Turbulent convection driven by surface cooling in shallow water

Abstract

We present the results of large-eddy simulations (LES) of turbulent thermal convection generated by surface cooling in a finite-depth stably stratified horizontal layer with an isothermal bottom surface. The flow is a simplified model of turbulent convection occurring in the warm shallow ocean during adverse weather events. Simulations are performed in a 6 × 6 × 1 aspect ratio computational domain using the pseudo-spectral Fourier method in the horizontal plane and finite-difference discretization on a high-resolution clustered grid in the vertical direction. A moderate value of the Reynolds number and two different values of the Richardson number corresponding to a weak initial stratification are considered. A version of the dynamic model is applied as a subgrid-scale (SGS) closure. Its performance is evaluated based on comparison with the results of direct numerical simulations (DNS) and simulations using the Smagorinsky model. Comprehensive study of the spatial structure and statistical properties of the developed turbulent state shows some similarity to Rayleigh–Bénard convection and other types of turbulent thermal convection in horizontal layers, but also reveals distinctive features such as the dominance of a large-scale pattern of descending plumes and strong turbulent fluctuations near the surface.

Instability and transition to turbulence in a free shear layer affected by a parallel magnetic field

“…A more detailed description of the numerical algorithm is available in Zikanov, Slinn & Dhanak (2004). The finite-difference grid is non-uniform with clustering in the area of strong basic shear.…”

A 3D second‐order accurate projection‐based Finite Volume code on non‐staggered, non‐uniform structured grids with continuity preserving properties: application to buoyancy‐driven flows

“…the dynamic 431 procedure) both for the momentum and thermal energy equation, e.g. see References [12,22], can be dramatically a ected by numerical errors. Therefore, it was analysed what happens by using the exact and approximate projection method and, since the standard exact projection method strongly su ers presence of nondivergent spurious modes whereas the approximate one does not satisfy the mass conservation, a strategy is suggested to obtain an exact projection but in two consecutive steps (DPM).…”

“…computed by means of (23), allow us to automatically satisfy the discrete continuity equation (22). They constitute a set of staggered velocities in a MAC-like arrangement but they do not su ce, by alone, to indicate the way to compute the divergence-free cell-centred updated velocities.…”

“…Along with the continuity errors an important issue to be analysed is the stability of the projection method for which it is required that the projector be bounded in some norm [9,13,14,22]. Hence, while deÿning the EPM-based projector P H such that v n+1 = P H (v * ), ∇· v n+1 = 0, it is well known that it is symmetric, idempotent and bounded, that is S(P H ) , sup x =0 ( P H (x) = x )61.…”

What does Finite Volume-based implicit filtering really resolve in Large-Eddy Simulations?

“…, is introduced.Then, instead of introducing the classical eddy viscosity expression m LES ¼ CD 2 eff jr s vj, a scaling formulation for the eddy viscosity function, originally developed by Wong and Lilly [48], is now used [41,42].This model directly adopts the Kolmogorov scaling law that is m LES ¼ C 2=3 D 4=3 eff e 1=3 , e being the dissipation rate, without equating this latter to the energy production.Thus, by assuming the same coefficient and the same rate of dissipation at primary filter and test-level (scale-invariance hypothesis),m LES ¼ C e D 4=3 eff and m 0…”