A DNS-based thermal second-moment closure for buoyant convection at vertical walls

Direct numerical simulations (DNS) of natural convection in a vertical chan nel by Versteegh & Nieuwstadt (1998) are used for assessing the budget of t he turbulent heat flux <(theta u(i))over bar> and the temperature variance <(theta(2))over bar>, and for modelling the transport equations governing t hese two properties. The analysis is confined to a simple fully developed s ituation in which the gravitational vector, as the sole driving force, is p erpendicular to the only non-zero component of the mean temperature gradien t. Despite its simplicity, the flow displays many interesting features and represents a generic case of the interaction of buoyancy-driven turbulent t emperature and velocity fields. The paper discusses the near-wall variation of the second moments and their budgets, as well as possible scaling of <( theta u(i))over bar> and <(theta(2))over bar> both in the near-wall region and away from the wall. Various proposals for the Reynolds-averaged modelli ng are analysed and new models are proposed for these two transport equatio ns using the term-by-term approach. An a priori test (using the DNS data fo r properties other than <(theta u(i))over bar> and <(theta(2))over bar>) re produced very well all terms in the transport equations, as well as their n ear-wall behaviours and wall limits, without the use of any wall-topology-d ependent parameters. The computational effort is still comparable to that f or the 'basic model'. The new term-by-term model of the <(theta u(i))over b ar> and <(theta(2))over bar> equations was then used for a full simulation in conjunction with a low-Reynolds-number second-moment velocity closure, w hich was earlier found to reproduce satisfactorily a variety of isothermal wall flows. Despite excellent term-by-term reproduction of thermal turbulen ce, the predictions with the full model show less satisfactory agreement wi th the DNS data than a priori validation, indicating a further need for imp rovement of the modelling of buoyancy effects on mechanical turbulence.