Pith Number

pith:L7ODIGUA

pith:2026:L7ODIGUASQB6D6HKXNNE2JBS7D

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Prandtl number dependence of rotating internally heated convection

Ali Arslan, Rodolfo Ostilla-M\'onico

Global mean temperature in internally heated convection depends little on Prandtl number and is set by the top unstable boundary layer.

arxiv:2602.21860 v2 · 2026-02-25 · physics.flu-dyn

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Claims

C1strongest claim

We show that the global mean temperature ⟨T¯⟩ is not very sensitive to Pr, and is primarily controlled by the dynamics of the unstably stratified top boundary layer. In contrast, the Prandtl number dictates the behavior of the lower, stably stratified region and affects the vertical convective heat flux ⟨wT¯⟩.

C2weakest assumption

The direct numerical simulations resolve all relevant scales across the Pr range 0.1–100 and correctly capture the transition between non-rotating and rotating regimes without significant numerical artifacts or domain-size effects.

C3one line summary

Global mean temperature in internally heated convection stays largely insensitive to Prandtl number and is set by the top unstable layer, while heat flux and stable-layer behavior vary strongly with Pr; rotation boosts flux for Pr at or above 1 via Ekman pumping.

References

27 extracted · 27 resolved · 0 Pith anchors

[1] Abbate, J. A. & Aurnou, J. M.2023 Rotating convective turbulence in moderate to high prandtl number fluids.Geophysical & Astrophysical Fluid Dynamics117(6), 397–436 2023

[2] & Wynn, A.2021 Bounds on heat transport for convection driven by internal heating.Journal of Fluid Mechanics919, A15 2021

[3] Arslan, A. & Rojas, R. E.2025 New bounds for heat transport in internally heated convection at infinite prandtl number.Journal of Mathematical Physics66(2), 023101. 18 𝑃𝑟 Γ ⟨𝑤𝑇⟩ ⟨𝑇⟩ 𝑅𝑒 𝑤 Γ ⟨𝑤𝑇⟩ ⟨𝑇⟩ 𝑅𝑒 2025

[4] Aurnou, J. M., Calkins, M. A., Cheng, J. S., Julien, K., King, E. M., Nieves, D., Soderlund, K. M. & Stellmach, S.2015 Rotating convective turbulence in earth and planetary cores.Physics of the Earth 2015

[5] Proceedings of the Royal Society of London 1953

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Receipt and verification

First computed	2026-05-18T03:09:23.352135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fdc341a809403e1f8eabb5a4d2432f8caadc611226bfe4b5e8b1e94d648db92

Aliases

arxiv: 2602.21860 · arxiv_version: 2602.21860v2 · doi: 10.48550/arxiv.2602.21860 · pith_short_12: L7ODIGUASQB6 · pith_short_16: L7ODIGUASQB6D6HK · pith_short_8: L7ODIGUA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L7ODIGUASQB6D6HKXNNE2JBS7D \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5fdc341a809403e1f8eabb5a4d2432f8caadc611226bfe4b5e8b1e94d648db92

Canonical record JSON

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    "abstract_canon_sha256": "7768ac6655fa9cbdf76b978d471b4ab2a9bd5f5666ac663b810bc2ffbc7584ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2026-02-25T12:36:30Z",
    "title_canon_sha256": "cbec39bf1bcfadb1544f2d29002add631191415c5637e197a79ab11e88c5396a"
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