Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

Global linear instability of rotating-cone boundary layers in a quiescent medium

Thomas, Christian and Davies, Christopher ORCID: https://orcid.org/0000-0002-5592-9541 2019. Global linear instability of rotating-cone boundary layers in a quiescent medium. Physical Review Fluids 4 , 043902. 10.1103/PhysRevFluids.4.043902

[thumbnail of PhysRevFluids.4.043902-1.pdf]
Preview
PDF - Published Version
Download (2MB) | Preview

Abstract

The global linear stability of the family of infinite rotating-cone boundary layers in an otherwise still fluid is investigated using a velocity-vorticity form of the linearized Navier-Stokes equations. The formulation is separable with respect to the azimuthal direction. Thus, disturbance development is simulated for a single azimuthal mode number. Numerical simulations are conducted for an extensive range of cone half-angles (ψ∈[20∘:80∘]) and stability parameters (Reynolds number, azimuthal mode number), where conditions are taken to be near those specifications necessary for the onset of absolute instability. A localized impulsive wall forcing is implemented that excites disturbances that form wave packets. This allows the disturbance evolution to be traced in the spatial-temporal plane. When a homogeneous flow approximation is utilised that neglects the spatial variation of the basic state, linear perturbations display characteristics consistent with local stability theory. For disturbances to the genuine spatially dependent inhomogeneous flow, global linear instability characterized by a faster than exponential temporal growth arises for azimuthal mode numbers greater than the conditions for critical absolute instability. Furthermore, a reasonable prediction for the azimuthal mode number needed to bring about a change in global behavior is achieved by coupling solutions of the Ginzburg-Landau equation with local stability properties. Thus, the local-global stability behavior is qualitatively similar to that found in the infinite rotating-disk boundary layer and many other globally unstable flows.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
T Technology > TA Engineering (General). Civil engineering (General)
Publisher: American Physical Society
ISSN: 2469-990X
Date of First Compliant Deposit: 1 May 2019
Date of Acceptance: 8 April 2019
Last Modified: 06 Jan 2024 04:51
URI: https://orca.cardiff.ac.uk/id/eprint/121995

Citation Data

Actions (repository staff only)

Edit Item Edit Item

Downloads

Downloads per month over past year

View more statistics