An exponential-based model for predicting velocity fields in partially vegetated channels

ABSTRACT

A model based on the exponential function was proposed to predict the velocity fields in partially vegetated channels. Eleven groups of experimental data obtained from this study and the published literature were used to verify the model. The predicted lateral profiles of velocities at different longitudinal positions had good agreement with measurements over wide ranges of flow and vegetation conditions, indicating that the proposed model is capable of predicting the velocity fields in the complicated partially vegetated flows. Combining the proposed model with an existing model that predicts the critical velocity for initiating the resuspension of noncohesive sediment in vegetated regions defined the patch length that would be sufficient to promote sediment deposition within the patch interior. For a sparser patch or finer sediment, a longer patch is required to promote deposition and thus protect beds from erosion.

Keywords:

• Exponential-based model
• flow modification
• sediment deposition
• vegetated channels
• velocity prediction

Disclosure statement

No potential conflict of interest was reported by the authors.

Notation

a	=	frontal area per patch volume (cm–1)
b	=	patch half-width for the patch in the channel centre (cm)
$C_d$	=	drag coefficient (–)
$C_f$	=	bed friction coefficient (–)
d	=	vegetation stem diameter (cm)
$d_s$	=	sediment mean size (µm)
F	=	Froude number (–)
g	=	gravitational acceleration (m s–2)
h	=	flow depth (cm)
$L_{d\left(bare\right)}$	=	e-folding length scale for Ud in the bare channel (cm)
$L_{d\left(bare\right)}\left(y\right)$	=	local e-folding length scales at different y positions (cm)
$L_{d\left(veg\right)}$	=	e-folding length scale for Ud in the vegetated region (cm)
$L_{d\left(veg\right)}\left(y\right)$	=	local e-folding length scale at the y position (cm)
$L_I$	=	length of the interior flow adjustment region (cm)
$L_{min}$	=	minimum patch length to promote deposition (cm)
$M$	=	number of measured velocities (–)
$N$	=	the number of predictions and measurements (–)
$N_{\left(y\right)}$	=	number of measured $U_{d\left(y\right)}$ between $U_{y=b}$ and $U_{veg}$ in the vegetated region (–)
n	=	stem density per bed area (cm–2)
R	=	hydraulic radius (cm)
Re	=	channel Reynolds number (–)
Re(d)	=	stem Reynolds number (–)
$S$	=	water surface slope (–)
$U_0$	=	mean channel velocity (cm s–1)
$U_{bare}$	=	steady velocity in the bare channel (cm s–1)
$U_c$	=	critical velocity for sediment resuspension in the vegetated region (cm s–1)
$U_{c-bare}$	=	critical velocity for sediment resuspension in the bare channel (cm s–1)
Ud	=	depth-averaged velocity (cm s–1)
$U_{d\left(y\right)}$	=	measured velocity at the y position (cm s–1)
$U_{veg}$	=	steady velocity in the vegetated region (cm s–1)
$U_{veg\left(0\right)}$	=	velocity at the leading edge of the patch (cm s–1)
$U_{veg\left(f\right)}$	=	velocity in the fully developed flow region (cm s–1)
$U_{y=b}$	=	velocity at the side edge of the patch (cm s–1)
u	=	time-averaged velocity in longitudinal direction (cm s–1)
v	=	time-averaged velocity in lateral direction (cm s–1)
w	=	time-averaged velocity in vertical direction (cm s–1)
$X_p$	=	predicted velocity (cm s–1)
$X_m$	=	measured velocity (cm s–1)
$x$	=	longitudinal direction (–)
$y$	=	lateral direction (–)
$z$	=	vertical direction (–)
$\gamma$	=	scale constant (–)
$\mathrm{\Delta }{U}_d$	=	velocity change (cm)
${\delta }_m$	=	width of the mixing layer (cm)
${\delta }_{m\left(eq\right)}$	=	width of the mixing layer in the fully developed flow region (cm)
${\delta }_p$	=	penetration distance (cm)
$\nu$	=	water kinematic viscosity (cm2 s–1)
$\rho$	=	water density (g cm–3)
${\rho }_s$	=	sediment density (g cm–3)
${\tau }_{\ast c}$	=	critical Shields parameter (–)
$\varphi$	=	solid volume fraction (–)
$\omega$	=	a parameter ($\omega =0.20\pm 0.01$, Soulsby, 1981) (–)

Additional information

Funding

This study received financial support from the National Natural Science Foundation of China [nos. 52022063 and 52179074], and the Sichuan Science and Technology Program [2021YFH0028].