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Show "scalar gradient boundary layers." These dissipation layers result solely from the hydrodynamics of scalar mixing in turbulent flows. and imaging measurements as well as direct numerical simulations confirm that they remain present even in flows undergOing highly exothermic combustion reactions. The same advection-diffusion balance in the vortiCity transport equation leads to a similar localization of velocity gradients as w 11. In both cases. the one-dimensional self-similar structure within the e vortic ity and scalar dissipation layers allows development of a computational method that xploits this simplifying feature by incorporating it directly into the olution method [Tryggvason & Dahm 1990: Chang. Dahm & Tryggvason 1991. Suresh. Dahm & Tryggvason 1994: Dahm. Try&:,ovason & Zhuang 19961. In particular. spatial derivatives of the scalar field in the plane of the layer are small in comparison with the derivative along the layer-normal direction. Discarding spatial derivatives in all but the layer-normal direction n gives the parabolized form of (1) as (2) where cr is the local strain rate along n. From the self-similarity of the scalar profiles within these layers. we define local integral moments Gj of all orders j for the scalar gradient profile across each layer as +<>0 as G == f nj - dll, j = 0, 1, 2, ... J -00 an (3) The exact set of transport equations for these scalar gradient moments can be readily derived from (2). cfiving the ordinary differential equations (ODE's) for the timeevol u lion of the local mOInents as d G()(s) = ° dt dG,(s) = -O'(s)G (s) dt I dG2(s)_ J ( G( __ 2_G() - -- 0' s) ., s) R S 0 s dt - e c (4a) ( 4h) ( 4c) where the coordinate s identifies the location on the surface on which the gradients are concentrated. These local integral moment equations are xact. The infinite set of ODE's for the integral moments G, for j = (I . .... 00) are equival nt to the partial differential equation (POE) in (2). Howev r. owing to the lin rity of the on - dil11 nsional strained diffusion equation in (2). lhe 10 a l integr I m 111 nl quation have the property that they are exactly closed at any level of tru n ti n f th in fi n i tc set. In other words. the set of equations for th int crral mon1 nls G, for j = II ..... k) , involves only th moments G, of ord r k and I w r. As a r'suIL. Lh lime evolution 0 f th > local ITI0l11cnts up to any desired order can b del'rmined from th 10 al integral l'quaLioI1s wiLhoul any closure approximaLi n . Th LIM model determines the time-evolution of the integral moments everywhere on |