Toward a Quantitative Understanding of Robert’s Rising Thermal Bubble as a Benchmark for 3D Atmospheric Codes

Abstract

Abstract Robert’s rising thermal bubble (RRTB) is a benchmark case used to assess atmospheric models. In this paper, RRTB is further studied both using an analytical and a numerical approach, improving to a greater extent the qualitative description found in the literature. The theoretical framework used is that of buoyant thermals and scaling theory that together are able to predict part of the expected behavior of the bubble as it rises and, therefore, can be used to further validate the simulations. For the numerical experiments, we simulate both a two-dimensional and three-dimensional RRTB using a variety of convection schemes under the Boussinesq approximation and with a higher resolution. While the results are in agreement with those presented by previous authors on the same benchmark and also with the theoretical framework established, we add the quantitative measures to validate the underlying physics of the numerical model. Our results also show that, due to its completely chaotic nature when confined in a 2D plane, RRTB becomes a very challenging candidate to be used as a benchmark if only compared in a qualitative way, and when the 3D bubble is simulated, the shape changes significantly.