Supergranule aggregation for constant heat flux-driven turbulent convection. (arXiv:2010.13383v2 [physics.flu-dyn] UPDATED)
<a href="http://arxiv.org/find/physics/1/au:+Vieweg_P/0/1/0/all/0/1">Philipp P. Vieweg</a>, <a href="http://arxiv.org/find/physics/1/au:+Scheel_J/0/1/0/all/0/1">Janet D. Scheel</a>, <a href="http://arxiv.org/find/physics/1/au:+Schumacher_J/0/1/0/all/0/1">Jörg Schumacher</a>
Turbulent convection processes in nature are often found to be organized in a
hierarchy of plume structures and flow patterns. The gradual aggregation of
convection cells or granules to a supergranule which eventually fills the whole
horizontal layer is reported and analysed in spectral element direct numerical
simulations of three-dimensional turbulent Rayleigh-B'{e}nard convection at an
aspect ratio of $60$. The formation proceeds over a time span of more than
$10^4$ convective time units for the largest accessible Rayleigh number and
occurs only when the turbulence is driven by a constant heat flux which is
imposed at the bottom and top planes enclosing the convection layer. The
resulting gradual inverse cascade process is observed for both temperature
variance and turbulent kinetic energy. An additional analysis of the leading
Lyapunov vector field for the full turbulent flow trajectory in its
high-dimensional phase space demonstrates that turbulent flow modes at a
certain scale continue to give rise locally to modes with longer wavelength in
the turbulent case. As a consequence successively larger convection patterns
grow until the horizontal extension of the layer is reached. This instability
mechanism, which is known to exist near the onset of constant heat flux-driven
convection, is shown here to persist into the fully developed turbulent flow
regime thus connecting weakly nonlinear pattern formation with the one in fully
developed turbulence. We discuss possible implications of our study for
observed, but not yet consistently numerically reproducible, solar
supergranulation which could lead to improved simulation models of surface
convection in the Sun.
Turbulent convection processes in nature are often found to be organized in a
hierarchy of plume structures and flow patterns. The gradual aggregation of
convection cells or granules to a supergranule which eventually fills the whole
horizontal layer is reported and analysed in spectral element direct numerical
simulations of three-dimensional turbulent Rayleigh-B'{e}nard convection at an
aspect ratio of $60$. The formation proceeds over a time span of more than
$10^4$ convective time units for the largest accessible Rayleigh number and
occurs only when the turbulence is driven by a constant heat flux which is
imposed at the bottom and top planes enclosing the convection layer. The
resulting gradual inverse cascade process is observed for both temperature
variance and turbulent kinetic energy. An additional analysis of the leading
Lyapunov vector field for the full turbulent flow trajectory in its
high-dimensional phase space demonstrates that turbulent flow modes at a
certain scale continue to give rise locally to modes with longer wavelength in
the turbulent case. As a consequence successively larger convection patterns
grow until the horizontal extension of the layer is reached. This instability
mechanism, which is known to exist near the onset of constant heat flux-driven
convection, is shown here to persist into the fully developed turbulent flow
regime thus connecting weakly nonlinear pattern formation with the one in fully
developed turbulence. We discuss possible implications of our study for
observed, but not yet consistently numerically reproducible, solar
supergranulation which could lead to improved simulation models of surface
convection in the Sun.
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