Original Article On the frame dependence and form invariance of the transport equations for the Reynolds stress tensor and the turbulent heat flux vector: its consequences on closure models in turbulence modelling

1996 ◽  
Vol 8 (6) ◽  
pp. 341-349 ◽  
Author(s):  
Amsini Sadiki ◽  
Kolumban Hutter
Keyword(s):  
Heat Flux ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Turbulent Heat Flux ◽  
Turbulence Modelling ◽  
Turbulent Heat ◽  
Flux Vector ◽  
Form Invariance ◽  
Heat Flux Vector ◽  
Frame Dependence

An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows

2013 ◽  
Vol 723 ◽  
pp. 91-125 ◽  
Author(s):  
W. M. J. Lazeroms ◽  
G. Brethouwer ◽  
S. Wallin ◽  
A. V. Johansson
Keyword(s):  
Heat Flux ◽  
Kinetic Energy ◽  
Temperature Gradient ◽  
Reynolds Stress ◽  
Turbulent Heat Flux ◽  
Turbulent Heat ◽  
Homogeneous Shear ◽  
Self Consistent ◽  
The Mean ◽  
Homogeneous Shear Flow

AbstractThis work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a$K\text{{\ndash}} \omega $model (where$K$is turbulent kinetic energy and$\omega $an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

scholarly journals Explicit Algebraic Reynolds-stress Modelling of a Convective Atmospheric Boundary Layer Including Counter-Gradient Fluxes

2020 ◽  
Author(s):  
Velibor Želi ◽  
Geert Brethouwer ◽  
Stefan Wallin ◽  
Arne V. Johansson
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Atmospheric Boundary Layer ◽  
Reynolds Stress ◽  
Turbulent Heat Flux ◽  
Gradient Term ◽  
Turbulent Heat ◽  
Bound Layer Meteorol ◽  
Wide Range ◽  
Stable Atmospheric Boundary Layer

AbstractIn a recent study (Želi et al. in Bound Layer Meteorol 176:229–249, 2020), we have shown that the explicit algebraic Reynolds-stress (EARS) model, implemented in a single-column context, is able to capture the main features of a stable atmospheric boundary layer (ABL) for a range of stratification levels. We here extend the previous study and show that the same formulation and calibration of the EARS model also can be applied to a dry convective ABL. Five different simulations with moderate convective intensities are studied by prescribing surface heat flux and geostrophic forcing. The results of the EARS model are compared to large-eddy simulations of Salesky and Anderson (J Fluid Mech 856:135–168, 2018). It is shown that the EARS model performs well and is able to capture the counter-gradient heat flux in the upper part of the ABL due to the presence of the non-gradient term in the relation for vertical turbulent heat flux. The model predicts the full Reynolds-stress tensor and heat-flux vector and allows us to compare other important aspects of a convective ABL such as the profiles of vertical momentum variance. Together with the previous studies, we show that the EARS model is able to predict the essential features of the ABL. It also shows that the EARS model with the same model formulation and coefficients is applicable over a wide range of stable and moderately unstable stratifications.

scholarly journals Mean-field theory of differential rotation in density stratified turbulent convection

2018 ◽  
Vol 84 (2) ◽  
Author(s):  
I. Rogachevskii ◽  
N. Kleeorin
Keyword(s):  
Field Theory ◽  
Heat Flux ◽  
Reynolds Stress ◽  
Differential Rotation ◽  
Mean Field Theory ◽  
Mean Field ◽  
Turbulent Heat Flux ◽  
Turbulent Convection ◽  
Turbulent Heat ◽  
Adopted Model

A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral $\unicode[STIX]{x1D70F}$ approach, which is valid for large Reynolds and Péclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.

Fluid Mechanics and Heat Transfer Measurements in Transitional Boundary Layers Conditionally Sampled on Intermittency

1994 ◽  
Vol 116 (3) ◽  
pp. 405-416 ◽  
Author(s):  
J. Kim ◽  
T. W. Simon ◽  
M. Kestoras
Keyword(s):  
Heat Flux ◽  
Plate Boundary ◽  
Turbulent Heat Flux ◽  
Transitional Flow ◽  
Turbulent Heat ◽  
Mean Velocity ◽  
Power Spectral ◽  
Turbulent Characteristics ◽  
Transition Models ◽  
Prandtl Numbers

An experimental investigation of transition on a flat-plate boundary layer was performed. Mean and turbulence quantities, including turbulent heat flux, were sampled according to the intermittency function. Such sampling allows segregation of the signal into two types of behavior—laminarlike and turbulentlike. Results show that during transition these two types of behavior cannot be thought of as separate Blasius and fully turbulent profiles, respectively. Thus, simple transition models in which the desired quantity is assumed to be an average, weighted on intermittency, of the laminar and fully turbulent values may not be entirely successful. Deviation of the flow identified as laminarlike from theoretical laminar behavior is due to a slow recovery after the passage of a turbulent spot, while deviation of the flow identified as turbulentlike from fully turbulent characteristics is possibly due to an incomplete establishment of the fully turbulent power spectral distribution. Measurements were taken for two levels of free-stream disturbance—0.32 and 1.79 percent. Turbulent Prandtl numbers for the transitional flow, computed from measured shear stress, turbulent heat flux, and mean velocity and temperature profiles, were less than unity.

PROPERTIES OF HEAT FLUX FUNCTIONS AND A LINEAR THEORY OF HEAT FLUX

1995 ◽  
Vol 09 (09) ◽  
pp. 1113-1122 ◽  
Author(s):  
LIQIU WANG
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Linear Function ◽  
Linear Theory ◽  
Strain Tensor ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Flux Vector ◽  
Heat Flux Vector

The symmetry and positive definiteness of thermal conductivity tensor K are used to derive some properties of heat flux functions ɸi (i=0, 1, 2). All ɸi are shown to be real-valued. Both ɸ0 and ɸ2 are found to be positive definite, and ɸ1 is constrained between −(ɸ0 + ɸ2) and (ɸ0 + ɸ2). By assuming heat flux vector q to be a linear function of temperature gradient ∇θ and velocity strain tensor D, ɸi reduce to three coefficients which are independent of D and ∇θ.

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