Mixing of scalars in turbulent flows using direct numerical simulations

Abstract

The research presented in this thesis focuses on scalar mixing in unstratified (neutral) flows and stably stratified flows using Direct Numerical Simulations (DNS). Such flows are ubiquitous in natural flows such as rivers, estuaries, oceans and the atmosphere. First, a detailed study was performed to investigate the effect of varying Schmidt numbers (Sc) on turbulent mixing of a passive scalar in a stationary homogeneous unstratified flow using forced DNS. A total of 6 simulations were performed for 0.1 ≤ Sc < 3. Qualitative and quantitative results of the flow field and the passive scalar fields are presented and discussed. The effect of the Schmidt number on the turbulent mixing was found to be negligible and becomes important (as it should) only when mixing occurs under laminar flow conditions. Using a model proposed by Venayagamoorthy and Stretch in 2006 for the turbulent diascalar diffusivity as a basis, a practical (and new) model for quantifying the turbulent diascalar diffusivity is proposed asKS = 1.1 γ' LT k1/2, where LT is defined as the Thorpe length scale, k is the turbulent kinetic energy and γ' is one-half of the mechanical to scalar time scale ratio, which was shown by previous researchers to be approximately 0.7. The novelty of the proposed model lies in the use of LT, which is a widely used length scale in stably stratified flows (almost exclusively used in oceanography), for quantifying turbulent mixing in unstratified flows. LT can be readily obtained in the field using a Conductivity, Temperature and Depth (CTD) profiler or obtained from density fields in a numerical model. The turbulent kinetic energy is mostly contained in the large scales of the flow field and hence can be measured in the field using devices such as an Acoustic Doppler Current Profiler (ADCP) or modeled in numerical simulations. Comparisons using DNS data show remarkably good agreement between the predicted and exact diffusivities. Finally, the suitability of the proposed model for stably stratified flows was explored for varying degrees of stratification ranging from mildly stable flow conditions to strongly stable conditions. In stably stratified flows, density variations of the fluid dynamically affect the flow field and hence the density acts as what is widely known as an active scalar. Under strongly stable conditions, the DNS results indicate an inverse relationship between the Thorpe scale LT and kinetic energy length scale Lkε, which is different to the direct (almost one to one correspondence) relationship that was found for unstratified flows. Hence, in order to account for this difference, a modified turbulent diascalar diffusivity model was proposed as Kd = 13 γ' LT3 k1/2. It must be noted that this modified model while dimensionally inconsistent (due to the inverse relationship between the length scales), provides reasonable quantitative estimates of the diffusivity under stably stratified flow conditions. The models proposed in this study require further (extensive) testing under higher Reynolds number flow conditions. If shown to be valid, they would be widely useful for quantifying turbulent mixing using field measurements of large scale quantities (i.e. LT and k) as well as a simple and improved turbulence closure scheme.