Resolved energy budget of superstructures in Rayleigh-B\'{e}nard convection

Turbulent superstructures, i.e. large-scale flow structures in turbulent flows, play a crucial role in many geo- and astrophysical settings. In turbulent Rayleigh-B\'{e}nard convection, for example, horizontally extended coherent large-scale convection rolls emerge. Currently, a detailed understanding of the interplay of small-scale turbulent fluctuations and large-scale coherent structures is missing. Here, we investigate the resolved kinetic energy and temperature variance budgets by applying a filtering approach to direct numerical simulations of Rayleigh-B\'{e}nard convection at high aspect ratio. In particular, we focus on the energy transfer rate between large-scale flow structures and small-scale fluctuations. We show that the small scales primarily act as a dissipation for the superstructures. However, we find that the height-dependent energy transfer rate has a complex structure with distinct bulk and boundary layer features. Additionally, we observe that the heat transfer between scales mainly occurs close to the thermal boundary layer. Our results clarify the interplay of superstructures and turbulent fluctuations and may help to guide the development of an effective description of large-scale flow features in terms of reduced-order models

The effect of spanwise heterogeneous surfaces on mixed convection in turbulent channels

Turbulent mixed convection in channel flows with heterogeneous surfaces is studied using direct numerical simulations. The relative importance of buoyancy and shear effects, characterised by the bulk Richardson number $\textit{Ri}_{b}$, is varied in order to cover the flow regimes of forced, mixed and natural convection, which are associated with different large-scale flow organisations. The heterogeneous surface consists of streamwise-aligned ridges, which are known to induce secondary motion in the case of forced convection. The large-scale streamwise rolls emerging under smooth-wall mixed convection conditions are significantly affected by the heterogeneous surfaces and their appearance is considerably reduced for dense ridge spacings. It is found that the formation of these rolls requires larger buoyancy forces than over smooth walls due to the additional drag induced by the ridges. Therefore, the transition from forced convection structures to rolls is delayed towards larger $\textit{Ri}_{b}$ for spanwise heterogeneous surfaces. The influence of the heterogeneous surface on the flow organisation of mixed convection is particularly pronounced in the roll-to-cell transition range, where ridges favour the transition to convective cells at significantly lower $\textit{Ri}_{b}$. In addition, the convective cells are observed to align perpendicular to the ridges with decreasing ridge spacing. We attribute this reorganisation to the fact that flow parallel to the ridges experience less drag than flow across the ridges, which is energetically more beneficial. Furthermore, we find that streamwise rolls exhibit a very slow dynamics for $\textit{Ri}_{b}\textit{ = 1}$ and $\textit{Ri}_{b}\textit{ = 3.2}$ when the ridge spacing is of the order of the rolls’ width. For these cases the up- and downdrafts of the rolls move slowly across the entire channel instead of being fixed in space, as observed for the smooth-wall cases

A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation

Turbulent plane jets are prototypical free shear flows of practical interest in propulsion, combustion and environmental flows. While considerable experimental research has been performed on planar jets, very few computational studies exist. To the authors’ knowledge, this is the first computational study of spatially evolving three-dimensional planar turbulent jets utilizing direct numerical simulation. Jet growth rates as well as the mean velocity, mean scalar and Reynolds stress profiles compare well with experimental data. Coherency spectra, vorticity visualization and autospectra are obtained to identify inferred structures. The development of the initial shear layer instability, as well as the evolution into the jet column mode downstream is captured well. The large- and small-scale anisotropies in the jet are discussed in detail. It is shown that, while the large scales in the flow field adjust slowly to variations in the local mean velocity gradients, the small scales adjust rapidly. Near the centreline of the jet, the small scales of turbulence are more isotropic. The mixing process is studied through analysis of the probability density functions of a passive scalar. Immediately after the rollup of vortical structures in the shear layers, the mixing process is dominated by large-scale engulfing of fluid. However, small-scale mixing dominates further downstream in the turbulent core of the self-similar region of the jet and a change from non-marching to marching PDFs is observed. Near the jet edges, the effects of large-scale engulfing of coflow fluid continue to influence the PDFs and non-marching type behaviour is observed.Peer ReviewedPostprint (published version

Large-eddy simulation of Rayleigh-Taylor turbulence with compressible miscible fluids

Turbulence developed from Rayleigh-Taylor instability between two compressible miscible fluids in an unbounded domain is addressed in this paper. It is demonstrated that the turbulent Mach number in the turbulent core has an upper bound, independent of the density ratio under a broad range of initial mean configurations. The initial thermodynamic state of the system determines the amount of potential energy per unit mass involved in the turbulent mixing stage, and thus the characteristic level of turbulent fluctuations that is achievable is linked to the characteristic speed of sound such that the turbulent Mach number is limited. For the particular case of an ideal gas, this bound on the turbulent Mach number is found to be between 0.25 and 0.6, depending on the particular initial thermodynamic state. Hence, intrinsic compressibility effects those owing to large Mach number are likely to be limited in the turbulent stage of a pure Rayleigh-Taylor problem. This result is confirmed by large-eddy simulations LES of systems with density jumps at the interface of 3: 1, a density ratio for which there is extensive data available in the literature. The LES predictions of the mixing depth growth and overall mixing agree with results previously obtained in incompressible configurations with a negligibly small Mach number, and the data fully describing the Reynolds stresses and the budget of the resolved turbulent kinetic energy equation are provided.Peer ReviewedPostprint (published version

On the role of large-scale updrafts and downdrafts in deviations from Monin-Obukhov similarity theory in free convection

