Boundaries behaviour of gravity currents

Gravity currents are buoyancy-driven flows generated by horizontal density gradients and govern the transport of mass, momentum, and scalars in both natural and engineered systems. A detailed understanding of their near-wall behavior is essential for accurately describing the turbulent mechanisms developing in this region, which is characterized by strong spatial variability, particularly at increasing Reynolds numbers (Re=UbH/ν, with H the initial height of the dense fluid, ν the cinematic viscosity, Ub=(g’H)0.5 a velocity scale related to the reduced gravity g’=g(ρ₁- ρ₀)/ ρ₀, where g is the gravitational acceleration,  ρ1 the density of the heavier fluid and ρ0 the ambient density).  

 Several numerical simulations were performed in straight channels under a lock-exchange configuration using a wall-resolved Large Eddy Simulation. The analyzed cases differ in terms of Reynolds number (in the range 34000-136000), both by increasing the height of the domain and by modifying the density difference. 

The analysis of the near-wall behavior focused on the head of the current, identified through mean density values. Subsequently, streamwise velocity profiles in the wall-normal direction were extracted, first averaged in the spanwise direction and then also along the streamwise direction. Although the latter direction is not homogeneous, this procedure provides an overall view of the behavior of the current head during its temporal evolution. 

The gradient of the streamwise velocity in the wall-normal direction was used to define the boundary-layer thickness δ. It was observed that the temporal evolution of the normalized thickness δ* = δ/H is similar for all the cases analyzed; moreover, after an initial increase, it tends to approach an asymptotic value during the self-similar phase. In accordance with the characteristics of this phase, it is also observed that the mean velocity profile tends to remain invariant over time during the evolution of the current. Moreover, the presence of a logarithmic region is identified, of the form u⁺=a(lny⁺)+bu⁺=aln⁡y⁺+b (where u⁺=u/u𝜏, and y⁺=yu𝜏/νy⁺=yu𝜏/𝜈, u𝜏 denoting the friction velocity), with an increase in the slope A (in a logarithmic plot) relative to the canonical value (A=2.44), consistent with the local presence of stable stratification. 

The results obtained may have important implications for the parameterization of simplified large-scale circulation models, particularly with regard to the definition of appropriate boundary conditions.