dorsal/arxiv
View SchemaThe effect of wall heating on instability of channel flow
| Authors | A. Sameen, Rama Govindarajan |
|---|---|
| Categories | |
| ArXiv ID | physics/0603245 |
| URL | https://arxiv.org/abs/physics/0603245 |
| DOI | 10.1017/S0022112007004636 |
| Journal | Journal of Fluid Mechanics 577 (2007) 417-442 |
Abstract
A comprehensive study of the effect of wall heating or cooling on the linear, transient and secondary growth of instability in channel flow is conducted. The effect of viscosity stratification, heat diffusivity and of buoyancy are estimated separately, with some unexpected results. From linear stability results, it has been accepted that heat diffusivity does not affect stability. However, we show that realistic Prandtl numbers cause a transient growth of disturbances that is an order of magnitude higher than at zero Prandtl number. Buoyancy, even at fairly low levels, gives rise to high levels of subcritical energy growth. Unusually for transient growth, both of these are spanwise-independent and not in the form of streamwise vortices. At moderate Grashof numbers, exponential growth dominates, with distinct Rayleigh-Benard and Poiseuille modes for Grashof numbers upto $\sim 25000$, which merge thereafter. Wall heating has a converse effect on the secondary instability compared to the primary, destabilising significantly when viscosity decreases towards the wall. It is hoped that the work will motivate experimental and numerical efforts to understand the role of wall heating in the control of channel and pipe flows.
{
"annotation_id": "f5efb1d4-9d30-4aa5-ac47-17b8091454d9",
"date_created": "2026-03-02T18:01:06.678000Z",
"date_modified": "2026-03-02T18:01:06.678000Z",
"file_hash": "26689b7ed3736b2f0e80385c02f354078c654f46a693fc917438228c1a921c47",
"private": false,
"record": {
"abstract": "A comprehensive study of the effect of wall heating or cooling on the linear,\ntransient and secondary growth of instability in channel flow is conducted. The\neffect of viscosity stratification, heat diffusivity and of buoyancy are\nestimated separately, with some unexpected results. From linear stability\nresults, it has been accepted that heat diffusivity does not affect stability.\nHowever, we show that realistic Prandtl numbers cause a transient growth of\ndisturbances that is an order of magnitude higher than at zero Prandtl number.\nBuoyancy, even at fairly low levels, gives rise to high levels of subcritical\nenergy growth. Unusually for transient growth, both of these are\nspanwise-independent and not in the form of streamwise vortices. At moderate\nGrashof numbers, exponential growth dominates, with distinct Rayleigh-Benard\nand Poiseuille modes for Grashof numbers upto $\\sim 25000$, which merge\nthereafter. Wall heating has a converse effect on the secondary instability\ncompared to the primary, destabilising significantly when viscosity decreases\ntowards the wall. It is hoped that the work will motivate experimental and\nnumerical efforts to understand the role of wall heating in the control of\nchannel and pipe flows.",
"arxiv_id": "physics/0603245",
"authors": [
"A. Sameen",
"Rama Govindarajan"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1017/S0022112007004636",
"journal_ref": "Journal of Fluid Mechanics 577 (2007) 417-442",
"title": "The effect of wall heating on instability of channel flow",
"url": "https://arxiv.org/abs/physics/0603245"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "ff3afa59-248e-451f-b792-53755c7fceb0",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}