TY - JOUR

T1 - Large eddy simulations of thermal convection at high Rayleigh number

AU - Cantin, Noä

AU - Vincent, Alain P.

AU - Yuen, David A.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - With the vastly improved speed and the new shared-memory architecture of the current massively parallel systems, it is now possible to simulate thermal convection at very high Rayleigh (Ra) number lying in the turbulent regime. However, both the dynamics and the interaction with the turbulence may be simultaneously important. Even when only the large scales are of interest, we cannot simply ignore the smallest scales because of the feedback from strong non-linearities everywhere in the flow. Large eddy simulation (LES), a time-honoured method in engineering fluid mechanics and meteorology, may be the only way to simulate the time-dependent physics in its full complexity, while keeping a reasonable accuracy at the largest scales in highly nonlinear geophysical fluid dynamical flows, such as mantle convection in the early Earth, convection inside the Jovian moons and the geodynamo. We have tested here a LES model based on the Smagorinsky assumption for 2-D turbulent convection for a finite Prandtl (Pr) number fluid with Pr = 1, free-slip boundary conditions and an aspect ratio of 3. The subgrid-scale model is only employed for the temperature equation, where the steepest gradients are developed. The same model can also be used for infinite Prandtl number convection. This LES model has been validated by comparison with direct numerical simulation (DNS) for Ra between 108 and 1010 with a grid up to 512 x 1536 points. Statistical properties of the flow based on LES are presented for the probability distribution functions (PDF) in space and also the spectra describing the thermal and kinetic energy distributions for Ra up to 1010.

AB - With the vastly improved speed and the new shared-memory architecture of the current massively parallel systems, it is now possible to simulate thermal convection at very high Rayleigh (Ra) number lying in the turbulent regime. However, both the dynamics and the interaction with the turbulence may be simultaneously important. Even when only the large scales are of interest, we cannot simply ignore the smallest scales because of the feedback from strong non-linearities everywhere in the flow. Large eddy simulation (LES), a time-honoured method in engineering fluid mechanics and meteorology, may be the only way to simulate the time-dependent physics in its full complexity, while keeping a reasonable accuracy at the largest scales in highly nonlinear geophysical fluid dynamical flows, such as mantle convection in the early Earth, convection inside the Jovian moons and the geodynamo. We have tested here a LES model based on the Smagorinsky assumption for 2-D turbulent convection for a finite Prandtl (Pr) number fluid with Pr = 1, free-slip boundary conditions and an aspect ratio of 3. The subgrid-scale model is only employed for the temperature equation, where the steepest gradients are developed. The same model can also be used for infinite Prandtl number convection. This LES model has been validated by comparison with direct numerical simulation (DNS) for Ra between 108 and 1010 with a grid up to 512 x 1536 points. Statistical properties of the flow based on LES are presented for the probability distribution functions (PDF) in space and also the spectra describing the thermal and kinetic energy distributions for Ra up to 1010.

KW - Finite Prandtl number

KW - Large eddy simulations (LES)

KW - Turbulent convection

KW - Very high Rayleigh numbers

UR - http://www.scopus.com/inward/record.url?scp=0034098184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034098184&partnerID=8YFLogxK

U2 - 10.1046/j.1365-246X.2000.00005.x

DO - 10.1046/j.1365-246X.2000.00005.x

M3 - Article

AN - SCOPUS:0034098184

VL - 140

SP - 163

EP - 174

JO - Geophysical Journal International

JF - Geophysical Journal International

SN - 0956-540X

IS - 1

ER -