In the last decades the urban population has increased a lot making cities objects of different studies. In this context, urban climate is an expanding research field and understanding the main features of the urban heat island (UHI) effect is one of the challenges. A discrete number of neighbourhoods has been object of study for this climate effect with growing interest in recent years, especially focusing on heat mitigation. Despite this, there is a lack of knowledge due to the complex nature of the problem given by the multi-physics involved, the multiple parameters that govern it and above all, the complexity of the city’s geometries that lack generality. In this respect, and to keep results applicable in a broader context, this work proposes an innovative approach to studying UHI effects, providing a unique framework for understanding the interaction between urban geometry and heat transport dynamics while addressing the complexities of urban configurations with a novel and methodological perspective.

Direct numerical simulations of channel flow and temporal boundary layer at a Reynolds number Reτ=1500 are used to assess the scale-by-scale mechanisms of wall turbulence. From the peak of turbulence production embedded at the small scales of the near-wall region, spatially ascending reverse cascades are generated that move through self-similar eddies growing in size with the wall distance. These fluxes are followed by spatially ascending forward cascades through detached eddies thus reaching sufficiently small scales where eventually scale energy is dissipated. This phenomenology is shared by both boundary layer and channel flow and is recognized as a robust physical feature characterizing wall turbulence in general. Specific features related to the flow configuration are indeed identified in the outer region. In particular, the central region of channels is characterized by a generalized Richardson energy cascade where large scales are in equilibrium with small scales at different wall distances through a combined forward cascade and spatial flux. On the contrary, the interface region of boundary layers is characterized by an almost two-dimensional physics where spatially ascending reverse cascades sustain long and wide interface structures with a forward cascade that survives only in the wall-normal scales. The overall scenario consists in a variety of scale motions that while protruding from the turbulent core towards the external region, squeeze at the interface thus sustaining vertical shear in a thin layer. The observed multidimensional physics sheds light on the complex interactions between outer entrainment and near-wall self-sustaining mechanisms with possible repercussions for theories.

The geometrically complex mechanisms of energy transfer in the compound space of scales and positions of wall turbulent flows are investigated in a temporally evolving boundary layer. The phenomena consist of spatially ascending reverse and forward cascades from the small production scales of the buffer layer to the small dissipative scales distributed among the entire boundary layer height. The observed qualitative behaviour conforms with previous results in turbulent channel flow, thus suggesting that the observed phenomenology is a robust statistical feature of wall turbulence in general. An interesting feature is the behaviour of energy transfer at the turbulent/non-turbulent interface, where forward energy cascade is found to be almost absent. In particular, the turbulent core is found to sustain a variety of large-scale wall-parallel motions at the turbulent interface through weak but persistent reverse energy cascades. This behaviour conforms with previous results in free shear flows, thus suggesting that the observed phenomenology is a robust statistical feature of turbulent shear flows featuring turbulent/non-turbulent interfaces in general.