Modeling Lobe‐And‐Cleft Instabilities on a River Plume

Abstract

AbstractThe lobe‐and‐cleft instability is a widely recognized mechanism leading to along‐front structure on density current fronts. Early studies based on laboratory and numerical simulations suggested that the lobe‐and‐cleft instability is due to convective instability in the nose of gravity currents traveling over a nonslip boundary. Horner‐Devine and Chickadel (2017, https://doi.org/10.1002/2017gl072997) reported the presence of lobe‐and‐cleft instabilities at the Merrimack River, which are generated at the river front in the absence of a no‐slip boundary. Hence, the observed lobe‐and‐cleft instabilities must be due to other mechanisms. In this study, we carried out non‐hydrostatic large eddy simulations of a riverine outflow into an idealized 3D domain. With a fine grid resolution of 0.15 × 0.31 m in two horizontal directions and about 0.125 m in the vertical direction, the model reproduced the lobe‐and‐cleft feature, with the magnitude and size of lobes consistent with the field observation. The model results revealed that instabilities start from the primary Kelvin‐Helmholtz instability, followed by the secondary instability through stretching and tilting, generating counter‐rotating streamwise vortices in the plume and at the plume head. The upwelling associated with streamwise vortex cells brings a slower flow to the plume surface, resulting in lobe‐and‐cleft patterns at the front and positive and negative vertical vorticity at the plume surface. The model also predicted a lobe width of about two to three times the plume thickness, consistent with the field observation and the lobe/cleft spacing associated with pairs of counter‐rotating streamwise vortices. Modeled turbulent dissipation rate shows a trend of exponential decay from 10−4 to 10−3 m2/s3 at the frontal head to 10−7 to 10−6 m2/s3 behind the front, similar to the findings in the previous field studies.