# On the topography-driven vorticity production in shallow lakes

## Authors

• BalÃ¡zs SÃ¡ndor Department of Hydraulic and Water Resources Engineering, Faculty of Civil Engineering, Budapest University of Technology and Economics, Budapest, H-1111, Hungary. Griffith School of Engineering, Griffith University, Queensland 4222, Australia
• PÃ©ter Torma Department of Hydraulic and Water Resources Engineering, Faculty of Civil Engineering, Budapest University of Technology and Economics, Budapest, H-1111, Hungary.
• GÃ¡bor SzabÃ³ Department of Hydraulic and Water Resources Engineering, Faculty of Civil Engineering, Budapest University of Technology and Economics, Budapest, H-1111, Hungary.
• Hong Zhang Griffith School of Engineering, Griffith University, Queensland 4222, Australia.

## Keywords:

vorticity equilibrium, shallow water, linear circulation model, large-scale environmental flow.

## Abstract

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. doi:10.1017/S1446181119000051

2019-06-10

## Section

Articles for Printed Issues