Energy dissipation rate limits for flow through rough channels and tidal flow across topography – CORRIGENDUM

Kerswell, Rich R.

doi:10.1017/jfm.2017.761

Cited by 1 publication

(1 citation statement)

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“…In particular, under the assumption that the profile h (which may differ at the top and bottom boundaries) is a continuous and piecewise differentiable function of the horizontal coordinates and has squared-integrable gradients, the authors showed Nu C( ∇h 2 2 )Ra 1 2 . Here we want to cite also [Ker16] and [Ker18], where Kerswell derives an upper bound for the energy dissipation rate per unit mass for a pressure-driven flow in a rough channel.…”

Section: Introductionmentioning

confidence: 99%

Bounds on heat transport for two-dimensional buoyancy driven flows between rough boundaries

Bleitner¹,

Nobili²

2023

Preprint

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We consider the two-dimensional Rayleigh-Bénard convection in a layer of fluid between rough Navier-slip boundaries. The top and bottom boundaries are described by the same height function h. We prove rigorous upper bounds on the Nusselt number which capture the dependence on the curvature of the boundary κ and the (non-constant) friction coefficient α explicitly. For h ∈ W 2,∞ and κ satisfying a smallness condition with respect to α, we find Nu Rawhich agrees with the predicted Spiegel-Kraichnan scaling when κ = 0. This bound is obtained via local regularity estimates in a small strip at the boundary. When h ∈ W 3,∞ and the functions κ and α are sufficiently small in L ∞ , we prove upper bounds using the background field method, which interpolate between Ra 1 2 and Ra 5 12 with non-trivial dependence on α and κ. These bounds agree with the result in [DNN22] for flat boundaries and constant friction coefficient. Furthermore, in the regime Pr ≥ Ra 5 7 , we improve the Ra 1 2 -upper bound, showing Nu α,κ Ra 3 7 , where α,κ hides an additional dependency of the implicit constant on α and κ.

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Section: Introductionmentioning

confidence: 99%