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Abstract Recent studies have demonstrated the sensitivity of simulated tropical cyclone (TC) intensity to horizontal diffusion in numerical models. It is unclear whether such sensitivity comes from the horizontal diffusion in or above the boundary layer. To address this issue, both an Ooyama-type model and a full-physics model are used to conduct sensitivity experiments with reduced or enlarged horizontal mixing length (lh) in the boundary layer and/or in the free atmosphere. Results from both models show that enlarging (reducing)lhthroughout the model domain considerably reduces (increases) the TC intensification rate and quasi-steady intensity. A new finding is that changinglhabove the boundary layer imposes a much greater influence than that in the boundary layer. Largelhabove the boundary layer is found to effectively reduce the radial gradient of tangential wind inside the radius of maximum tangential wind and thus the inward flux of absolute vorticity, reducing the positive tangential wind tendency and the TC intensification rate and the steady-state intensity. In contrast, although largerlhin the boundary layer reduces the boundary layer tangential wind tendency, it also leads to the more inward-penetrated inflow and thus enhances the inward flux of absolute vorticity, which offsets part of the direct negative contribution by horizontal diffusion, making the net change in tangential wind tendency not obvious. Results from three-dimensional simulations also show that the resolved eddies contribute negatively to TC spinup whenlhis small, while its effect weakens whenlhis enhanced either in or above the boundary layer.
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Asymptotic analysis of unsteady neutron transport equation
Consider the unsteady neutron transport equation with diffusive boundary condition in 2D convex domains. We establish the diffusive limit with both initial layer and boundary layer corrections. The major difficulty is the lack of regularity in the boundary layer with geometric correction. Our contribution relies on a detailed analysis of asymptotic expansions inspired by the compatibility condition and an intricateL2m − L∞framework, which yields stronger remainder estimates.
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- Award ID(s):
- 1853002
- PAR ID:
- 10453266
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Mathematical Methods in the Applied Sciences
- Volume:
- 42
- Issue:
- 8
- ISSN:
- 0170-4214
- Page Range / eLocation ID:
- p. 2544-2585
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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