Regimes of two-dimensionality of decaying shallow axisymmetric swirl flows with background rotation

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Abstract

Both background rotation and small depths are said to enforce the two-dimensionality of flows. In the current paper, we describe a systematic study of the two-dimensionality of a shallow monopolar vortex subjected to background rotation. Using a perturbation analysis of the Navier–Stokes equations for small aspect ratio [formula] (with H the fluid depth and L a typical radial length scale of the vortex), we found nine different regimes in the parameter space where the flow is governed to lowest order by different sets of equations. From the properties of these sets of equations, it was determined that the flow can be considered as quasi-two-dimensional in only five of the nine regimes. The scaling of the velocity components as given by these sets of equations was compared with results from numerical simulations to find the actual boundaries of the different regimes in the parameter space (hEk, hRe ), where hEk is the Ekman boundary layer thickness and hRe is the equivalent boundary layer thickness for a monopolar vortex without background rotation. Even though background rotation and small depths do promote the two-dimensionality of flows independently, the combination of these two characteristics does not necessarily have that same effect.
LanguageEnglish
Pages214-244
Number of pages31
JournalJournal of Fluid Mechanics
Volume691
DOIs
StatePublished - 2012

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axisymmetric flow
boundary layer thickness
Vortex flow
vortices
Boundary layers
Navier-Stokes equation
Navier Stokes equations
aspect ratio
Aspect ratio
scaling
perturbation
Fluids
fluids
Computer simulation
simulation

Cite this

@article{7bf96d9fc0df4c30a66b99e0cfcd67ec,
title = "Regimes of two-dimensionality of decaying shallow axisymmetric swirl flows with background rotation",
abstract = "Both background rotation and small depths are said to enforce the two-dimensionality of flows. In the current paper, we describe a systematic study of the two-dimensionality of a shallow monopolar vortex subjected to background rotation. Using a perturbation analysis of the Navier–Stokes equations for small aspect ratio [formula] (with H the fluid depth and L a typical radial length scale of the vortex), we found nine different regimes in the parameter space where the flow is governed to lowest order by different sets of equations. From the properties of these sets of equations, it was determined that the flow can be considered as quasi-two-dimensional in only five of the nine regimes. The scaling of the velocity components as given by these sets of equations was compared with results from numerical simulations to find the actual boundaries of the different regimes in the parameter space (hEk, hRe ), where hEk is the Ekman boundary layer thickness and hRe is the equivalent boundary layer thickness for a monopolar vortex without background rotation. Even though background rotation and small depths do promote the two-dimensionality of flows independently, the combination of these two characteristics does not necessarily have that same effect.",
author = "{Duran Matute}, M. and L.P.J. Kamp and R.R. Trieling and {Heijst, van}, G.J.F.",
year = "2012",
doi = "10.1017/jfm.2011.470",
language = "English",
volume = "691",
pages = "214--244",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

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TY - JOUR

T1 - Regimes of two-dimensionality of decaying shallow axisymmetric swirl flows with background rotation

AU - Duran Matute,M.

AU - Kamp,L.P.J.

AU - Trieling,R.R.

AU - Heijst, van,G.J.F.

PY - 2012

Y1 - 2012

N2 - Both background rotation and small depths are said to enforce the two-dimensionality of flows. In the current paper, we describe a systematic study of the two-dimensionality of a shallow monopolar vortex subjected to background rotation. Using a perturbation analysis of the Navier–Stokes equations for small aspect ratio [formula] (with H the fluid depth and L a typical radial length scale of the vortex), we found nine different regimes in the parameter space where the flow is governed to lowest order by different sets of equations. From the properties of these sets of equations, it was determined that the flow can be considered as quasi-two-dimensional in only five of the nine regimes. The scaling of the velocity components as given by these sets of equations was compared with results from numerical simulations to find the actual boundaries of the different regimes in the parameter space (hEk, hRe ), where hEk is the Ekman boundary layer thickness and hRe is the equivalent boundary layer thickness for a monopolar vortex without background rotation. Even though background rotation and small depths do promote the two-dimensionality of flows independently, the combination of these two characteristics does not necessarily have that same effect.

AB - Both background rotation and small depths are said to enforce the two-dimensionality of flows. In the current paper, we describe a systematic study of the two-dimensionality of a shallow monopolar vortex subjected to background rotation. Using a perturbation analysis of the Navier–Stokes equations for small aspect ratio [formula] (with H the fluid depth and L a typical radial length scale of the vortex), we found nine different regimes in the parameter space where the flow is governed to lowest order by different sets of equations. From the properties of these sets of equations, it was determined that the flow can be considered as quasi-two-dimensional in only five of the nine regimes. The scaling of the velocity components as given by these sets of equations was compared with results from numerical simulations to find the actual boundaries of the different regimes in the parameter space (hEk, hRe ), where hEk is the Ekman boundary layer thickness and hRe is the equivalent boundary layer thickness for a monopolar vortex without background rotation. Even though background rotation and small depths do promote the two-dimensionality of flows independently, the combination of these two characteristics does not necessarily have that same effect.

U2 - 10.1017/jfm.2011.470

DO - 10.1017/jfm.2011.470

M3 - Article

VL - 691

SP - 214

EP - 244

JO - Journal of Fluid Mechanics

T2 - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -