2021
DOI: 10.1017/jfm.2021.360
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Bounds on heat transport for convection driven by internal heating

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Cited by 17 publications
(35 citation statements)
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References 61 publications
(132 reference statements)
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“…On the theoretical side, we show how to formulate the background method systematically within a more general framework for bounding infinite-time averages, which is based on auxiliary functions [71][72][73] and is known to be sharp for well-posed ordinary and partial differential equations [74,75]. This interpretation of the background method, detailed in §3 and already discussed in [30,50,51,71,73,76], is especially useful because it always reduces the search for a bound to a convex variational principle. We also explain how this variational principle can be simplified using symmetries and, sometimes, improved by incorporating constraints such as maximum principles.…”
Section: Flow Analysis Computationsmentioning
confidence: 96%
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“…On the theoretical side, we show how to formulate the background method systematically within a more general framework for bounding infinite-time averages, which is based on auxiliary functions [71][72][73] and is known to be sharp for well-posed ordinary and partial differential equations [74,75]. This interpretation of the background method, detailed in §3 and already discussed in [30,50,51,71,73,76], is especially useful because it always reduces the search for a bound to a convex variational principle. We also explain how this variational principle can be simplified using symmetries and, sometimes, improved by incorporating constraints such as maximum principles.…”
Section: Flow Analysis Computationsmentioning
confidence: 96%
“…Rayleigh-Bénard convection [10,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] [ 20,21,30,31,[33][34][35][36][37][38], [39] † Bénard-Marangoni convection [40,41] [42] Porous-media convection [43] [ [44][45][46] Internally heated convection [26,[47][48][49][50][51] [50, 51] Double-diffusive convection [52] none Horizontal convection [53] none Parallel shear flows [7,8,11,15,…”
Section: Flow Analysis Computationsmentioning
confidence: 99%
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