Search for: All records

Abstract This study adopts a curvature dynamics approach to understand and predict the trajectory of an idealized depth-averaged barotropic outflow onto a slope in shallow water. A novel equation for streamwise curvature dynamics was derived from the barotropic vorticity equation and applied to a momentum jet subject to bottom friction, topographic slope, and planetary rotation. The terms in the curvature dynamics equation have a natural geometric interpretation whereby each physical process can influence the flow direction. It is shown that a weakly spreading jet onto a steep slope admits the formulation of a 1D ordinary differential equation system in a streamline coordinate system, yielding an integrable ordinary differential equation system that predicts the kinematical behavior of the jet. The 1D model was compared with a set of high-resolution idealized depth-averaged circulation model simulations where bottom friction, planetary rotation, and bottom slope were varied. Favorable performance of the 1D reduced physics model was found, especially in the near field of the outflow. The effect of nonlinear processes such as topographic stretching and bottom torque on the fate of the jet outflow is explained using curvature dynamics. Even in the tropics, planetary rotation can have a surprisingly strong influence on the near-field deflection of an intermediate-scale jet, provided that it flows across steep topography. 

In the coastal ocean, interactions of waves and currents with large roughness elements, similar in size to wave orbital excursions, generate drag and dissipate energy. These boundary layer dynamics differ significantly from well-studied small-scale roughness. To address this problem, we derived spatially and phase-averaged momentum equations for combined wave–current flows over rough bottoms, including the canopy layer containing obstacles. These equations were decomposed into steady and oscillatory parts to investigate the effects of waves on currents, and currents on waves. We applied this framework to analyse large-eddy simulations of combined oscillatory and steady flows over hemisphere arrays (diameter $$D$$ ), in which current ( $$U_c$$ ), wave velocity ( $$U_w$$ ) and period ( $$T$$ ) were varied. In the steady momentum budget, waves increase drag on the current, and this is balanced by the total stress at the canopy top. Dispersive stresses from oscillatory flow around obstacles are increasingly important as $$U_w/U_c$$ increases. In the oscillatory momentum budget, acceleration in the canopy is balanced by pressure gradient, added-mass and form drag forces; stress gradients are small compared to other terms. Form drag is increasingly important as the Keulegan–Carpenter number $$KC=U_wT/D$$ and $$U_c/U_w$$ increase. Decomposing the drag term illustrates that a quadratic relationship predicts the observed dependences of steady and oscillatory drag on $$U_c/U_w$$ and $KC$ . For large roughness elements, bottom friction is well represented by a friction factor ( $$f_w$$ ) defined using combined wave and current velocities in the canopy layer, which is proportional to drag coefficient and frontal area per unit plan area, and increases with $KC$ and $$U_c/U_w$$ .