Multi scale roll structures in the atmospheric boundary layer

Large scale structures intensify the vertical transport of momentum, heat, and humidity in the atmospheric boundary layer. This effect can be more pronounce when intensity of surface fluxes strongly depend on the local wind, e.g. in hurricane boundary layer over the sea. Under certain conditions large eddies realized as roll vortices with axis of helical circulation pattern parallel the underlying surface. Such vortex usually have vertical scale of the order the ABL depth and horizontal scale from hundreds meters up to a few kilometers (Wurman & Winslow 1998, Gall et al. 1998). There are many studies for linear and weakly nonlinear regimes of this phenomena (Lilly 1966, Brown 1970, Mikhailova & Ordanovich 1988, Foster 1996), but really nonlinear regimes were studied only in a few works ( Kaylor& Faller 1972, Hoffmann et al. 1998). The main feature of the strong nonlinearity is the big asymmetry of positive and negative rolls amplitude and a possibility of the existence of the multi-scale regimes (Foster 1996, Mourad & Brown 1990, Ponomarev et al. 2005).

Tropical cyclone represents an intensive vortex with pronounced helical pattern of the flow which can produce helicity in the turbulent flow component observed in the Ekman boundary layer (Koprov et al. 2005). In turn the helical properties of turbulence can change the structure of the Reynolds stress tensor (Chkhetiani 2001,Ponomarev & Chkhetiani 2005)

(v_x v_z)=-K dU/dz+K_h dV/dz,

(vy v_z)=-K dV/dz-K_h dU/dz.

Here K_h is proportional to the turbulent helicity.

This expression was used in numerical simulation of the roll structures at various conditions. It is shown the influence of helicity on the stability characteristics and structure of the developed rolls (Ponomarev et al. 2003, Ponomarev et al. 2005) (fig.1).

The nonlinear rolls are usually unsteady and can merge and split (fig.2).

In addition some results of roll simulation for the flow with cylindrical geometry are discussed.

This study was supported by the Russian Foundation for Basic Research (project nos. 03-05-64593, 05-05-64735).