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The main interest in this study originated from the need to understand the mixing and entrainment processes occurring in the upper plenum of pool-type Liquid Metal Fast Breeder Reactors (LMFBRs) under conditions of natural convection and thermal stratification, and related problems such as thermal striping and associated material fatigue resulting from large temperature fluctuations. Since the mechanisms of turbulent heat and momentum exchange as well as mixing in stratified shear flows strongly depend on the fluid conductivity, basic numerical and experimental studies have been considered necessary for analyzing these effects. Analytically, these processes can be optimally studied in a temporally-developing mixing-layer configuration, which provides a useful and relatively simple general flow prototype. In this work, the mixing layer behavior is analyzed by means of very accurate numerical simulations, which yield detailed flow information since the flow fields can be derived at each location, and at each time step. Therefore, numerical simulations provide accurate, high-order statistics to complement the observational data from experiments. The technique used is Direct Numerical Simulation (DNS), no turbulence models are required, and all scales of the involved fields are resolved down to the dissipative scales. The spatial discretization scheme relies on the use of high-order basis functions. Fourier series are used in the homogenous, horizontal directions and, in the inhomogeneous, cross-stream direction, timeand field-dependent, exponentially-mapped, high-order Chebyshev polynomials are employed. With this spatial discretization scheme, fields of very different characteristic length scales, and including stratification and thermal conductivity effects, can be resolved and optimally followed in their time evolution. Time-stepping is also adaptive, based on several stability criteria, and therefore the CPU time required to perform transient simulations is reduced to a minimum. A large number of simulations has been performed. In all of these the initial Reynolds number (Re) is kept fixed at 400. The Prandtl number (Pr) varies from 0.00535 (liquid sodium at 350°C) to 6.9 (water at 20°C), for the two-dimensional simulations, but only to 2.2 (water at 80°C) for the three-dimensional simulations, due to resolution difficulties. The Richardson number (Ri) varies from 0.0 (no stratification) to 0.2 (close to critical, stable stratification). Besides the initial profile for the average velocity, various initial conditions for the velocity field perturbations are used, from purely deterministic, combined deterministicrandom, to purely random. The deterministic part is obtained by solving the related linear problem (the Orr-Sommerfeld equation for unstratified and the Taylor-Goldstein equation for stratified flows) to obtain eigenfunctions, which are then used to set up the initial conditions. With increasing randomness, the evolution of the layer approaches a more natural linear growth whereas, for the purely-deterministic simulation cases, very distinct periods of rapid growth and periods of nearly no growth (resulting from the saturation of the excited modes) can be observed.

Direct numerical simulation of a temporally-developing, stably-stratified mixing layer for a wide range of Richardson and Prandtl numbers