Analytical and Chebyshev pseudospectral numerical solutions for a class of axisymmetric horizontal flows dominated by mass or heat sources

SUMMARY A class of axisymmetric horizontal flows dominated by strong heat or mass sources are considered here, which systematically arise in multiscale atmospheric and oceanic flows in various spatiotemporal scales such as hurricane embryos. Various linear and nonlinear analytical solutions are proposed, and several examples are given to illustrate them. On the basis of the proposed exact solutions, stability of the flow under various conditions is examined. The proposed exact solutions serve as benchmarks for validation of numerical models. A Chebyshev pseudospectral model is also developed for these flows. The numerical results are compared with the developed analytical solutions as well as a high-resolution numerical solution, which showed an excellent performance of the numerical model in terms of numerical diffusion and oscillation. The numerical method is also efficient because expensive calculations such as LU decomposition are only needed once, at the beginning of calculations. The model could be used in studying small-scale and multiple-scale phenomena such as hot towers and hurricane embryos, which are the subject of future studies. Copyright © 2011 John Wiley & Sons, Ltd.