## Benchmark problem

Conference: BIFURCATIONS AND INSTABILITIES IN FLUID DYNAMICS

Date: 8 - 11 July 2013

Place: Haifa, Israel

Session: Computational methods for bifurcation and stability analysis

Organizers: Henk Dijkstra (Utrecht University) and Fred Wubs (University of Groningen)

## 3D Lid Driven Cavity

- Problem description and numerical results in Oscillatory instability of a three-dimensional lid-driven flow in a cube by Yu. Feldman and A. Yu. Gelfgat, Phys. Fluids 22, 093602 (2010).
- Experiments: Experimental observation of the steady-oscillatory transition in a cubic lid-driven cavity by A. Liberzon, Yu. Feldman and A.Yu. GelfGat, Phys. Fluids 23, 084106 (2011)
- They used the finite volume method on grids ranging from $128^3$ to $200^3$.
- Aim: Efficient analysis of transition from steady to periodic flow.

## Boussinesq equations on a sector North Atlantic model

- Problem description: In De Niet et al. (2007) and Thies et al. (2009), the steady hydrostatic equations for wind and thermohaline ocean flows were solved versus parameters. The domain is a 60 degrees W-E sector over latitudes 10N-74N on the sphere with a constant depth of 4000m. Flow is forced by a wind stress, a surface temperature distribution and a freshwater flux.
- Aim is to compute the bifurcation diagram of the flow in the parameter measuring the strength of the freshwater flux for a high-resolution model (down to 1/4 degree horizontally).
- References:
- De Niet, A., Wubs, F., Terwisscha van Scheltinga, A. and Dijkstra, H. A., A tailored solver for bifurcation analysis of ocean-climate models, J. Comp. Physics, 227, 654--679, (2007).
- Thies, J., F. W. Wubs and Dijkstra, H. A., Bifurcation analysis of 3D ocean flows using a parallel fully implicit ocean model, Ocean Modelling, 30, 287–297. (2009).

## Requirements

- Accuracy of results should be determined
- Description of the used methodology
- Performance analysis of the method
- Estimate of the human effort to get the results

Those interested in participating are asked to send a one page abstract in pdf format to bifd2013@technion.ac.il before January 15, 2013.