Turbulence Structure in Depth-Limited, Vegetated Flow:

Transition Between Emergent and Submerged Regimes

 

H. M. NEPF and E. R. VIVONI

 

Parsons Laboratory, Department of Civil and Environmental Engineering

Massachusetts Institute of Technology

48-425 MIT, Cambridge, MA, 02139

(P) 617.253.8622; (F) 617.258.7009; hmnepf@mit.edu

 

 

ABSTRACT

Laboratory experiments were used to explore the flow characteristics and turbulence structure within and above submerged vegetation. The study focused on the role of water depth in limiting shear-layer development above the vegetation, and in particular on the as yet unexplored transition between submerged and emergent regimes. The experiments were carried out in an open channel flume with a model vegetative meadow. Velocity was measured using both acoustic (three-components) and laser (two-components) Doppler velocimetry. The momentum and turbulence fields within the canopy were characterized by the penetration of turbulent stress from the overlying flow; the balance of sweep and ejection events; and the relative contribution of terms to the turbulent kinetic energy budget. Turbulence production within the canopy was associated with two components: generation within the strong shear-layer at the top of the canopy, and generation within the stem wakes. The relative importance of these sources varied with characteristic depth, H/h, where H was the total flow depth and h the canopy height. Across the range of H/h considered [1 (emergent) to 2.75], the transition from emergent to submerged conditions was captured by a shift in penetration depth, h_p, a measure of the region within the canopy for which vertical turbulent exchange with the overlying water was dynamically significant to the momentum and turbulence structure within the canopy.

 

Keywords: Turbulence, Vegetated Flow, Depth-Limited Flow, Experimental Hydrodynamics

 

INTRODUCTION

Aquatic vegetation plays a central role in defining the mean and turbulent structure of flow, and thus impacts the fate and transport of sediment and contaminants. The additional drag contributed by plants reduces the mean flow within vegetated regions relative to unvegetated ones. This baffling of flow promotes the accumulation of particles by reducing near-bed stress and subsequent erosion (e.g. Ward et al., 1984). Vegetative drag also impacts flood routing by significantly altering flood-plain conveyance, and can control wetland circulation and thus function (Kadlec, 1990, 1995). Finally, the presence of vegetation alters turbulence structure by promoting additional generation in the shear-layer created at the top of the canopy and in the wakes of individual plant-elements. The later, wake-generation, is particularly important for emergent conditions, where it can augment turbulence intensity while shifting the dominant turbulent length scale downward, with the net effect of reducing turbulent diffusivity relative to unvegetated conditions (Nepf, 1999).

A great deal is known about unconfined canopy flow through work on terrestrial canopies (e.g., Raupach and Thom, 1981), which serve as a reasonable model for deeply submerged aquatic canopies, i.e. for H/h large enough that the free surface imposes no limitation on vertical structure and turbulent transport, where, H is the flow depth and h is the canopy height. However, for many aquatic canopies H/h is small enough that depth-limitation alters turbulence structure relative to the unconfined canopy regime described by the terrestrial literature. Most papers addressing hydrodynamic systems of vegetated flow have focused on fully submerged vegetation, e.g. laboratory and numerical studies of open channel flow through flexible and rigid artificial plants (e.g., Murota et al, 1984; Lopéz and García, 1996). Only a few studies have examined the extreme condition of emergent vegetation (Burke and Stolzenbach; 1983, Nepf, 1999). This paper explores the as yet undescribed transition between the emergent and the fully submerged regime. As the depth ratio, H/h, increases from 1, the turbulence structure shifts from stem-wake turbulence to shear-layer turbulence, with larger depth ratios approaching the structure of an unconfined canopy.

 

EXPERIMENTAL METHODS

Laboratory experiments were conducted in a 24 m long by 38 cm wide, glass-wall flume. A 7.4 m long model array of flexible vegetation was constructed from 0.025 cm thick vinyl plastic, using similarity in geometry and flexural rigidity to known aquatic vegetation (Kouwen and Li, 1980). Individual plants consisted of six 0.3 cm wide blades bundled to a short (2 cm) cylindrical (dia. = 0.6 cm) base. The stems were mounted on a Plexiglas baseboard in a random distribution to produce a model canopy 16 cm high with a vegetation density, a = 5.5 m^-1. The flow depth, H, was varied to produce depth ratios, H/h, from 1 to 2.75. The depth Reynolds' number (UH/n) was between 4 x 10³ and 4 x 10⁴. Finally, to reduce flow disruption the baseboard was extended 3 m upstream of the canopy and tapered to the flume bottom. Smooth inlet conditions were achieved using mats of rubberized fiber to dampen inlet turbulence, and a honeycomb flow straightener to eliminate swirl.

The mean (U, V, W) and turbulent (u, v, w) velocity components corresponding to the stream-wise, lateral and vertical directions, respectively, were measured using a 3-D acoustic Doppler velocimeter (ADV) and a 2-D laser Doppler velocimeter (LDV) at a test section located 6.6 m from the leading edge. The position of the test section was selected based on a longitudinal transect which delineated the region of uniform flow, unaffected by the leading and trailing edge of the array. Six-minute records were collected at 25 and 100 Hz for the ADV and LDV, respectively. Because the flow field within the canopy was inhomogeneous at the stem scale, a horizontal average of three lateral positions, denoted by < >, was used to represent the mean, homogeneous statistics (Kaimal and Finnigan, 1994, p. 84).

Conditional sampling was used to decompose the instantaneous Reynolds' stress, uw, into four quadrants, S_i, defined as (see e.g. Raupach, 1981),

S1: u > 0 and w > 0 outward interaction

S2: u < 0 and w > 0 ejection

S3: u < 0 and w < 0 inward interaction

S4: u > 0 and w > 0 sweep

With z positive upwards, ejection and sweep events (S2 and S4) contributed to a downward transfer (i.e. towards the bed) of positive momentum, and the interaction events (S1 and S3) represented upward transfers.

