Drag coefficient and flow structure downstream of mangrove root-type models through PIV and direct force measurements

Mangrove trees form dense networks of prop roots in coastal intertidal zones. The interaction of mangroves with tidal and river flows is fundamental to the preservation of estuaries and shorelines by providing water filtration, protection against erosion, and habitat for aquatic animals. The impact of mangrove roots on unidirectional flows is mainly characterized by hydrodynamics including drag, flow structures, transport, and fluid-structure interaction. In this work, we focus on the drag coefficient and flow structure downstream of simplified mangrove root models. The mangrove roots were modeled as a cluster of uniformly distributed rigid circular cylinders (patch), with a frontal area per unit volume $\left(a\right)$. Direct force measurements were made in a recirculating water flume. In addition, the unsteady wake was measured using particle image velocimetry (PIV). The models were tested for a Reynolds number range of 600 to 12 000 based on the patch diameter $\left(\mathrm{R}{\mathrm{e}}_D=\frac{\rho UD}{\mu }\right)$, in order to resemble natural conditions. A new length scale, the “effective diameter,” is proposed by comparing the Strouhal number of the patches with the analytical Strouhal number of a canonical cylinder in the flow field that produces the same vortex shedding. We compared different length scales to characterize the hydrodynamics, including the patch diameter $\left(D\right)$, equivalent length proposed by Mazda $\left(L_E\right)$, and an effective diameter $D_{\mathrm{eff}}$. A universal empirical curve describing the drag coefficient based on $\left(L_E\right)$ and $D_{\mathrm{eff}}$ is also presented. It was found that the effective diameter was able to capture competing parameters including patch diameter, porosity, and cylinder diameters into a single parameter to obtain the drag coefficient of the physical models. The results revealed that the time-average drag coefficient decreased with an increased Reynolds number and porosity. It was found that the ratio of $\frac{C_D}{\mathrm{St}}$ to the blockage parameter $(C_{D}aD)$ exhibits a linear relationship, indicating that the parameter $\mathrm{St}aD$ is constant for all patches considered. This finding was also valid using equivalent length and effective diameter as the characteristic lengths. In addition, based on time-resolved PIV results downstream of the physical model, we found that the vorticity magnitude decays and the vortex structure is more streamlined with an increase in porosity. This analysis of the hydrodynamics of mangrove rootlike models can also be extended to predict values of drag coefficient in other canopy flows, including submerged arrays, flexible elements, and bio-inspired coastal infrastructures.

Figure 1

Prop roots of red mangroves (Rhizophora mangle). Mangrove roots involve a complex system, comprising intricate, long tidal creeks, and surrounding mangrove swamps which form heavily vegetated floodplains. The roots buffer against damage to coastal communities and provide services such as nursery areas for fish production, biodiversity, and carbon sequestration. Scales in the figures are approximate values.

Figure 2

Schematic of the flow field (a) and physical models (b), (c). (a) Sketch of the mean flow structure around a circular patch of the cylinders. The flow patterns are characterized by the formation of the symmetrical steady wake region in the near wake. The length of the steady wake, ${\mathit{L}}_1$, is measured from the back of the cylinder in the streamwise direction. Wavelength of the vortex shedding (λ), defined as the distance between two sequences of vortex shedding (b) Patch configuration for cases 1–3. (c) Patch configuration for cases 4–7.

Figure 3

Schematic of experimental setup and field of view (FOV) located in the middepth. Isometric view of the experimental setup (a) picture of one physical model (b) top view of the experimental loadcell (c). The closed-loop water tunnel cross section is 25 cm × 25 cm with the blockage ratio of 10%. The setup includes a recirculating flume, an air-bearing system to mount the models, a load cell, a high-speed camera, and a laser to perform PIV measurements. A 45° mirror was used to have a bottom-up view of the flow field. The velocities in the streamwise and spanwise directions are denoted by $u$ and $v$, respectively.

Figure 4

(a) Drag force measured on the entire patch with respect to the upstream velocity. (b) Variation of Strouhal number, based on patch diameter versus Reynolds number. Strouhal number increases by porosity growth. (c) Strouhal number increases with $\frac{1}{aD}$ for different Reynolds numbers. (d) Effective diameter normalized by patch diameter as a function of Reynolds number.

Figure 5

Time-average flow fields for different porosities. Left column: case 1, ${\phi }_1=47\%$; middle column: case 2, ${\phi }_2=70\%$ and right column: case 3, ${\phi }_3=86\%$. (a)–(c) Streamwise velocity; (d)–(f) contour of vorticity; (g)–(i) contour of Reynolds stress; (j)–(l) contour of turbulence intensity (TI). All results are at Re = 3000 with time step $\mathrm{\Delta }t=0.008\mathrm{s}$ and $T=0.568$ s.

Figure 6

The instantaneous $z$-vorticity field for Re = 3000 and $\phi =47\%$ at different time instants. $T=0.568$ s is the time of one vortex shedding period. The features of time-resolved vorticity field indicate that the von Kármán vortex street behind the porous patch has a shorter period time compared to a canonical cylinder $(T=1.2$ s).

Figure 7

The effect of porosity of patch on the time-resolved vorticity field. The panels compare the vertical vorticity magnitude behind the patch for $\phi =47\%,\phi =70\%$, and $\phi =86\%$ at the vortex shedding period $(T=0.568$ s) for Re = 3000. The vortices in the separated shear layers at $\phi =47\%$ create coherent vortex structure. The steady wake length $L_1$, is defined as the streamwise distance from the back of patch to minimum velocity point. Greater porosity increases $L_1$ and λ (detached vortex wavelength).

Figure 8

Total drag coefficient as a function of Reynolds number based on patch diameter (a), equivalent length $L_E$ (b), and effective diameter (c). Vertical bars show the 95% confidence interval. (d), (e), (f): Blockage ratio $\left(C_{D}aD\right)$ vs energy released per vortex shedding based on patch diameter (d), equivalent length (e), and effective diameter (f).

Figure 9

Longitudinal (a) and cross-sectional (b) time-averaged $x$-velocity profiles for cases 1–3. Longitudinal (c) and cross-sectional (d) time-averaged $z$-vorticity profiles for cases 1–3. Panels show the comparison between different porosities. The vorticity magnitude decays with porosity increase. Dotted lines represent the line of measurement with the line origin (dark dot).

Figure 10

Drag coefficient with respect to porosity based on force measurement (diamond), flow measurements (square) and empirical fit from Eq. (19) (star). Vertical bar shows 95% confidence interval. The values are for $\mathrm{R}{\mathrm{e}}_D=3000$ and cases 1–3. Vertical bar shows 95% confidence interval.