Statistical Model of Turbulent Dispersion Recapitulated

A comprehensive summary and update is given of Brouwers’ statistical model that was developed during the previous decade. The presented recapitulated model is valid for general inhomogeneous anisotropic velocity statistics that are typical of turbulence. It succeeds and improves the semiempirical and heuristic models developed during the previous century. The model is based on a Langevin and diffusion equation of which the derivation involves (i) the application of general principles of physics and stochastic theory; (ii) the application of the theory of turbulence at large Reynolds numbers, including the Lagrangian versions of the Kolmogorov limits; and (iii) the systematic expansion in powers of the inverse of the universal Lagrangian Kolmogorov constant C0, C0 about 6. The model is unique in the collected Langevin and diffusion models of physics and chemistry. Presented results include generally applicable expressions for turbulent diffusion coefficients that can be directly implemented in numerical codes of computational fluid mechanics used in environmental and industrial engineering praxis. This facilitates the more accurate and reliable prediction of the distribution of the mean concentration of passive or almost passive admixture such as smoke, aerosols, bacteria, and viruses in turbulent flow, which are all issues of great societal interest.

Vertical distribution of Kolmogorov Constants of Atmospheric Turbulence over an Urban Surface

<p>The Kolmogorov constant is fundamental in stochastic models of turbulence, and significant in boundary layer meteorology especially. Though lots of experiments have been conducted to study Kolmogorov Constant, constant at high elevation and over urban surface was rarely researched. Therefore, in this paper, ultrasonic data at seven levels over an urban underlying surface were used to calculate the Kolmogorov constants of velocity. The results of Kolmogorov constants at the different floors indicated that the constants below 47m were smaller because of the influence of the urban canopy layer. Besides, the time-varying result showed that constants were universally independent of stability. Furthermore, Kolmogorov constant in this paper was close to the result determined by former experiments.</p>

Numerical study of isotropic ocean swell

A new algorithm is used for detailed numerical study of the evolution of isotropic swell in a homogeneous ocean. It is shown that the Zakharov-Filonenko spectrum occurs in an explosive manner in a short time. The Kolmogorov constant of the solution is estimated numerically.

Velocity-Based EDR Retrieval Techniques Applied to Doppler Radar Measurements from Rain: Two Case Studies

In this article, five velocity-based energy dissipation rate (EDR) retrieval techniques are assessed. The EDR retrieval techniques are applied to Doppler measurements from Transportable Atmospheric Radar (TARA)—a precipitation profiling radar—operating in the vertically fixed-pointing mode. A generalized formula for the Kolmogorov constant is derived, which gives potential for the application of the EDR retrieval techniques to any radar line of sight (LOS). Two case studies are discussed that contain rain events of about 2 and 18 h, respectively. The EDR values retrieved from the radar are compared to in situ EDR values from collocated sonic anemometers. For the two case studies, a correlation coefficient of 0.79 was found for the wind speed variance (WSV) EDR retrieval technique, which uses 3D wind vectors as input and has a total sampling time of 10 min. From this comparison it is concluded that the radar is able to measure EDR with a reasonable accuracy. Almost no correlation was found for the vertical wind velocity variance (VWVV) EDR retrieval technique, as it was not possible to sufficiently separate the turbulence dynamics contribution to the radar Doppler mean velocities from the velocity contribution of falling raindrops. An important cause of the discrepancies between radar and in situ EDR values is thus due to insufficient accurate estimation of vertical air velocities.

Effects of helicity on dissipation in homogeneous box turbulence

The dimensionless dissipation coefficient$\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D700}L/U^{3}$, where$\unicode[STIX]{x1D700}$is the dissipation rate,$U$the root-mean-square velocity and$L$the integral length scale, is an important characteristic of statistically stationary homogeneous turbulence. In studies of$\unicode[STIX]{x1D6FD}$, the external force is typically isotropic and large scale, and its helicity$H_{f}$either zero or not measured. Here, we study the dependence of$\unicode[STIX]{x1D6FD}$on$H_{f}$and find that it decreases$\unicode[STIX]{x1D6FD}$by up to 10 % for both isotropic forces and shear flows. The numerical finding is supported by static and dynamical upper bound theory. Both show a relative reduction similar to the numerical results. That is, the qualitative and quantitative dependence of$\unicode[STIX]{x1D6FD}$on the helicity of the force is well captured by upper bound theory. Consequences for the value of the Kolmogorov constant and theoretical aspects of turbulence control and modelling are discussed in connection with the properties of the external force. In particular, the eddy viscosity in large-eddy simulations of homogeneous turbulence should be decreased by at least 10 % in the case of strongly helical forcing.

Effects of fluctuating energy input on the small scales in turbulence

In the standard cascade picture of three-dimensional turbulent fluid flows, energy is input at a constant rate at large scales. Energy is then transferred to smaller scales by an intermittent process that has been the focus of a vast literature. However, the energy input at large scales is not constant in most real turbulent flows. We explore the signatures of these fluctuations of large-scale energy input on small-scale turbulence statistics. Measurements were made in a flow between oscillating grids, with ${R}_{\lambda } $ up to 262, in which temporal variations in the large-scale energy input can be introduced by modulating the oscillating grid frequency. We find that the Kolmogorov constant for second-order longitudinal structure functions depends on the magnitude of the fluctuations in the large-scale energy input. We can quantitatively predict the measured change with a model based on Kolmogorov’s refined similarity theory. The effects of fluctuations of the energy input can also be observed using structure functions conditioned on the instantaneous large-scale velocity. A linear parametrization using the curvature of the conditional structure functions provides a fairly good match with the measured changes in the Kolmogorov constant. Conditional structure functions are found to provide a more sensitive measure of the presence of fluctuations in the large-scale energy input than inertial range scaling coefficients.

Experimental study of the influence of anisotropy on the inertial scales of turbulence

We ask whether the scaling exponents or the Kolmogorov constants depend on the anisotropy of the velocity fluctuations in a turbulent flow with no shear. According to our experiment, the answer is no for the Eulerian second-order transverse velocity structure function. The experiment consisted of 32 loudspeaker-driven jets pointed toward the centre of a spherical chamber. We generated anisotropy by controlling the strengths of the jets. We found that the form of the anisotropy of the velocity fluctuations was the same as that in the strength of the jets. We then varied the anisotropy, as measured by the ratio of axial to radial root-mean-square (r.m.s.) velocity fluctuations, between 0.6 and 2.3. The Reynolds number was approximately constant at around ${R}_{\lambda } = 481$. In a central volume with a radius of 50 mm, the turbulence was approximately homogeneous, axisymmetric, and had no shear and no mean flow. We observed that the scaling exponent of the structure function was $0. 70\pm 0. 03$, independent of the anisotropy and regardless of the direction in which we measured it. The Kolmogorov constant, ${C}_{2} $, was also independent of direction and anisotropy to within the experimental error of 4 %.