Localized Transverse Bursts in Inclined Layer Convection

We investigate a novel bursting state in inclined layer thermal convection in which convection rolls exhibit intermittent, localized, transverse bursts. With increasing temperature difference, the bursts increase in duration and number while exhibiting a characteristic wave number, magnitude, and size. We propose a mechanism which describes the duration of the observed bursting intervals and compare our results to bursting processes in other systems.

Figure 1

(a)–(d) Sequence of background-divided shadowgraph images and associated contrast-enhanced power spectra for cell 1 at $\theta =78°$ and $ϵ=0.08$: (a) quiescent, (b) modulations during early bursting, (c) developed bursting, and (d) end of burstlet. Times correspond to points marked in Fig. 3. Uphill direction is at left. (e) Disordered bursting at $\theta =78°$ and $ϵ=0.09$. Also see movies in [11]. (f) Magnified power spectrum showing three primary modes.

Figure 2

Phase diagram near the codimension-two point. Stability curves are from [13]; solid lines are primary instabilities and dashed lines are extensions. Shaded area corresponds to region of data collection.

Figure 3

(a) Sample segment of $S_q(t)$, $S_{pq}(t)$, and $S_p(t)$ at $ϵ=0.08$ and $\theta =78°$ in cell 1. Gray bars indicated bursting; time intervals $T_B$, $T_Q$, and ${\tau }_b$ defined in text. Labeled black dots correspond to the images in Fig. 1. (b) Ensemble average $⟨S(t-t_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}})⟩$ over all bursts where $t_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{t}}$ is the rising edge of $S_{pq}$ for each burst. Power is in same arbitrary units for both figures.

Figure 4

Wave number of transverse bursts $p$ (determined from power spectra) as a function of $\theta$, $ϵ$, and cell length $L$. In each graph the wave number is plotted against the given variable, and averaged over the other two. Dashed lines are $p_c/2$ for $p_c=(2.82\pm 0.04)d$ at $ϵ=0$ (onset) and $\theta =80°$ (weak dependence on $\theta$).

Figure 5

Burst width ($\widehat{\mathbf{x}}$, gray) and length ($\widehat{\mathbf{y}}$, black) directions: (a) vs cell width $L$ at onset of bursting for $\theta =78°$, (b) vs $\theta$ at onset of bursting in cell 2, and (c) vs $ϵ$ in cell 2 at $\theta =78°$.

Figure 6

(a),(b),(c) Sample PDFs of $T_Q$, ${\tau }_b$, and $N$, respectively, at $ϵ=0.08$ and $\theta =78°$. (b) Dashed line is exponential distribution fit to data excluding the first bin. (c) Dashed line is Eq. (3) plotted from the measured mean. (d) Mean quiescent period as a function of $ϵ$ at $\theta =78°$. (e) Effective (from fit) mean burstlet period and (f) mean number of burstlets and mean bursting interval as a function of $ϵ$ at $\theta =78°$.