A canonical model for stratified flow in estuaries and rivers

Abstract

We present both fully resolved direct numerical simulation and large eddy simulation results for turbulent stratified flow in an open channel with periodic boundaries in the stream-wise direction and no-slip vertical sidewalls in the span-wise direction. A uniform heat source term is applied in the top 20% of the domain, approximating the solar heat flux into a river system. After each time step the total scalar flux input into the domain is uniformly removed allowing a fully developed flow field to be evolved and statistics collected. This approach allows fully developed stratified flow to be simulated with a density profile which includes a lower non-stratified region, steep thermocline and an upper laminar mixed layer region. The Reynolds number for the flows is in the range 5400-7300 and the bulk Richardson number in the range 0-0.4. References R. P. Garg, J. H. Ferziger, S. G. Monismith, and J. R. Koseff. Stably stratified turbulent channel flows. I. Stratification regimes and turbulence suppression mechanism. Phys. Fluids , 12(10):2569--2594, 2000. doi:10.1063/1.1288608 . S. Komori, H. Ueda, F. Ogino, and T. Mizushina. Turbulence structure in stably stratified open-channel flow. J. Fluid Mech. , 130:13--26, 1983. doi:10.1017/S0022112083000944 . Lei Wang and Xi-Yun Lu. Large eddy simulation of stably stratified turbulent open channel flows with low- to high-Prandtl number. Int. J. Heat and Mass Transfer , 48(10):1883 -- 1897, 2005. doi:10.1016/j.ijheatmasstransfer.2004.12.017 . J. R. Taylor, S. Sarkar, and V. Armenio. Large eddy simulation of stably stratified open channel flow. Phys. Fluids , 17(11):116602, 2005. doi:10.1063/1.2130747 . J. S. Turner. A note on wind mixing at the seasonal thermocline. Deep-Sea Res. , 16(Suppl.):297--300, 1969. P. E. Holloway. A criterion for thermal stratification in a wind-mixed System. J. Phys. Oceanogr. , 10:861--869, 1980. 2.0.CO;2>doi:10.1175/1520-0485(1980)010 2.0.CO;2 J. H. Simpson and J. R. Hunter. Fronts in the Irish sea. Nature , 250:404--406, 1974. doi:10.1038/250404a0 . M. Bormans and I. T. Webster. A mixing criterion for turbid rivers. Environmental Modelling and Software with Environment Data News , 12(4):329--333, 1997. doi:10.1016/S1364-8152(97)00032-7 . M. Germano, U. Piomelli, P. Moin, and W. H. Cabot. A dynamic subgrid-scale stress model. Phys. Fluids A , 3(7):1760--1765, 1991. doi:10.1063/1.857955 . S. B. Pope. Turbulent Flows . Cambridge University Press, 2000. S. W. Armfield and R. Street. Fractional step methods for the Navier--Stokes equations on non-staggered grids. ANZIAM Journal , 42:C134--C156, 2000. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/593 . S. W. Armfield, S. E. Norris, P. Morgan, and R. Street. A parallel non-staggered Navier--Stokes solver implemented on a workstation cluster. In S. Armfield, P. Morgan, and K. Srinvas, editors, Proceedings of the Second International Conference on Computational Fluid Dynamics , pages 30--45, Sydney, July 15-19 2002. J. H. Ferziger and M. Peric. Computational Methods for Fluid Dynamics . Springer, third edition, 2002.