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ON THE TOPOGRAPHY-DRIVEN VORTICITY PRODUCTION IN SHALLOW LAKES

Part of: Incompressible viscous fluids Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  03 May 2019

BALÁZS SÁNDOR Open the ORCID record for BALÁZS SÁNDOR [Opens in a new window] ,
PÉTER TORMA Open the ORCID record for PÉTER TORMA [Opens in a new window] ,
K. GÁBOR SZABÓ Open the ORCID record for K. GÁBOR SZABÓ [Opens in a new window]  and
HONG ZHANG Open the ORCID record for HONG ZHANG [Opens in a new window]
BALÁZS SÁNDOR*
Affiliation:
Department of Hydraulic and Water Resources Engineering, Faculty of Civil Engineering, Budapest University of Technology and Economics, H-1111 Budapest, Hungary email [email protected], [email protected], [email protected] Griffith School of Engineering, Griffith University, Queensland 4222, Australia email [email protected]
PÉTER TORMA
Affiliation:
Department of Hydraulic and Water Resources Engineering, Faculty of Civil Engineering, Budapest University of Technology and Economics, H-1111 Budapest, Hungary email [email protected], [email protected], [email protected]
K. GÁBOR SZABÓ
Affiliation:
Department of Hydraulic and Water Resources Engineering, Faculty of Civil Engineering, Budapest University of Technology and Economics, H-1111 Budapest, Hungary email [email protected], [email protected], [email protected]
HONG ZHANG
Affiliation:
Griffith School of Engineering, Griffith University, Queensland 4222, Australia email [email protected]
*
✉[email protected]
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Abstract

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We analyse the vorticity production of lake-scale circulation in wind-induced shallow flows using a linear elliptic partial differential equation. The linear equation is derived from the vorticity form of the shallow-water equation using a linear bed friction formula. The features of the wind-induced steady-state flow are analysed in a circular basin with topography as a concave paraboloid, having a quadratic pile in the middle of the basin. In our study, the size of the pile varies by a size parameter. The vorticity production due to the gradient in the topography (and the distance of the boundary) makes the streamlines parallel to topographical contours, and beyond a critical size parameter, it results in a secondary vortex pair. We compare qualitatively and quantitatively the steady-state circulation patterns and vortex evolution of the flow fields calculated by our linear vorticity model and the full, nonlinear shallow-water equations. From these results, we hypothesize that the steady-state topographical vorticity production in lake-scale wind-induced circulations can be described by the equilibrium of the wind friction field and the bed friction field. Moreover, the latter can also be considered as a linear function of the velocity vector field, and hence the problem can be described by a linear equation.

Keywords

vorticity equilibriumshallow waterlinear circulation modellarge-scale environmental flow

MSC classification

Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 76D17: Viscous vortex flows
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 2 , April 2019 , pp. 148 - 160
Copyright
© 2019 Australian Mathematical Society 

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