On the merging and splitting processes in the lobe-and-cleft structure at a gravity current head

Abstract

High-resolution simulations are performed for gravity currents propagating on a no-slip boundary to study the merging and splitting processes in the lobe-and-cleft structure at a gravity current head. The simulations reproduce the morphological features observed in the laboratory and provide more detailed flow information to elucidate the merging and splitting processes. Our mean lobe width$\tilde {b}$and mean maximum lobe width$\tilde {b}_{max}$satisfy the empirical relationships$\tilde {b}/\tilde {d}=7.4 Re^{-0.39}_f$and$\tilde {b}_{max}/\tilde {d}=12.6 Re^{-0.38}_f$, respectively, over the front Reynolds number in the range$383 \le Re_f \le 3267$, where the front Reynolds number is defined as$Re_f= \tilde {u}_f \tilde {d} / \tilde {\nu }, \tilde {u}_f$is the front velocity,$\tilde {d}$is the height of the gravity current head and$\tilde {\nu }$is the fluid kinematic viscosity. When measured in terms of the viscous length scale$\tilde {\delta }_\nu = \tilde {\nu }/\tilde {u}^*$, where$\tilde {u}^*$is the shear velocity at the gravity current head, the mean lobe width and the mean maximum lobe width increase with increasing front Reynolds number and asymptotically approach$126 \tilde {\delta }_\nu$and$230 \tilde {\delta }_\nu$at$Re_f=3267$, respectively. The vortical structure inside a lobe has an elongated tooth-like shape and a pair of counter-rotating streamwise vortices are positioned on the left- and right-hand sides of each cleft. For the merging process, it requires the interaction of three tooth-like vortices and the middle tooth-like vortex breaks up and reconnects with the two neighbouring tooth-like vortices. Therefore, a cleft may continually merge with another neighbouring cleft but may never disappear. For the splitting process, even before the new cleft appears, a new born streamwise vortex is created by the parent vortex of opposite orientation and the parent vortex can be either the left part or the right part of the existing tooth-like vortex inside the splitting lobe. The new born streamwise vortex then induces the other counter-rotating streamwise vortex as the new cleft develops. The initiation of the splitting process can be attributed to the Brooke–Hanratty mechanism reinforced by the baroclinic production of vorticity. Depending on the orientation of the parent vortex, the resulting new cleft after the splitting process can shift laterally in the positive or negative spanwise direction along the leading edge of the gravity currents as the lobe-and-cleft structure moves forward in the streamwise direction. For gravity currents propagating on a no-slip boundary, the lobe-and-cleft structure is self-sustaining and the manifestations of the merging and splitting processes are in accord with reported laboratory observations.