Confined Rayleigh-Bénard, Rotating Rayleigh-Bénard, and Double Diffusive Convection: A Unifying View on Turbulent Transport Enhancement through Coherent Structure Manipulation

Many natural and engineering systems are simultaneously subjected to a driving force and a stabilizing force. The interplay between the two forces, especially for highly nonlinear systems such as fluid flow, often results in surprising features. Here we reveal such features in three different types of Rayleigh-Bénard (RB) convection, i.e., buoyancy-driven flow with the fluid density being affected by a scalar field. In the three cases different stabilizing forces are considered, namely (i) horizontal confinement, (ii) rotation around a vertical axis, and (iii) a second stabilizing scalar field. Despite the very different nature of the stabilizing forces and the corresponding equations of motion, at moderate strength we counterintuitively but consistently observe an enhancement in the flux, even though the flow motion is weaker than the original RB flow. The flux enhancement occurs in an intermediate regime in which the stabilizing force is strong enough to alter the flow structures in the bulk to a more organized morphology, yet not too strong to severely suppress the flow motions. Near the optimal transport enhancements all three systems exhibit a transition from a state in which the thermal boundary layer (BL) is nested inside the momentum BL to the one with the thermal BL being thicker than the momentum BL. The observed optimal transport enhancement is explained through an optimal coupling between the suction of hot or fresh fluid and the corresponding scalar fluctuations.

Figure 1

Nusselt number $Nu$ or $N{u}_S$ and Reynolds number Re versus ${\mathrm{\Gamma }}_{\text{opt}}/\mathrm{\Gamma }$ for CRB in (a) and (d), ${\mathrm{Ro}}_{\text{opt}}/\mathrm{Ro}$ for RRB in (b) and (e) and $\mathrm{\Lambda }/{\mathrm{\Lambda }}_{\text{opt}}$ for DDC in (c) and (f). Both quantities are normalized by the value obtained from cases $1/\mathrm{\Gamma }=1$, $1/\mathrm{Ro}=0$, or $\mathrm{\Lambda }=0$ (represented by $N{u}_0$ and ${\mathrm{Re}}_0$ in CRB and RRB and by $N{u}_S^{RB}$ and ${\mathrm{Re}}^{RB}$ in DDC).

Figure 2

Instantaneous scalar fields for the three systems (a) $1/\mathrm{\Gamma }=2$, (b) $1/\mathrm{Ro}=1$, (c) $\mathrm{\Lambda }=0.01$, (d) $1/\mathrm{\Gamma }=10$, (e) $1/\mathrm{Ro}=7$, and (f) $\mathrm{\Lambda }=4$ (all at $\mathrm{Ra}=10^8$). The scalar fields are taken at the middle vertical plane and it is midway along the confinement direction in CRB. Here the reddish (bluish) color represents the hot (cold) fluid in CRB and RRB, and the fresher and saltier fluid in DDC. Note that in RRB and DDC, only part of the periodic domain is shown here. Plume coverage $A_{\mathrm{pl}}/A$ evaluated at the edge of the thermal or salinity BL versus (g) ${\mathrm{\Gamma }}_{\text{opt}}/\mathrm{\Gamma }$, (h) ${\mathrm{Ro}}_{\text{opt}}/\mathrm{Ro}$, and (i) $\mathrm{\Lambda }/{\mathrm{\Lambda }}_{\text{opt}}$ where $A_{\mathrm{pl}}$ is the area covered by cold or saline fluid and $A$ is the total area (see Supplemental Material [41] for the details). Here black (red) dashed lines indicate the cases shown in the top (middle) panel.

Figure 3

Ratio of the thermal or salinity boundary layer thickness over momentum one versus (a) ${\mathrm{\Gamma }}_{\text{opt}}/\mathrm{\Gamma }$, (b) ${\mathrm{Ro}}_{\text{opt}}/\mathrm{Ro}$, and (c) $\mathrm{\Lambda }/{\mathrm{\Lambda }}_{\text{opt}}$. Plume coverage $A_{\mathrm{pl}}/A$ versus the relative thickness ${\lambda }_T/{\lambda }_p$ for CRB in (d) and RRB in (e), ${\lambda }_S/{\lambda }_p$ for DDC in (f). Normalized temperature or salinity standard deviation at the edge of momentum boundary layer versus the relative thickness in (g)–(i).