We study the flow topology dynamics in terms of the paramount nonlinearities of enstrophy and strain production at hard turbulent regimes of Rayleigh-Bénard convection (RBC). To do so, a data set of direct numerical simulations for air turbulent RBC at Rayleigh numbers $\text{Ra}=\{{10}^8,{10}^{10},{10}^{11}\}$ is analyzed. Considering the bulk dynamics therein, the classical two-dimensional mean Lagrangian evolution of $Q_{\mathsf{G}}$ and $R_{\mathsf{G}}$ invariants of $\mathsf{G}\equiv \mathbf{\nabla }\mathit{u}$ is extended to three dimensions by decomposing $R_{\mathsf{G}}$ into two parts: the strain production $R_{\mathsf{S}}$ and the enstrophy production $\text{tr}\left({\mathrm{\Omega }}^2\mathsf{S}\right)$. In this way, the three-dimensional phase space $(Q_{\mathsf{G}},R_{\mathsf{S}},\text{tr}\left({\mathrm{\Omega }}^2\mathsf{S}\right))$ allows us to identify separately the nonlinear straining and rotational mechanisms in turbulence. The main resultant observations attest that, when the turbulent regime is notably hard, a rising local self-amplification of the velocity gradient takes place in strain-dominated areas. This process is strongly aided by vortex contraction. Concomitantly, a pronounced increase in the linear contributions of vortex stretching is also identified, particularly relevant to strain-dominated slots.

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• Boundary layers
• Flow boundary instabilities
• Rayleigh-Bénard convection
• Thin fluid films
• Turbulence