Wave damping by flexible marsh plants influenced by current

This study considered how the presence of current impacted wave dissipation within a meadow of flexible marsh plants. A wave-damping model was developed from a prediction of current- and wave-induced force on individual plants. The model was validated with laboratory experiments. Wave decay was measured over a meadow of flexible model plants geometrically similar to Spartina alterniflora with and without a following current. Consistent with previous observations, the wave energy dissipation depended on the ratio of current velocity ($U_c$) to wave velocity ($U_w$). Compared to the same pure wave condition, wave energy dissipation was enhanced by large $U_c/U_w$ but can be decreased for small $U_c/U_w$. Once validated, the wave-damping model was used to explore a wider range of wave, current, and meadow conditions in order to illustrate the influence of reconfiguration on wave forces; the impact of current on wave group velocity; and the modification of in-canopy time-mean and wave orbital velocity associated with canopy drag.

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Figure 1

Light and dark green plants represent positions at trough and crest, respectively. Due to canopy resistance, in-canopy time-mean current (${\alpha }_c{U}_c$) and wave orbital velocity (${\alpha }_w{U}_w$) are reduced compared to imposed current ($U_c$, defined over $h$) and wave orbital velocity $[U_w$, defined over the erect plant height $h_p$, Eq. (7)]. The reduction in canopy height ($h_d)$ due to reconfiguration feeds back to ${\alpha }_c{U}_c$ and ${\alpha }_w{U}_w$ by changing the in-canopy solid volume fraction and plant force per unit volume of in-canopy fluid.

Figure 2

(a) Model Spartina alterniflora. (b) Arrangement of plants (filled circles) within the staggered baseboard holes (open circles). Red plus signs are the locations of velocity profiles inside the meadow.

Figure 3

Schematic of experiment setup, not to scale. The wave paddle and current inlet are located at the left and the beach to the right. Free-surface displacement was simultaneously measured at a fixed position (wave gage 1) and multiple positions along the meadow (wave gage 2). A Nortek Vectrino+ measured velocity profiles 2 m upstream of the meadow (P1) and one wavelength into meadow (P2).

Figure 4

Measured wave amplitude (symbols) starting from meadow leading edge ($x=0$) and Eq. (17) (curves) for W6 (pure wave), W6C1 (wave 6+current 1), and W6C2 (wave 6+current 2). Based on fitted Eq. (17), $K_D=1.24\pm 0.05$, $1.51\pm 0.08$, and $1.52\pm 0.11{\mathrm{m}}^{–2}$ with 95% CI, respectively.

Figure 5

The measured velocity for (a) pure current (C2, $U_c=7.8$ cm/s), (b) pure wave ($a_w=2.2$ cm), and (c) combined current and waves ($U_c=7.8\mathrm{cm}/\mathrm{s}$, $a_w=2.2$ cm), with each column a different water depth, $h=18$, 27, and 40 cm from left to right. The corresponding case names were shown on the top right of each subplot. Black symbols denote profile P1 (2 m in front of the meadow) and red symbols denote the average of five measurements at P2 [Fig. 2], with horizontal bar indicating standard deviation of the five values. Circles are time-mean velocity. Squares and diamonds denote maximum and minimum velocity over the wave period, when waves were present. The horizontal solid and dashed lines indicate erect stem height and full plant height, $h_p$. For the cases considered, the deflected canopy height $h_d\approx h_p$.

Figure 6

(a) The ratio of wave decay coefficient in combined currents and waves,$K_D$, to that in pure waves, $K_{D,pw}$ plotted against $U_c/U_w$. (b) The predicted vs the measured wave decay coefficient $K_D$. Measured error indicates 95% CI for fitting method [Eq. (17)]. Predictions were estimated to have 20% uncertainty. The vertical line separates the submerged (left) to near-emergent and emergent conditions (right).

Figure 7

Wave decay coefficient $K_D$ vs velocity ratio for a meadow of rigid stems ($l_s=0.6$ m, $D=5$ mm, and $N_s=280$ $\mathrm{stems}/{\mathrm{m}}^2$, $h=1$ m, $a_w=0.1$ m, and $T_w=2$ s). The different curves (see legend) consider different mechanisms that influence wave dissipation.

Figure 8

Wave decay coefficient vs velocity ratio for (a) meadow of stems with different stem rigidity, and (b) plants with and without leaves. $N_s=280$ $\mathrm{stems}/{\mathrm{m}}^2$, $l_s=0.6$ m, and $D=5$ mm with elastic modulus given in legend. Wave conditions were constant ($h=1$ m, $a_w=0.1$ m, and $T_w=2$ s). Full plants have $N_l=10$ leaves each $l_l=0$.3 m long, $b=10$ mm width, and, $d=0$.3 mm thick.