Dynamics of line plumes on horizontal surfaces in turbulent convection

Abstract

We study the dynamics of line plumes on the bottom plate in turbulent convection over six decades of Rayleigh number $(10^5<Ra_w<10^{11})$ and two decades of Prandtl number $(0.7<Pr<600)$. We qualitatively identify the main dynamics as motion along the plumes, lateral merging of the plumes and initiation of the plumes; various other minor types of motion also occur along with these main dynamics. The mean velocity along the length of the plumes scales as the large scale flow velocity, with the fraction of the length of the plumes affected by shear increasing with $Ra_w$ as $L_{ps}/L_p\sim Ra_w^{0.04} Pr^{-0.1}$. In agreement with \cite{how}, the mean time of initiation of the plumes $\bar{t^*}$, scales as the diffusive time scale near the plate, $Z_w^2/\alpha$, where $Z_w$ is the appropriate length scale near the plate. The fraction of the length of the plumes that undergoes merging decreases with increase in $Ra_w$ as, $L_{pm}/L_p \sim Ra_w^{-0.04} Pr^{0.1}$. The plumes merge with a constant velocity during their merging cycle, however, the values of these constant velocities depend on the location and the time of measurement. The merging velocities at all $Ra_w$ and $Pr$ have a common lognormal distribution, but their mean and variance increased with increasing $Ra_w$ and decreasing $Pr$. $\bar{V_m}$, which are an order lower than the large scale velocities, scale as the average entrainment velocity at the sides of the plumes. This implies that $\bar{V_m}$ scales as the velocity scale near the plate $\nu/Z_w$. $Re_H$, the Reynolds number interms of $\bar{V_m}$ and the layer height $H$ scales as $Ra^{1/3}$, in the same way as the Nusselt number $Nu$; therefore $Re_{H}\sim Nu$. These relations imply that $Re_w=\bar{V_m}Z_w/\nu$ the Reynolds number near the plate is an invariant for a given fluid in turbulent convection.Comment: 36 pages, submitted to Journal of Fluid Mechanic

Turbulent Rayleigh–Bénard convection in spherical shells

“…The predicted average interplume area is in good agreement with the peaks of the statistical distributions for the three cases discussed here. The expression (3.15) therefore provides a reasonable estimate of the average plume separation (Puthenveettil & Arakeri 2005;Puthenveettil et al 2011;Gunasegarane & Puthenveettil 2014). The comparable observed plume density at both thermal boundary layers thus yields…”

Role of critical points of the skin friction field in formation of plumes in thermal convection

“…They are formed in the vicinity of the heated (cooled) plate, then rise (fall) into the bulk of the turbulent convection layer and provide the major contribution to the near-wall turbulent heat transfer and its local fluctuations. Their dynamics and size have been studied, for example, in experiments [15][16][17] and direct numerical simulations [18][19][20][21]. Here, we will describe the formation of thermal plumes by the vertical temperature derivatives in connection to the two-dimensional velocity gradient vector field directly at the heated (cooled) plate.…”

Scaling in concentration-driven convection boundary layers with transpiration

“…given by Gunasegarane & Puthenveettil (2014). The corresponding large-scale flow velocity is U LS = 0.42 cm s −1 .…”

“…The light green lines in the image are the line plumes created by the instability of the natural convection boundary layers in between these plumes, which are subjected to a transpiration through the membrane. In addition to the fact that the boundary layer lengths are spatially random, the flow induced by these plumes causes these plumes to keep merging (Gunasegarane & Puthenveettil 2014) so that the random pattern in figure 6( a ) keeps evolving spatially and temporally with time. These boundary layers then form and are destroyed by the plume motion at various random locations and at various temporal instants above a horizontal porous surface.…”

“…Using (2.21) and since , the Rayleigh number based on the boundary layer length in the transpiration case is The near-wall Rayleigh number based on the width of the fluid layer, cm, is then Here, is chosen to be the width of the tank in the present experiments (see § 4.1). The large-scale flow Reynolds number corresponding to this is calculated using given by Gunasegarane & Puthenveettil (2014). The corresponding large-scale flow velocity is .…”