DYNAMICS OF DIRECT LARGE-SMALL SCALE COUPLINGS IN COHERENTLY FORCED TURBULENCE - CONCURRENT PHYSICAL-SPACE AND FOURIER-SPACE VIEWS

As discussed in a recent paper by Brasseur & Wei (1994), scale interac tions in fully developed turbulence are of two basic types in the Four ier-spectral view, The cascade of energy from large to small scales is embedded within 'local-to-non-local' triadic interactions separated i n scale by a decade or less. 'Distant' triadic interactions between wi dely disparate scales transfer negligible energy between the largest a nd smallest scales, but directly modify the structure of the smallest scales in relationship to the structure of the energy-dominated large scales. Whereas cascading interactions tend to isotropize the small sc ales as energy moves through spectral shells from low to high wavenumb ers, distant interactions redistribute energy within spectral shells i n a manner that leads to anisotropic redistributions of small-scale en ergy and phase in response to anisotropic structure in the large scale s. To study the role of long-range interactions in small-scale dynamic s, Yeung & Brasseur (1991) carried out a numerical experiment in which the marginally distant triads were purposely stimulated through a coh erent narrow-band anisotropic forcing at the large scales readily inte rpretable in both the Fourier- and physical-space views. It was found that, after one eddy turnover time, the smallest scales rapidly became anisotropic as a direct consequence of the marginally distant triadic group in a manner consistent with the distant triadic equations. Beca use these asymptotic equations apply in the infinite Reynolds number l imit, Yeung and Brasseur argued that the observed long-range effects s hould be applicable also at high Reynolds numbers. We continue the ana lysis of forced simulations in this study, focusing (i) on the detaile d three-dimensional restructuring of the small scales as predicted by the asymptotic triadic equations, and (ii) on the relationship between Fourier- and physical-space evolution during forcing. We show that th e three-dimensional restructuring of small-scale energy and vorticity in Fourier space from large-scale forcing is predicted in some detail by the distant triadic equations. We find that during forcing the dist ant interactions alter small-scale structure in two ways: energy is re distributed anisotropically within high-wavenumber spectral. shells, a nd phase correlations are established at the small scales by the dista nt interactions. In the numerical experiments, the long-range interact ions create two pairs of localized volumes of concentrated energy in t hree-dimensional Fourier space at high wavenumbers in which the Fourie r modes are phase coupled. Each pair of locally phase-correlated volum es of Fourier modes separately corresponds to aligned vortex tubes in physical space in two orthogonal directions. We show that the dynamics of distant interactions in creating mall-scale anisotropy may be desc ribed in physical space by differential advection and distortion of sm all-scale vorticity by the coherent large-scale energy-containing eddi es, producing anisotropic alignment of small-scale vortex tubes. Scali ng arguments indicate a disparity in timescale between distant triadic interactions and energy-cascading local-to-non-local interactions whi ch increases with scale separation. Consequently, the small scales res pond to forcing initially through the distant interactions. However, a s energy cascades from the large-scale to the small-scale Fourier mode s, the stimulated distant interactions become embedded within a sea of local-to-non-local energy cascading interactions which reduce (but do not eliminate) small-scale anisotropy at later times. We find that wh ereas the small-scale structure is still anisotropic at these later ti mes, the second-order velocity moment tenser is insensitive to this an isotropy. Third-order moments, on the ether hand, do detect the anisot ropy. We conclude that whereas a single statistical measure of anisotr opy can be used to indicate the presence of anisotropy, a null result in that measure does not necessarily imply that the signal is isotropi c. The results indicate that non-equilibrium non-stationary turbulence is particularly sensitive to ion-range interactions and deviations fr om local isotropy.