An arrangement of a large-eddy simulation (LES) is described that facilitates a spatially developing thermally stratified atmospheric boundary layer (ABL). When the inflow and outflow boundary conditions are specified, the LES of stably stratified ABL turns out to be challenging because spurious reflections of waves at the boundary accumulate inside the domain. To tackle this problem, a fringe method with an auxiliary LES running concurrently is applied to enforce upstream/downstream boundary

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... nditions. An artificial forcing term is applied within a fringe region located at the beginning of the main LES domain in order to ensure statistically stationary inflow boundary conditions. The auxiliary LES, which is horizontally homogeneous in a doubly periodic domain, is used to determine the inflow condition of the main LES domain. The present scheme is used to provide an Eulerian perspective of the stratocumulus to shallow cumulus cloud (Sc-Cu) transition, one of the key cloud regimes over the subtropical ocean. In this study, the transition is triggered by increasing the sea surface temperature (SST) and the LES runs until a statistically steady evolution of the Sc-Cu transition is achieved. The flow statistics are compared with those from a recycling-type method and it is found that the fringe method is more suitable for the current applications.