Interaction of a buoyant plume with a turbulent canopy mixing layer

This study aims to understand the impact of instabilities and turbulence arising from canopy mixing layers on wind-driven wildfire spread. Using an experimental flume (water) setup with model vegetation canopy and thermally buoyant plumes, we study the influence of canopy-induced shear and turbulence on the behavior of buoyant plume trajectories. Using the length of the canopy upstream of the plume source to vary the strength of the canopy turbulence, we observed behaviors of the plume trajectory under varying turbulence yet constant cross-flow conditions. Results indicate that increasing canopy turbulence corresponds to increased strength of vertical oscillatory motion and variability in the plume trajectory/position. Furthermore, we find that the canopy coherent structures characterized at the plume source set the intensity and frequency at which the plume oscillates. These perturbations then move longitudinally along the length of the plume at the speed of the free stream velocity. However, the buoyancy developed by the plume can resist this impact of the canopy structures. Due to these competing effects, the oscillatory behavior of plumes in canopy systems is observed more significantly in systems where the canopy turbulence is dominant. These effects also have an influence on the mixing and entrainment of the plumes. We offer scaling analyses to find flow regimes in which canopy induced turbulence would be relevant in plume dynamics.

Figure 1

Visual representation of a canopy mixing layer developing over a forest canopy. The buoyant plume is introduced at some distance along the canopy and interacts with the Kelvin Helmholtz rollers.

Figure 2

Diagrams of experimental setup. (a) Side-view of the experimental setup. The flow going from left to right has a free-stream flow speed ($U_{\infty }$) corresponding to either Flow A or B. On interacting with the canopy, the flow develops an overflow ($U_2$), through-flow ($U_1$), and shear layer with a inflection point slightly above the canopy height, $h_c$. The plume setup, as shown, has PVC piping with fixed flow rate $Q_0$. This pvc piping leads to a plume release mechanism at the canopy height. The distance from the leading edge of the canopy to this release point is given by $X_p$, while the length of the whole canopy is $L_c$. The temperature of the plume is $T_p$ (a function of $x$ and $z$), while the ambient is $T_a$. The trajectory of the plume is given by the distance from the canopy height to the centerline of the plume, $\mu \left(x_{\mathrm{dp}}\right)$, and the upper edge, $z_{\mathrm{pt}}\left(x_{\mathrm{dp}}\right)$. The vertical length of the plume is given by $R\left(x_{\mathrm{dp}}\right)$. (b) Plan-view of plume release. $y_p$ is the distance from the flume wall, which is equidistant in either spanwise direction. $d_p$ is the diameter of the plume diffuser. (c) Diagram of the synthetic Schlieren setup. A dotted pattern is placed in the background with LED lighting, so that the camera can track distortions caused by the plume's density gradients.

Figure 3

Schlieren methodology: (a) Raw image of plume release with heated plume in front of dot pattern. (b) Schlieren image with background subtraction, and outline of centerline, $\mu$, and plume top, $z_{\mathrm{pt}}$ in blue and red, respectively. The $z$ axis, $z$, is in cm above the canopy top.

Figure 4

Mean velocity [(a) and (c)] and Reynolds stress profiles [(b) and (d)] for both flow cases, measured above the canopy height. As on legend, each shape corresponds to distance from the leading edge of the canopy (in cm).

Figure 5

Time mean trajectory for various experimental cases. The $x$ axis represents the streamwise distance from the plume outlet ($x_{\mathrm{dp}}$) while the $z$ axis represents the plume position (cm above canopy top). [(a) and (b)] The position of the centerline, $\mu$, and [(c) and (d)] the plume-top $z_{\mathrm{pt}}$. The left and right columns are for cases with source plume temperature of $\mathrm{\Delta }T={10}^{\circ }$ and $50{}^{\circ }\mathrm{C}$, respectively. The solid lines correspond to Flow A cases while the dotted lines correspond to Flow B cases. The colors correspond to different turbulent conditions ($X_p$). Uncertainty: Below the plots, we provide the average uncertainty for each experimental case, as observed for the trajectories at $x_{\mathrm{dp}}$ of 20, 40, and 60 cm. The Flow A cases are in solid lines while the Flow B cases are given by the dotted lines. Each color corresponds to the different $X_p$ cases as in the legend.

Figure 6

Instantaneous plume trajectory centerlines $\mu$ for different cases over 45 s. The color bar ranging from light blue to dark purple corresponds to seconds, from 0 to 45 s. All cases plotted are for $\mathrm{\Delta }T=50{}^{\circ }\mathrm{C}$ source plumes. Panels (a) and (b) compare the $X_p$ = 0.3 m case to the 1.2-m case for Flow A (A03dT50 to A12dT50). Panels (c) and (d) repeat it for the Flow B case (B03dT50 to B12dT50). The units of the colorbar are in seconds. Although not plotted, uncertainty in these instantaneous realizations of the plume trajectory is at maximum around 3 cm.

Figure 7

Plume height variability ($s_{\mu }$) against normalized friction velocity ($u_{*}$). The friction velocity is normalized by the maximal friction velocity observed for each flow rate (which is the $u_{*}$ measured at $x=120$ cm). The plotted variability is observed at $x_{\mathrm{dp}}=11$ cm or 11 cm downstream from the plume release. Panels (a) and (b) plot correspond to Flow A and B, respectively. Each symbol corresponds to different source temperature in $\mathrm{\Delta }T$.

