Prosperetti, Andrea2020-03-102020-03-1012/7/2011Copyright 2011 Physics of Fluids. Recommended citation: Prosperetti, Andrea. "A simple analytic approximation to the Rayleigh-Bénard stability threshold." Physics of fluids 23, no. 12 (2011): 124101. DOI: 10.1063/1.3662466 URL: https://aip.scitation.org/doi/abs/10.1063/1.3662466 Reproduced in accordance with the original publisher’s licensing terms and with permission from the author(s).https://hdl.handle.net/10657/6140The Rayleigh-Bénard linear stability problem is solved by means of a Fourier series expansion. It is found that truncating the series to just the first term gives an excellent explicit approximation to the marginal stability relation between the Rayleigh number and the wave number of the perturbation. Where the error can be compared with published exact results, it is found not to exceed a few percent over the entire wave number range. Several cases with no-slip boundaries of equal or unequal thermal conductivities are considered explicitly.en-USControl theoryThermal diffusionLinear stability analysisFourier analysisPorous mediaMatrix calculusarticle