On a solution of the closure problem for dry convective boundary layer turbulence and beyond

We consider the closure problem of representing the higher order moments (HOMs) in terms of lower-order moments, a central feature in turbulence modelling based on the Reynolds-Averaged Navier-Stokes (RANS) approach. Our focus is on models suited for the description of asymmetric, non-local and semi-organized turbulence in the dry atmospheric convective boundary layer (CBL). We establish a multivariate probability density function (PDF) describing populations of plumes which are embedded in a sea of weaker randomly spaced eddies, and apply an assumed Delta-PDF approximation. The main content of this approach consists of capturing the bulk properties of the PDF. We solve the closure problem analytically for all relevant higher order moments (HOMs) involving velocity components and temperature and establish a hierarchy of new non-Gaussian turbulence closure models of different content and complexity ranging from analytical to semi-analytical. All HOMs in the hierarchy have a universal and simple functional form. They refine the widely used Millionshchikov closure hypothesis and generalize the famous quadratic skewness-kurtosis relationship to higher-order. We examine the performance of the new closures by comparison with measurement, LES and DNS data and derive empirical constants for semi-analytical models, which are best for practical applications. We show that the new models have a good skill in predicting the HOMs for atmospheric CBL. Our closures can be implemented in second-, third- and fourth-order RANS turbulence closure models of bi-, tri-and four-variate levels of complexity. Finally, several possible generalizations of our approach are discussed.

A Fine Grid Tide-Wave-Ocean Circulation Coupled Model for the Yellow Sea: Comparison of Turbulence Closure Schemes in Reproducing Temperature Distributions

The performance of three turbulence closure schemes (TCSs), the generic length scale scheme (GLS), the Mellor–Yamada 2.5 scheme (MY2.5) and the K-profile parameterization scheme (KPP), embedded in the ocean model ROMS, was compared with attention to the reproduction of summertime temperature distribution in the Yellow Sea. The ROMS model has a horizontal resolution of 1/30° and 30 vertical sigma layers. For model validation, root mean square errors were checked, comparing model results with wave and temperature buoy data as well as tidal station data supplied by various organizations within the Republic of Korea. Computed temperature and vertical temperature diffusion coefficients were mainly compared along Lines A (36° N) and B (125° E) crossing the central Yellow Sea, Lines C (32° N) and E (34° N) passing over the Yangtze Bank and Line D off the Taean Peninsula. Calculations showed that GLS and MY2.5 produced vertical mixing stronger than KPP in both the surface and bottom layers, but the overall results were reasonably close to each other. The lack of observational data was a hindrance in comparing the detailed performance between the TCSs. However, it was noted that the simulation capability of cold patches in the tidal mixing front can be useful in identifying the better performing turbulence closure scheme. GLS and MY2.5 clearly produced the cold patch located near the western end of Line E (122° E–122.3° E), while KPP hardly produced its presence. Similar results were obtained along Line D but with a less pronounced tidal mixing front. Along Line C, GLS and MY2.5 produced a cold patch on the western slope of the Yellow Sea, the presence of which had never been reported. Additional measurements near 125° E–126° E of Line C and along the channel off the Taean Peninsula (Line D) are recommended to ensure the relative performance superiority between the TCSs.