The mean and turbulent velocity records were also used to calculate turbulent kinetic energy budget. The total turbulent kinetic energy, k = u² + v² + w². The vertical turbulent transport, T = ; and the bed-shear production, P_s =, where the overbar indicates a temporal average. The rate of turbulent dissipation, e, was evaluated from an inertial subrange fit to the velocity spectra, S_uu, (see e.g. Kundu, 1990, p. 441). Finally, the surface slope, ∂H/∂x, was measured using a pair of resistance-type surface displacement gages (0.2 mm resolution), positioned 5 cm up- and downstream of the canopy. The drag coefficient, C_D(z), was then estimated from the profiles of Reynolds' stress and the surface slope, following the technique of Dunn et al. (1996). The turbulence production associated with the stem wakes, P_w, was estimated as the work input by the stem drag, i.e. per unit mass,

 

(1)

 

This assumes that all energy extracted from the mean flow by stem drag appears as turbulent kinetic energy. This assumption is limited below Re_d < ≈ 200 where the viscous drag, which dissipates mean flow energy without generating turbulence, becomes increasingly important. As the fraction of viscous drag increases, P_w decreases from the value given in (1).

 

RESULTS

To begin we examine profiles of mean velocity and Reynolds' stress for the limiting cases of submerged and emergent canopies (fig. 1). For a submerged canopy vegetation drag created significant vertical heterogeneity in the mean velocity profile. The Reynolds' stress peaked at the top of the canopy, and decayed rapidly downward into the canopy. The vertical penetration of stress can be taken

 

 

 

Figure 1. Representative profiles of mean velocity and turbulent stress for

emergent (H/h =1.0) and submerged (H/h=2.75) conditions.

 

as one measure of penetration depth, h_p, where h_p indicates the region within the canopy that actively exchanges momentum with the overlying water. Specifically, h_p was defined as the distance from the top of the canopy at which the turbulent stress had decayed to 10% of its maximum value. Near the bed, z < (h-h_p), turbulent transfers of momentum were negligible and the flow was driven by the pressure-gradient associated with the surface slope. In contrast, the emergent canopy had only limited vertical structure associated with vertical variation in foliage density, and the turbulent stresses was essentially zero.

For submerged conditions (fig. 2, H/h = 2.75) the shear at the top of the canopy dominated turbulence production, P_s, and the in-canopy turbulence was characterized by vertical transport (T) from this zone. As H/h decreased, the vertical penetration of turbulence into the canopy (T>0) also decreased. For emergent conditions (H/h =1) T = 0, as P_s was small and turbulence generation was dominated by the local production within the plant wakes, P_w. As indicated above, P_w was strongly dependent on stem Reynolds' number. For example, P_w given by (1) produced reasonable values for Re = 400, correctly balancing the observed dissipation, but overestimated P_w for Re=140.

 

 

Figure 2. Turbulent kinetic energy budget for submerged (H/h = 2.75) and

emergent (H/h = 1.0, Re = 140 and 400) conditions, normalized by the

canopy height, h, and shear velocity, U_m=√gHS, where S = surface slope.

 

Figure 3. Profiles of the quadrant stress differential, S4-S2, for submerged (H/h =

1.75), emergent (H/h = 1.0), and unobstructed conditions. S4-S2 < 0

indicates a sweep-dominated structure.

 

The relative magnitude of sweep (S4) and ejection (S2) events is another indicator of turbulence structure that demonstrated the transition from unconfined to depth-limited vegetated flows (fig. 3). For an unconfined canopy sweep events dominated momentum transport near the top of the canopy (S4-S2 < 0), and the extent of sweep penetration provided another measure of h_p. As H/h declined, the vertical extent of the sweep dominated region shrunk, until the sweeps and ejections were balanced over the entire canopy height (emergent condition). Although superficially similar to the smooth boundary condition (included in figure 3 for reference), the emergent case lacked both strong sweeps and ejections, rather than having a balance of large contributions by both types of events, as is the case for the smooth boundary.

The transition from emergent to unconfined flow depends on both the depth ratio, H/h, as well as the vegetation density, a. Figure 4 summarizes this transition using the penetration depth, h_p, derived from the stress profiles as described above. The transition was most gradual for dense canopies, e.g. a > 5 m^-1, and appeared to asymptote to the unconfined limit at H/h ≈ 2.5 - 3. As expected, the penetration ratio, h_p/h, increased as the vegetation density decreased, i.e. as the canopy provided less momentum absorption.

 

 

 

 

 

 

Figure 4. Transition from emergent (H/h=1) to unconfined submerged conditions.

Penetration depth, h_p, was based on the turbulent stress profiles

present study (dark squares); Dunn et al. '96 (triangles and diamonds);

Murato et al. '84 (square with cross); Seginer et al. (open square).

 

CONCLUSION

The transition from emergent to fully submerged vegetated flow can be described in terms of a shift in both the momentum balance as well as the turbulence budget. As the depth of submergence increased from the emergent condition (H/h =1) the in-canopy momentum was increasingly derived from the vertical turbulent transport of momentum from the overlying water layer and the direct contribution of pressure-forcing (surface slope) declined. In addition, there was a shift in the relative importance of mean-shear and wake-shear production of turbulence, although even for the fully submerged case wake production remained important very close to the bed when the stem Reynolds' number, Re > ≈ 200. The transition from emergent to submerged conditions was captured by a shift in penetration depth, h_p, which measured the region of flow within the canopy for which exchange with the overlying water was dynamically significant.

 

ACKNOWLEDGMENTS

This work was completed under NSF CAREER Award, EAR 9629259

 

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