Figure 8

Probability density function of the time record of plume heights $\left[\mu \right(x_{\mathrm{dp}}=32.4$ cm)] for various flow and turbulence cases. The left and right plots correspond to Flow A and B, respectively. The blue and orange bars correspond to $X_p$ = 0.3 and 1.2 m, respectively.

Figure 9

Spectra for the time records of $\mu$ fluctuations, ${\varphi }_{\mu }\left(f\right)$, and for vertical velocity fluctuations, ${\varphi }_{ww}\left(f\right)$. The spectral calculation for $\mu$ uses the deviation from the mean, $\mu -\overline{\mu }$. The left [(a) and (c)] and right [(b) and (d)] columns correspond to Flow A and B, respectively. The top row plots the spectra measured for $\mu (x_{\mathrm{dp}}=32.4$ cm) for varying $X_p$ conditions, in a log-log plot. For all cases, the source plume is characterized by $\mathrm{\Delta }T=50{}^{\circ }\mathrm{C}$. The bottom row plots the vertical velocity spectra, also measured at various $X_p$ locations in a log-linear plot, as shown on the legend in plot (a). The velocity spectra for $X_p$ = 0.3 m (blue line) is omitted because no peak is observable.

Figure 10

(a) An example of the plume and its outline ($z_{\mathrm{pt}}$ at an instant in time when the trajectory is strongly distorted. This snapshot is from the B12dT50 experimental case. (b) Time record of $\mu$ over 70 s for various streamwise location ranging from $x_{\mathrm{dp}}=$ 0 to 66 cm. The units for the legend are in cm. Local maximum data points are marked with black dot symbols.

Figure 11

(a) A contour of the plume-top position normalized by mean height, $(z_{\mathrm{pt}}-\overline{z_{\mathrm{pt}}})/\overline{z_{\mathrm{pt}}}$ in the $x\text{−}t$ plane. The red corresponds to local max while blue corresponds to local min. (b) Plot comparing the plume feature propagation velocity, $U_{\mathrm{pl}}$ to the free stream velocity, $U_{\infty }$. The extracted values of $U_{\mathrm{pl}}$ are for $X_p=$ 0.3, 0.9, 1.2 m cases. The cluster of point on the lower end is for Flow A, and those on the higher end are for Flow B. Each symbol color corresponds to different $\mathrm{\Delta }T$ cases, while the star and square symbols correspond to values are for tracked troughs and peaks, respectively. The black dotted line provided is a 1:1 plot.

Figure 12

Variations in plume variability $s_{\mu }$ with source plume temperature for each Flow A and B cases. Each plot provides the values of $s_{\mu }$ measured at $x_{\mathrm{dp}}$ = 32.4 cm for different $\mathrm{\Delta }T$ and $X_p$ as shown in legend.

Figure 13

(a) Entrainment coefficient, $\beta$ versus the friction velocity, $u_{*}$. (b) Entrainment coefficient versus the variability, $s_{\mu }/\overline{Z}$. Each marker color corresponds to different source plume temperature as found on the legend.

Figure 14

(a) Plot of $s_{\mu }/\overline{Z}$ averaged over $z_{\mathrm{dp}}=$ 32 to 36 cm against nondimensional quantity $N_c=2B_R/\left(U_{\infty }^3\right)$. Black and red symbols correspond to Flow A and B. Each symbol shape correspond to different source temperature, as on legend. (b) Same plot repeated for the altered power comparison, $B_R/u_{*}^3$. The blue line provides a power-law fit of $s_{\mu }/\overline{Z}=a*{(B_R/u_{*}^3)}^b$ for which $a=0.55$ and $b=-0.22$. The fit gives an $R^2$ value of 0.75. The dotted lines are for $a$ values within 95% confidence interval.

Figure 15

Bulk Richardson scaling against $s_{\mu }$ and $\beta$. The black markers correspond to Flow A while the red markers correspond to Flow B. Each marker symbol corresponds to different $X_p$, as in the legend. We have omitted outlier data points from cases A06dT30, A06dT50, A09dT50, and B12dT30.

Figure 16

Plots of plume radius, $R\left(x\right)$, vs the plume height givendefined by the centerline, $\mu$. All of the provided plots are for experimental cases with $\mathrm{\Delta }T=50{}^{\circ }\mathrm{C}$ and cross-flow setting of Flow A. Each subplot corresponds to different $X_p$ conditions as denoted in the title. The black dashed lines are linear fits to the data points.

Figure 17

(a) Example of $w_{\mathrm{eff}}$ extraction. A linear fit is provided in red, to the time mean trajectory, $\mu \left(x_{\mathrm{dp}}\right)$, for the A03dT50 case. (b) The extracted $w_{\mathrm{eff}}$ plotted for both Flow A and B (as on legend) across different $\mathrm{\Delta }T$. The values for extracted for experimental cases of $X_p$ = 0.3 m. Other $X_p$ have similar effective velocities because mean trajectory are similar as shown on Fig. 5.