Abstract
Abstract
Highlights
Thermal convection refers to fluid flows that are driven by buoyancy forces due to density variations, which in turn are caused by gradients in temperature (Chandrasekhar 2013)
In addition to considering the bulk heat transport, we studied the behaviour of the bulk Reynolds number (Re) with Ra and p to further characterize the response of the flow
We have systematically studied turbulent thermal convection in two-dimensional domains with a fractal upper boundary for Ra ∈ [107, 1010] using the lattice
Summary
Thermal convection refers to fluid flows that are driven by buoyancy forces due to density variations, which in turn are caused by gradients in temperature (Chandrasekhar 2013). If one assumes that the dimensional heat flux becomes independent of the molecular properties of the fluid when Ra → ∞, one obtains Nu ∼ (Pr Ra)1/2 This ‘mixing length’ theory is originally due to Spiegel (1963) and such scaling behaviour – with possible logarithmic corrections (Kraichnan 1962; Chavanne et al 1997) – is often referred to as the ultimate regime of thermal convection. As emphasized by Toppaladoddi et al (2017), when a given experiment or simulation has a fixed roughness geometry, the boundary-layer core flow interaction may evolve as the Rayleigh number increases. It is for this reason that surfaces with a spectrum of roughness length scales are of interest. The choice of the domain and roughness properties is motivated by our aim to understand the interactions between rough Arctic sea ice and the underlying ocean
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