Turbulence Characteristics Across a Range of Idealized Urban Canopy Geometries

Good representation of turbulence in urban canopy models is necessary for accurate prediction of momentum and scalar distribution in and above urban canopies. To develop and improve turbulence closure schemes for one-dimensional multi-layer urban canopy models, turbulence characteristics are investigated here by analyzing existing large-eddy simulation and direct numerical simulation data. A range of geometries and flow regimes are analyzed that span packing densities of 0.0625 to 0.44, different building array configurations (cubes and cuboids, aligned and staggered arrays, and variable building height), and different incident wind directions ($$0^\circ $$ 0 ∘ and $$45^\circ $$ 45 ∘ with regards to the building face). Momentum mixing-length profiles share similar characteristics across the range of geometries, making a first-order momentum mixing-length turbulence closure a promising approach. In vegetation canopies turbulence is dominated by mixing-layer eddies of a scale determined by the canopy-top shear length scale. No relationship was found between the depth-averaged momentum mixing length within the canopy and the canopy-top shear length scale in the present study. By careful specification of the intrinsic averaging operator in the canopy, an often-overlooked term that accounts for changes in plan area density with height is included in a first-order momentum mixing-length turbulence closure model. For an array of variable-height buildings, its omission leads to velocity overestimation of up to $$17\%$$ 17 % . Additionally, we observe that the von Kármán coefficient varies between 0.20 and 0.51 across simulations, which is the first time such a range of values has been documented. When driving flow is oblique to the building faces, the ratio of dispersive to turbulent momentum flux is larger than unity in the lower half of the canopy, and wake production becomes significant compared to shear production of turbulent momentum flux. It is probable that dispersive momentum fluxes are more significant than previously thought in real urban settings, where the wind direction is almost always oblique.

Numerical Analysis of a Hybrid Stochastic Turbulence Model for Stable Stratification

<p>We present results on the modeling of intermittent turbulence in the nocturnal boundary<br>layer using a data-driven approach. In high stratification and weak wind conditions, the<br>bulk shear can be too weak to sustain continuous turbulence and the sporadic submesoscale<br>motions trigger the turbulence production.<br>The main idea is to extend a TKE-based, 1.5 order turbulence closure model by in-<br>troducing a stochastic differential equation (SDE) for the nondimensional correction of the<br>mixing length. Such a nonstationary SDE model is built upon the traditional surface-layer<br>scaling functions, which model the effect of the static stability on the surface-layer profiles<br>using scaling with the Richardson (Ri) number . The nonstationary parameters of the SDE<br>equation are determined from data with a model-based clustering approach. Furthermore, it<br>is found that parameters scale with the local gradient Ri number, resulting in a closed-form<br>nonstationary stability correction depending only on this local gradient Ri number. Benefi-<br>cial is the interpretation of the noise term of the SDE. This term is interpreted as an effect<br>of the submesoscale motions on turbulent mixing. Furthermore, the SDE model provides<br>a conceptual view on intermittent turbulence, whereby in the noise-free limit, the steady-<br>state solution converges to the traditional functional scaling. Per construction, the SDE<br>is readily incorporated in a turbulence closure by modifying the definition of the stability<br>correction. Details will be provided.<br>We will present a numerical analysis of such a hybrid model for quasi-steady-state so-<br>lutions with different model settings. Furthermore, we investigate the regime transitions<br>between weakly and strongly stable flows under intermittent mixing based on the temper-<br>ature inversion characteristics.</p>

Flow Physics in a Large Rotor Tip Gap in a Multi-Stage Axial Compressor

The flow physics in a large rotor tip gap in a 1.5-stage axial compressor is investigated in the current study. The flow structure in the rotor tip region is complex with several dominant vortical structures of opposite rotation, resulting in inhomogeneous and highly anisotropic turbulence. Earlier measurements show that eddy viscosity is negative over large parts of the tip region and eddy viscosity varies among stress/strain components. The present study aims to understand how the complex nature of rotor tip leakage flow affects compressor performance when the tip gap size is greater than 4–5% of the rotor span, which is typical of advanced small core engines. Unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) techniques are applied to study flow physics in a large rotor tip gap (5.5% of rotor span) in a 1.5-stage axial compressor. Calculated flow fields from the two different approaches are compared with available measurements and examined in detail. LES calculates the pressure rise in the present compressor fairly well, while URANS with a standard two-equation turbulence closure underpredicts the pressure rise by 15–20% of the measured values. The current study shows that URANS with the current turbulence closure produces much higher all-positive eddy viscosity in the tip-gap region compared to measurements and LES. The distribution of eddy viscosity in the URANS simulation is also wrong. Consequently, the flow in the tip region is highly damped with significantly larger blockage generation, which results in the tip leakage vortex (TLV) staying closer to the blade suction side compared to the measurement. When the TLV stays closer to the blade, both flow turning and the pressure rise across the compressor are reduced compared to the measurements. It appears that this effect is amplified by a large rotor tip gap.