Thermal convection in 1, 2, 3 and 4 dimensions

Ambrish Pandey; Harshit Tiwari; Katepalli R. Sreenivasan

Thermal convection in 1, 2, 3 and 4 dimensions

Fluid Dynamics 2026-07-29 v1

Authors: Ambrish Pandey , Harshit Tiwari , Katepalli R. Sreenivasan

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 1D, 2D, 3D and 4D. 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.

Keywords

thermal convection dimensionality direct numerical simulation transient time steady state ultimate state

Cite

@article{arxiv.2607.26372,
  title  = {Thermal convection in 1, 2, 3 and 4 dimensions},
  author = {Ambrish Pandey and Harshit Tiwari and Katepalli R. Sreenivasan},
  journal= {arXiv preprint arXiv:2607.26372},
  year   = {2026}
}

Comments

To appear in the Journal of Fluid Mechanics