without floodplains. This effect is also seen elsewhere in the River Severn during high in-bank flows [Carling, 1991; Beven and Carling, 1992]. Nevertheless, because of the asymmetrical geometry of the cross section, the flow pattern in the right-hand side is quite different. The existence of the floodplain provides the space required for the flow to develop. The flow is clearly biased to the right, with the maximum velocity (flow core) being in the immediate vicinity of the interface between the main channel and the floodplain. More notably, the vertical variation of the flow structure is seen to be as substantial as the transverse change. By this fact it is characterized that both the vertical and transverse resolution in model developments of com-

8 6-8 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL Figure 6. Turbulent kinetic energy from ADV data and analytical formulations: (a) y = m; (b) y = 25.0 m; and (c) y = 27.0 m. pound channel flow requires close attention. Clearly the traditional 1-D model with a bulk roughness parameter (say the Manning roughness) and depth-averaged 2-D model with transversely differing roughness are not fine enough for simulating the complicated compound channel flow structure. This observation represents the most telling case for the need for more advanced 3-D modeling tools. [14] A test of the applicability of the log wake formula equation (1) to compound channel flows was made by tuning the wake strength parameter to get the optimal fit to the measured velocity in the sense of least squares. The tuned velocity profiles are also shown in Figures 2 and 3a (dashed lines). Qualitatively, equation (1) can be fitted to the measured velocities fairly well with reduced wake strength parameters (Table 1). In general, the wake strength parameter is smaller than those reported by, for instance, Nezu and Nakagawa [1993] and may be negative for verticals in the main channel and around the main channel-floodplain interface. [15] It is well known that the wake strength parameter does not have a universal value. For air flows, Coles [1956] suggested a value of Nezu and Nakagawa [1993] show that it is a function of the Reynolds number, varying between 0 and 0.2. Further, it can be negative for both smooth and rough bed flows [Cardoso et al., 1989; Kironoto and Graf, 1994, 1995], in line with small aspect ratio and the presence of longitudinal pressure gradient. Hence the use of negative values of the wake strength parameter in fitting mean velocity profiles with equation (1) is not unusual. A further example is for suspension flows, in which turbulence is modified by sediments, and thus the mean velocity structure is altered. For clay suspension Table 2. Coefficients in Turbulent Intensity Formulations (2) Through (4) Modified for ADV Verticals Location of Verticals y, m D u D v D w C k

9 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL 6-9 flows, Wang and Plate [1996] reported negative values of the wake strength parameter (as low as 0.83), which is further confirmed by recent analysis [Wang et al., 2001]. Clearly, in these latter cases, it is the presence of sediment that leads to the negative wake parameters. The present paper deals with essentially clear water flows in a natural compound channel; for this case it is the compound channel geometry that results in the strong interaction between the main channel and the floodplain and subsequently the negative values of the wake strength parameter. [16] Further it is noted that the wake strength parameter can be affected by unsteady nature and longitudinal pressure gradient of the flow [Nezu and Nakagawa, 1995; Kironoto and Graf, 1995; Song and Graf, 1996]. As stated earlier, the natural compound channel flows in flooding conditions under consideration were unsteady in a strict sense, and longitudinal pressure gradient appears to be existent. Therefore, at least qualitatively, both the unsteadiness and pressure gradient could to a certain extent have contributed to the reduced values of the wake parameter (Table 1). The uncertainty, arising from both factors in the estimation of is inevitable due to the nature of measurement under natural conditions, in contrast to well-controlled laboratory experiments. [17] Conventionally the wake component is interpreted as a large-scale mixing process in concurrence with the smallscale wall effect due to viscosity, and the magnitude of the wake strength parameter represents a comparison between the large-scale and small-scale motions, and between the constraints imposed by inertia and viscosity [Coles, 1956]. The reduced wake strength parameter is precisely an indication of the significantly modulated large-scale motions in compound channels with respect to single channels. In the event of compound channels, the large-scale motions appear to retard the flow away from the bed (Figures 2 and 3a), in line with the reduced and even negative wake strength parameter. Physically the reduced wake strength parameter implies decreased mean flow energy, in accord with the increased turbulent kinetic energy in the outer region (as will be shown in Figure 6). [18] For obvious reasons further work, using more measured data sets, is required to determine an objective means of selecting the wake intensity parameter so as to improve flow modeling (e.g., discharge estimation and channel conveyance assessment, etc.). 