This demanded additional user input, which in this context, it is preferable to minimise. The two key issues to be addressed here are the performance of the adaptive mesh simulations relative to those on a fixed mesh and the influence, if any, of the metric on the adaptive mesh simulations. The paper is organised as follows: Sections 2 and 3 describe the physical lock-exchange set-up, Fluidity-ICOM and the adaptive mesh techniques employed. Section 4 introduces the diagnostics. Section 5 presents and discusses the results from the numerical simulations, comparing them to one another and previously

published results. Finally, Section 6 closes with the key conclusions of this work. The system is governed by the Navier-Stokes Akt activation equations under the Boussinesq approximation, a linear equation of state and the thermal advection-diffusion equation: equation(1) ∂u∂t+u·∇u=-∇p-ρρ0gk+∇·(ν¯¯∇u), equation(2) ∇·u=0,∇·u=0, equation(3) ρ=ρ0+Δρ=ρ0(1-α(T-T0)),ρ=ρ0+Δρ=ρ0(1-α(T-T0)), equation(4) ∂T∂t+u·∇T=∇·(κ¯¯T∇T),with u=(u,v,w)Tu=(u,v,w)T: velocity, p  : pressure, ρρ: density, ρ0ρ0:

background density, g  : acceleration due to gravity, ν¯¯: kinematic viscosity, T  : temperature, T0T0: background temperature, κ¯¯T: thermal diffusivity, αα: thermal expansion coefficient and k=(0,0,1)Tk=(0,0,1)T. The model considered here is two-dimensional and consequently variation in the cross-stream (y) direction is neglected. The diffusion term, ∇·(κ¯¯T∇T) in Eq. (4), is neglected in the Fluidity-ICOM simulations. However, the discretised system can still act as if a diffusion term were present, leading to spurious Epacadostat supplier diapycnal mixing. This diffusion can be attributed to the numerics and occurs because, fundamentally, the numerical solution is an approximation to the true solution. It will be referred to here

as numerical diffusion and it is preferable to minimise its effect. By removing the diffusion term, one level of parameterisation of the system is removed. This allows the response of the fixed and adaptive meshes and a comparison of the inherent numerical diffusion to be made more readily without the need to distinguish between diapycnal mixing due to parameterised diffusion and that inherent in the system. Fixed and adaptive mesh simulations with the diffusion term included were analysed in Hiester HSP90 (2011) where the best performing adaptive mesh simulations (the same as discussed here) were found to perform as well as the second highest resolution fixed mesh. The values for gg, ν¯¯, αα and T0T0 are given in Table 1, following the values of Härtel et al., 2000 and Hiester et al., 2011. Note, when (3) is substituted into (1), the buoyancy term ρ/ρ0gkρ/ρ0gk becomes (1-α(T-T0))gk(1-α(T-T0))gk and hence buoyancy forcing due to the temperature perturbation is included but no value of ρ0ρ0 needs to be specified. The domain is a two-dimensional rectangular box, 0⩽x⩽L0⩽x⩽L, L=0.8L=0.