We investigate by means of direct numerical simulation how large-scale circulations produce deviations from Monin–Obukhov similarity theory (MOST) in the limit of free convection, disentangling the role of large-scale downdrafts from updrafts using conditional analysis. We compare the convective boundary layer to two other free-convective flows: Rayleigh–Bénard convection with an adiabatic top lid and classical Rayleigh–Bénard convection. This serves a dual purpose: firstly, to ascertain how changes in the upper boundary conditions and thereby in the large-scale circulations modify the near-surface behaviour and secondly, to assess to what extent we can extrapolate results from idealized systems to the unstable atmospheric surface layer. Using a low-pass filter to define the large scales we find that, whilst deviations from MOST occur within large-scale downdraft regions, strong deviations also occur within large-scale updraft regions. The deviations within updrafts are independent of the filter length scale used to define the large-scale circulations, independent of whether updrafts are defined as ascending air, or as air that is both ascending and positively buoyant, and are not due to changes with height of the updraft area fraction. This suggests that even updraft properties are not just determined locally, but also by outer scales. Cold, strong downdrafts in classical Rayleigh–Bénard convection notably modify the near-surface behaviour compared to the other two systems. For the moderate Reynolds numbers considered, Rayleigh–Bénard convection with an adiabatic top lid thus seems more appropriate than classical Rayleigh–Bénard convection for studying the unstable atmospheric surface layer in the limit of free convection.Peer ReviewedPostprint (published version

A refined statistical cloud closure using double-Gaussian probability density functions

We introduce a probability density function (PDF)-based scheme to parameterize cloud fraction, average liquid water and liquid water flux in large-scale models, that is developed from and tested against large-eddy simulations and observational data. Because the tails of the PDFs are crucial for an appropriate parameterization of cloud properties, we use a double-Gaussian distribution that is able to represent the observed, skewed PDFs properly. Introducing two closure equations, the resulting parameterization relies on the first three moments of the subgrid variability of temperature and moisture as input parameters. The parameterization is found to be superior to a single-Gaussian approach in diagnosing the cloud fraction and average liquid water profiles. A priori testing also suggests improved accuracy compared to existing double-Gaussian closures. Furthermore, we find that the error of the new parameterization is smallest for a horizontal resolution of about 5–20 km and also depends on the appearance of mesoscale structures that are accompanied by higher rain rates. In combination with simple autoconversion schemes that only depend on the liquid water, the error introduced by the new parameterization is orders of magnitude smaller than the difference between various autoconversion schemes. For the liquid water flux, we introduce a parameterization that is depending on the skewness of the subgrid variability of temperature and moisture and that reproduces the profiles of the liquid water flux well.Peer ReviewedPostprint (published version

Controlling entrainment in the smoke cloud using level set-based front tracking

Although large-eddy simulation (LES) has been shown to produce a reasonable representation of the turbulent circulations within the stratocumulus-topped boundary layer, it has difficulties to accurately predict cloud-top entrainment rates. In this paper, we present a front-tracking algorithm for LES to untangle the numerical and physical contributions to entrainment. Instead of resolving the cloud-top inversion, we treat it as a discontinuity separating the boundary layer from the free atmosphere and use the level set method to track its location. We apply our method to the smoke cloud test case as presented by Bretherton et al. (1999) which is simpler than stratocumulus in that it is only driven by radiative cooling avoiding evaporative feedbacks on entrainment. We present three-dimensional LES results with and without use of the level set method varying the grid resolution and the flux limiter. With the level set method, we prescribe zero entrainment and use this case to evaluate our method’s ability to maintain a non-entraining smoke-cloud layer. We use an empiricallybased entrainment law to estimate numerical errors. With the level set method, the prescribed entrainment rate was maintained with errors about one order of magnitude smaller than the entrainment errors found in the standard LES. At the same time, the dependence of the entrainment errors on the choice of the limiter was reduced by more than a factor of 10.Peer ReviewedPostprint (published version

Implications of non-local transport and conditionally averaged statistics on Monin- Obukhov similarity theory and Townsend ´s attached eddy hypothesis

According to Townsend’s hypothesis, so-called wall-attached eddies are the main contributors to turbulent transport in the atmospheric surface layer (ASL). This is also one of the main assumptions of Monin–Obukhov similarity theory (MOST). However, previous evidence seems to indicate that outerscale eddies can impact theASL, resulting in deviations from the classic MOST scaling. We conduct largeeddy simulations and direct numerical simulations of a dry convective boundary layer to investigate the impact of coherent structures on the ASL. A height-dependent passive tracer enables coherent structure detection and conditional analysis based on updrafts and subsidence. The MOST similarity functions computed from the simulation results indicate a larger deviation of the momentum similarity function fm from classical scaling relationships compared to the temperature similarity function fh. The conditionalaveraged fm for updrafts and subsidence are similar, indicating strong interactions between the inner and outer layers. However, fh conditioned on subsidence follows the mixed-layer scaling, while its updraft counterpart is well predicted by MOST. Updrafts are the dominant contributors to the transport of momentum and temperature. Subsidence, which comprises eddies that originate from the outer layer, contributes increasingly to the transport of temperature with increasing instability. However, u0 of different signs are distributed symmetrically in subsidence unlike the predominantly negative u0 as instability increases. Thus, the spatial patterns of u0w0 differ compared to u0w0 in regions of subsidence. These results depict the mechanisms for departure from the MOST scaling, which is related to the stronger role of subsidence.Peer ReviewedPostprint (published version