4. Reynolds Shear Stress [19] Figure 4 shows the representative (ADV) Reynolds shear stresses for three verticals ( y = 23.95, 25.0, and 27.0 (m), corresponding to the solid symbols in Figure 1b). Also shown is a linear profile (sold line) for uw based on the same bed shear velocity (Table 1), which is valid for straight single channel flow [Nezu and Nakagawa, 1993]. It is seen from Figure 4 that near the bed, uw follows approximately a linear profile, as illustrated by the dashed lines (Figures 4a and 4b), which leads to a log velocity profile as shown in Figures 2 and 3a. Physically this result indicates the dominance of vertical flow shearing under the control of the wall, though the primary Reynolds shear stress uw decreases more quickly with increasing distance from the bed than in a single channel flow with equivalent bed shear velocity, as represented by the solid lines. [20] Echoing the mean velocity profiles shown in Figures 2 and 3a, the shear stress near the free surface deviates substantially from the near-bed linear distribution. In particular, for verticals closer to the main channel (Figure 4a), uw almost vanishes, which suggests considerably reduced vertical shearing and velocity gradient (Figures 2 and 3a). The existence of the two-layer structure of the primary shear stress uw within the vertical is apparent. Away from the main channel, above the floodplain, this two-layer structure becomes less evident (Figure 4c). The occurrence and feature of the vertically two-layer structure is qualitatively consistent with that found in the Flood Channel Facility experiments at HR Wallingford [Knight and Shiono, 1990]. 5. Turbulent Intensities and Kinetic Energy [21] Figures 5 and 6 present the turbulent intensity components and kinetic energy, respectively, on three verticals (y = 23.95, 25.0, and 27.0 (m), corresponding to the solid symbols in Figure 1b). Existing formulations for open channel flows are limited to situations with single channels, which are derived on the basis of balance between turbulence production and dissipation. The following formulations [Nezu and Nakagawa, 1993] for 2-D steady and uniform open channel flows are introduced to compare with the present ADV measurements, i.e., u rms ¼ D u expð C k z=hþ ð2þ U * v rms ¼ D v expð C k z=hþ ð3þ U * w rms ¼ D w expð C k z=hþ ð4þ U * K U * 2 ¼ D k expð 2C k z=hþ; ð5þ where D k =(D u 2 + D v 2 + D w 2 )/2; D u, D v, D w, and C k are empirical coefficients; and u rms, v rms, and w rms are the root of mean square of the fluctuating velocity components u, v, w, respectively. For single channel flows, D u, D v, D w, and C k are equal to 2.30, 1.63, 1.27, and 1.0, respectively [Nezu and Nakagawa, 1993]. In the present case of compound channel flows, it is found that turbulent intensity and kinetic energy can be represented reasonably well by equations (2) through (5) only with modified coefficients as listed in Table 2. These altered coefficients are estimated by applying a least squares method to equations (2) through (4) using the ADV data within z/h 0.4 in accord with the vertically two-layer structure demonstrated by the mean velocity and Reynolds shear stress (Figures 2, 3, and 4). The use of modified coefficients in equations (2) through (4) has been reported by, for instance, Sukhodolov et al. [1998] for single natural channel flows. It is noted from Figures 5a and 6a that on the measurement vertical closest to the main channel (y = m), turbulent intensities and kinetic energy near the free surface are enhanced compared to those estimated by equations (2) through (4) with the modified coefficients for the near-bed fraction of flow (z/h 0.4). This effect can be ascribed to the strong turbulent momentum exchange. Once again, this characteristic reveals the vertically two-

10 6-10 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL Figure 7. Turbulence temporal spectra from 3-D ADV data at two verticals: (a c) y = m; and (d f) y = 27.0 m. layer structure for compound channel flows, although it becomes less pronounced approaching the floodplain ( y = 25.0 m and 27.0 m in Figures 5 and 6). Of further note are the values of C k (C k = 2.4 and 0.23 for verticals at y = m and 27.0 m, respectively; Table 2). These values are respectively larger, or smaller, than the value of unity applied to single channel flows [Nezu and Nakagawa, 1993; Sukhodolov et al., 1998], which corresponds to a vertically suppressed (closest to the main channel and near the bed) or intensified (on floodplain) momentum exchange. 6. Turbulence Temporal Spectrum [22] The form of turbulence spectra for natural river flows is still incompletely known because of the lack of quality measured data. For single channel flows, Yokoshi [1967] reported the occurrence of double inertial subranges, in which the Kolmogorov 5/3 power law is observed. The recent measurements by Sukhodolov et al. [1998] reveal the anisotropy of turbulence near the channel bed and the free surface. For compound channel turbulent flows, Figure 7 shows the typical turbulence temporal spectral density at six locations on two verticals ( y = and 27.0 (m); Figure 1b), which is calculated from and S i ðwþ 2 p R i ðtþ lim T!1 Z T R i ðtþcosðwtþdt ð6þ Z T T u i ðt þ tþu i ðþdt; t where S i (w) is the temporal spectrum density in relation to ith fluctuating velocity component u i, R i (t) is the autocovariation function, t is a time lag, w is the cyclical frequency, and the subscripts i = 1, 2, and 3 denote the x, y, and z directions, respectively. ð7þ

