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Thermal convection in one, two, three and four dimensions
Abstract
We study by means of direct numerical simulations the influence of the dimensionality of convection on flow properties. We call attention to a few general principles from considering in totality the results from one dimension, two dimensions, three dimensions and four dimensions. In particular, we explore two practical aspects: (1) the transient time, or the amount of time it takes for the flow to reach the steady state; and (2) possible implications for the so-called ultimate state.
Versions
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BibTeX
@misc{pandey2026thermal,
title = {{Thermal convection in one, two, three and four dimensions}},
author = {Ambrish Pandey and Harshit Tiwari and Katepalli R. Sreenivasan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.26372},
eprint = {2607.26372},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.26372},
}
RIS
TY - UNPB
TI - Thermal convection in one, two, three and four dimensions
AU - Ambrish Pandey
AU - Harshit Tiwari
AU - Katepalli R. Sreenivasan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2607.26372
UR - https://arxiv.org/abs/2607.26372
AB - We study by means of direct numerical simulations the influence of the dimensionality of convection on flow properties. We call attention to a few general principles from considering in totality the results from one dimension, two dimensions, three dimensions and four dimensions. In particular, we explore two practical aspects: (1) the transient time, or the amount of time it takes for the flow to reach the steady state; and (2) possible implications for the so-called ultimate state.
ER -