J. Fluid Mech. (2001), vol. 427, pp. 205–239. Printed in the United Kingdom c  2001 Cambridge University Press 205 Buoyancy- to inertial-range transition in forced stratified turbulence By GEORGE F. CARNEVALE 1 , M. BRISCOLINI 2 AND P. ORLANDI 3 1 Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0225, USA 2 IBM Italia S.p.A., Via Shangai 53, 00144 Roma, Italy 3 Dipartimento di Meccanica e Aeronautica, University of Rome, ‘La Sapienza’, via Eudossiana 18, 00184 Roma, Italy (Received 19 November 1999 and in revised form 7 August 2000) The buoyancy range, which represents a transition from large-scale wave-dominated motions to small-scale turbulence in the oceans and the atmosphere, is investigated through large-eddy simulations. The model presented here uses a continual forcing based on large-scale standing internal waves and has a spectral truncation in the isotropic inertial range. Evidence is presented for a break in the energy spectra from the anisotropic k −3 buoyancy range to the small-scale k −5/3 isotropic inertial range. Density structures that form during wave breaking and periods of high strain rate are analysed. Elongated vertical structures produced during periods of strong straining motion are found to collapse in the subsequent vertically compressional phase of the strain resulting in a zone or patch of mixed fluid. 1. Introduction Much of the large-scale variability in the atmosphere and oceans can be described as internal wave activity, while isotropic turbulence dominates at small scales. Between these extremes, the dynamics is a competition between waves and turbulence. The nature of this intermediate range, called the buoyancy or the saturation range, is highly controversial. A direct numerical simulation which could faithfully span the full range of the scales involved would be a great benefit; however, such simulations remain impractical because of the large range of scales that would need to be represented. On the other hand, as we shall argue below, techniques of large-eddy simulation (LES) should afford us the possibility of at least simulating flow in the buoyancy range and capturing the transition to the inertial range. The goal of this paper is to present some results that might confirm this hope and also give us some insight into the kinds of structures one should be able to observe in the density field of the buoyancy range. To be concrete about spatial scales, we will concentrate on the oceanic application, although much of the basic ideas that follow should hold for the atmospheric problem as well. The spectra of density and velocity fluctuations in the ocean have several distinguishable ranges. As a guide to these ranges, we follow the description in Holloway (1981) and use a similar schematic diagram (figure 1). Here φ represents either the spectrum of the vertical shear or the vertical gradient of temperature as a function of the vertical wavenumber k z . The axis of the vertical wavenumber is