JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. C2, 10.1029/2001JC000871, 2002

2. Scaling Criteria for Model Vegetation

Figure 4. Definition of geometric characteristics of eelgrass blades, including h, the total length of the blade, and h_d, the deflected height of the blade in the flow.

[9] The model vegetation (subscript m) was designed to satisfy both dynamic and geometric similarity with a prototypical eelgrass (Zostera marina) meadow (subscript p). The motion of an eelgrass blade is governed by a drag force (F_D), a buoyancy force (F_B), and a restoring force due to the blade's rigidity (F_R). Dynamic similarity is achieved by matching the two independent ratios of these governing forces. With important geometric parameters of eelgrass blades defined in Figure 4, the internal moment in a bent blade, M_I, is given by

where J (= Ewt³/12, E denoting the modulus of elasticity) represents the flexural rigidity of the blade. Therefore

Since l = h_d tan alpha ( approximately hsin alpha for small deflections), (4) becomes

where

Therefore for small deflections the ratios of the governing forces will have the following scales:

and

where rho _w and rho _s are the densities of water and of the blade, respectively; g is gravitational acceleration; A_f is the frontal area of the blade; U_c is the mean in-canopy velocity; and C_D is the blade drag coefficient. As alpha describes plant geometry, it is expected that it will have a pronounced effect on flow geometry, so individual experimental flow scenarios only faithfully model a prototypical flow for which alpha _m= alpha _p. Under this caveat we require that cos alpha _m = cos alpha _p and f₁( alpha _m) = f₁( alpha _p). Additionally, the drag coefficient of a plate aligned normal to the flow displays only a weak dependence on Reynolds number [Gerhart et al., 1992, p. 597]. Therefore, given geometric similarity, C_D can be treated as a constant. By excluding parameters that are approximately equal in the model and in the identically deflected prototype (i.e., g, rho _w, C_D, f₁( alpha ) and cos alpha ), the dynamic ratios (6) and (7), dimensional after parameter exclusion, become,

and

respectively.The dependence of lambda ₂ on U_c² makes its value vary tremendously in the field, so lambda ₁ was chosen as the critical design parameter. However, if lambda _1,m = lambda _1,p and alpha _m = alpha _p, then lambda ₂ will automatically be matched between the model and the prototype. Given the uncertainty of several field parameters, the value of lambda _1,p conceivably ranges between 10^-3 and 10⁰ s²m^-1 (for details, see Ghisalberti [2000]). Trial plants encompassing a range of values of lambda ₁ (0.006–0.092 s²m^-1) were subjected to a wave-current environment. The plant with lambda ₁ = 0.055 s² m^-1 exhibited the most realistic behavior, as compared with video footage of oceanic seagrass meadows (E. Koch, University of Maryland, personal communication, 1998), whose buoyancy and low rigidity create a whip-like motion, dissimilar to the rigid motion of a cantilever.

Figure 5. Photograph of the model eelgrass meadow. The meadow comprised 850 randomly placed model plants, each consisting of six thin blades affixed to a wooden stem.

[10] Additional dimensionless parameters needed to fully describe the flume and canopy conditions include the following:

[Vivoni, 1998], where H is the flow depth and p_i represents the set of {w,t}. The frontal area of plants per unit volume, a (m^-1), is defined by a = mw, where m is the planting density (blades m^-2). Equation of the parameters in (10) between model and prototype necessitated the use of the following model parameters: h_m = 12.7 cm, w_m = 3.0 mm and m_m = 1890 blades m^-2 (cf h_p = 15–250 cm, w_p = 2.5–5.0 mm, and m_p = 400–6000 blades m^-2), as detailed by Ghisalberti [2000]. Each model eelgrass plant consisted of a stem region and six thin blades (Figure 5), based on the typical morphology of Massachusetts Bay eelgrass [Chandler et al., 1996]. Wooden dowels (0.63 cm in diameter, 2.0 cm in height) were used to mimic the eelgrass stem. Model blades were cut from low-density polyethylene film ( rho _s = 920 kg m^-3, E = 3.0 × 10⁸ Pa) of thickness (t) 0.10 mm such that lambda _1,m = 0.055 s² m^-1. Because of a general absence of ordered arrays in eelgrass meadows [Fonseca, 1998] the 850 model plants were placed randomly in holes drilled into six 1.2-m-long, 38-cm-wide Plexiglas boards (total area of 2.7 m²).

[11] While matching of the blade height Reynolds number, Re_h (= Uh/v, where v is the kinematic viscosity of water), is desirable, it is difficult given the range of flow velocities and blade heights in the field. Using the depth-averaged current, Re_h,p varies between 0 and O(10⁵); the values of Re_h,m (1100–9400) are well within the observed field range. In the model the hydraulic radius Reynolds number of the open channel (Re_RH = UR_H/v) ranged between 840 (transitional) and 10,000 (fully turbulent). However, given that the flow is of a mixing layer type, with the large, coherent structures dominating momentum transport, the effects of Re_RH (which describes boundary layer flow) were expected to be insignificant. Importantly, the mixing layer structure and associated vortices were observed under all experimental conditions.

Citation: Ghisalberti, M., and H. M. Nepf, Mixing layers and coherent structures in vegetated aquatic flows, J. Geophys. Res., 107(C2), 10.1029/2001JC000871, 2002.