A Compressible Turbulence Model for Pressure—Strain

This work focuses on the performance and validation of compressible turbulence models for the pressure-strain correlation. Considering the Launder Reece and Rodi (LRR) incompressible model for the pressure-strain correlation, Adumitroaie et al., Huang et al., and Marzougui et al., used different modeling approaches to develop turbulence models, taking into account compressibility effects for this term. Two numerical coefficients are dependent on the turbulent Mach number, and all of the remaining coefficients conserve the same values as in the original LRR model. The models do not correctly predict the compressible turbulence at a high-speed shear flow. So, the revision of these models is the major aim of this study. In the present work, the compressible model for the pressure-strain correlation developed by Khlifi−Lili, involving the turbulent Mach number, the gradient, and the convective Mach numbers, is used to modify the linear mean shear strain and the slow terms of the previous models. The models are tested in two compressible turbulent flows: homogeneous shear flow and the newly developed plane mixing layers. The predicted results of the proposed modifications of the Adumitroaie et al., Huang et al., and Marzougui et al., models and of its universal versions are compared with direct numerical simulation (DNS) and experiment data. The results show that the important parameters of compressibility in homogeneous shear flow and in the mixing layers are well predicted by the proposal models.

Large Eddy Simulation and Dynamic Mode Decomposition of Turbulent Mixing Layers

Turbulent mixing layers are canonical flow in nature and engineering, and deserve comprehensive studies under various conditions using different methods. In this paper, turbulent mixing layers are investigated using large eddy simulation and dynamic mode decomposition. The accuracy of the computations is verified and validated. Standard dynamic mode decomposition is utilized to flow decomposition, reconstruction and prediction. It was found that the dominant-mode selection criterion based on mode amplitude is more suitable for turbulent mixing layer flow compared with the other three criteria based on singular value, modal energy and integral modal amplitude, respectively. For the mixing layer with random disturbance, the standard dynamic mode decomposition method could accurately reconstruct and predict the region before instability happens, but is not qualified in the regions after that, which implies that improved dynamic mode decomposition methods need to be utilized or developed for the future dynamic mode decomposition of turbulent mixing layers.

Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

In this paper, the Richtmyer–Meshkov instabilities in spherical and cylindrical converging geometries with a Mach number of approximately 1.5 are investigated by using the high resolution implicit large eddy simulation method, and the influence of the geometric effect on the turbulent mixing is investigated. The heavy fluid is sulphur hexafluoride (SF6), and the light fluid is nitrogen (N2). The shock wave converges from the heavy fluid into the light fluid. The Atwood number is 0.678. The total structured and uniform Cartesian grid node number in the main computational domain is 20483. In addition, to avoid the influence of boundary reflection, a sufficiently long sponge layer with 50 non-uniform coarse grids is added for each non-periodic boundary. Present numerical simulations have high and nonlinear initial perturbation levels, which rapidly lead to turbulent mixing in the mixing layers. Firstly, some physical-variable mean profiles, including mass fraction, Taylor Reynolds number, turbulent kinetic energy, enstrophy and helicity, are provided. Second, the mixing characteristics in the spherical and cylindrical turbulent mixing layers are investigated, such as molecular mixing fraction, efficiency Atwood number, turbulent mass-flux velocity and density self-correlation. Then, Reynolds stress and anisotropy are also investigated. Finally, the radial velocity, velocity divergence and enstrophy in the spherical and cylindrical turbulent mixing layers are studied using the method of conditional statistical analysis. Present numerical results show that the geometric effect has a great influence on the converging Richtmyer–Meshkov instability mixing layers.

Control of the abyssal ocean overturning circulation by mixing-driven bottom boundary layers

An emerging paradigm posits that the abyssal overturning circulation is driven by bottom-enhanced mixing, which results in vigorous upwelling in the bottom boundary layer (BBL) along the sloping seafloor and downwelling in the stratified mixing layer (SML) above; their residual is the overturning circulation. This boundary-controlled circulation fundamentally alters abyssal tracer distributions, with implications for global climate. Chapter 1 describes how a basin-scale overturning circulation arises from the coupling between the ocean interior and mixing-driven boundary layers over rough topography, such as the sloping flanks of mid-ocean ridges. BBL upwelling is well predicted by boundary layer theory, whereas the compensation by SML downwelling is weakened by the upward increase of the basin-wide stratification, which supports a finite net overturning. These simulated watermass transformations are comparable to best-estimate diagnostics but are sustained by a crude parameterization of boundary layer restratification processes. In Chapter 2, I run a realistic simulation of a fracture zone canyon in the Brazil Basin to decipher the non-linear dynamics of abyssal mixing layers and their interactions with rough topography. Using a hierarchy of progressively idealized simulations, I identify three physical processes that set the stratification of abyssal mixing layers (in addition to the weak buoyancy-driven cross-slope circulation): submesoscale baroclinic eddies on the ridge flanks, enhanced up-canyon flow due to inhibition of the cross-canyon thermal wind, and homogenization of canyon troughs below the level of blocking sills. Combined, these processes maintain a sufficiently large near-boundary stratification for mixing to drive globally significant BBL upwelling. In Chapter 3, simulated Tracer Release Experiments illustrate how passive tracers are mixed, stirred, and advected in abyssal mixing layers. Exact diagnostics reveal that while a tracer’s diapycnal motion is directly proportional to the mean divergence of mixing rates, its diapycnal spreading depends on both the mean mixing rate and an additional non-linear stretching term. These simulations suggest that the theorized boundary-layer control on the abyssal circulation is falsifiable: downwelling in the SML has already been confirmed by the Brazil Basin Tracer Release Experiment, while an upcoming experiment in the Rockall Trough will confirm or deny the existence of upwelling in the BBL.