11 CARLING ET AL.: TURBULENT FLOW ACROSS A NATURAL COMPOUND CHANNEL 6-11 [23] Figure 7 shows that, unlike single channel flows, the occurrence of the inertial subrange can be found only in a rather narrow range of frequency (at the widest w 2 [2, 5] rad/s), where the 5/3 power law applies approximately. This behavior precludes a reliable estimation of the turbulence dissipation rate and, subsequently, of the turbulence scales using existing semiempirical formulations [Tennekes and Lumley, 1972; Sukhodolov et al., 1998]. The similarly important feature seen in Figure 7 is the apparent anisotropy of turbulence because of the distinct spectrum densities of different spatial directions, irrespective of the vertical and transverse locations. [24] It is noted that at high frequencies, the values of the spectrum densities approach constants asymptotically and thus increasingly deviate from the 3/5 power law. In evaluating ADV for turbulence measurements, Voulgaris and Trowbridge [1998] reported similar characteristics in laboratory open channel flows. They also suggested that the spectra estimations of the horizontal and vertical flow components agree with Kolmogorov s theoretical spectra model if correction is applied for viscous dissipation effects, production effects, spatial averaging of the sampling volume, and measurement noise variance. Yet reconciling the spectra estimation from Kolmogorov s model with that of ADV records for compound channel flows, as by Voulgaris and Trowbridge [1998], appears impractical due to the lack of reliable estimation of the turbulence dissipation rate in this complex case. This may point to the need for a through evaluation of ADV, for turbulence spectra estimation, when applied to hostile in situ conditions such as compound channel flows during flooding. 7. Conclusions [25] The measurements and basic characteristics of turbulent flow in the near-bank region of a natural compound channel are presented. A vertically two-layer structure around the main channel-floodplain interface and substantial anisotropy of turbulence are found. Near the channel bed, the wall-bounded vertical flow shearing dominates, while close to the free surface transverse flow shearing dominates along with enhanced turbulent mixing. This twolayer structure results in large hydrodynamic roughness values that may not be commonly found in single channel flows with similar averaged velocity, depth, and bed material. Existing formulations for single channel flows can be tuned to fit the measured mean velocity, turbulent intensities, and kinetic energy profiles only within limited flow zones. The present finding necessitates more refined models for compound channel flows. In particular the vertical structure needs to be resolved as with a complete Reynolds stress closure model for turbulence (rather than with an isotropic turbulence-based model) to better understand the complicated 3-D flow and to render a reliable estimation of the channel conveyance, etc. Notation C k, D k, D u, D v, D w g h R parameters in equations (2) through (5). gravitational acceleration. local flow depth. hydraulic radius. R i (t) autocovariation function. S i (w) ith temporal spectrum density. U, V, W mean velocity. u i ith fluctuating velocity (= u, v, w). u rms, v rms, w rms turbulent intensity. U * bed shear velocity. x, y streamwise and transverse coordinates. z distance above the bed. z 0 hydrodynamic roughness. r water density. k von Karman coefficient. t time lag. t 0 bed shear stress. w cyclical frequency. wake strength parameter. [26] Acknowledgments. This study was funded by the Engineering and Physical Sciences Research Council of the United Kingdom, under grant GR/L The authors are grateful to the anonymous reviewers and also to Walter H. Graf and Keith Beven for their constructive comments and helpful suggestions on the analysis reported. References Ackers, P., Hydraulic design of two-stage channels, Water Maritime Energy, Proc. Inst. Civ. Eng., 96, , Beven, K., and P. A. Carling, Velocities, roughness and dispersion in the lowland River Severn, in Lowland Floodplain Rivers: Geomorphological Perspectives, edited by P. A. Carling and G. E. Petts, pp , John Wiley, New York, Cardoso, A., W. H. Graf, and G. Gust, Uniform flow in smooth open channel, J. Hydraul. Res., 27(5), , Carling, P. A., An appraisal of the velocity-reversal hypothesis for stable pool-riffle sequences in the River Severn, England, Earth Surf. Processes Landforms, 16, 19 31, Coles, D., The law of the wake in the turbulent boundary layer, J. 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