Emergence of optimal disturbances in a stratified turbulent shear flow under the stochastic forcing

Large-scale inclined organized structures in stably stratified turbulent shear flows were revealed in the numerical simulation and indirectly confirmed by the field measurements in the stable atmospheric boundary layer. Spatial scales and forms of these structures coincide with those of the optimal disturbances of a simplified linear model. In this paper, we clarify the relation between the organized structures and the optimal disturbances, analyzing a time series of turbulent fields obtained by the RANS model with eddy viscosity/diffusivity and stochastic forcing generating the small-scale turbulence.

Velocity gradient statistics in turbulent shear flow: an extension of Kolmogorov's local equilibrium theory

This paper presents an extension of Kolmogorov's local similarity hypotheses of turbulence to include the influence of mean shear on the statistics of the fluctuating velocity in the dissipation range of turbulent shear flow. According to the extension, the moments of the fluctuating velocity gradients are determined by the local mean rate of the turbulent energy dissipation $\left \langle \epsilon \right \rangle$ per unit mass, kinematic viscosity $\nu$ and parameter $\gamma \equiv S (\nu /\left \langle \epsilon \right \rangle )^{1/2}$ , provided that $\gamma$ is small in an appropriate sense, where $S$ is an appropriate norm of the local gradients of the mean flow. The statistics of the moments are nearly isotropic for sufficiently small $\gamma$ , and the anisotropy of moments decreases approximately in proportion to $\gamma$ . This paper also presents a report on the second-order moments of the fluctuating velocity gradients in direct numerical simulations (DNSs) of turbulent channel flow (TCF) with the friction Reynolds number $Re_\tau$ up to $\approx 8000$ . In the TCF, there is a range $y$ where $\gamma$ scales approximately $\propto y^ {-1/2}$ , and the anisotropy of the moments of the gradients decreases with $y$ nearly in proportion to $y^ {-1/2}$ , where $y$ is the distance from the wall. The theoretical conjectures proposed in the first part are in good agreement with the DNS results.

Spatial and statistical analysis of coherent vortical structures within a stress-driven free-surface turbulent shear flow

<p>The water surface under high wind condition is characterized by elongated high-speed streaks and randomly emerged low-speed streaks, which are attributed to underneath coherent vortical motions. These vortical structures within aqueous turbulent boundary layer plays a critical role in turbulent exchange, their characteristics and statistics are therefore of interest in this study. Direct numerical simulation of an aqueous turbulent flow bounded by a stress-driven flat free surface was performed. Simulation results of cases with high wind condition (surface friction velocity = 1.22 cm/s) as well as weak wind condition (surface friction velocity = 0.71 cm/s) are analyzed. To identify the underlying vortical structures, an indicator of swirling strength derived from local velocity-gradient tensor is adopted. A formal classification scheme, based on the topological geometry of the vortex core, is then applied to classify the identified structures. Surface layers with the two wind conditions reveal similar results in statistics and spatial distribution of vortical structures. Two types of characteristic vortices which induce the surface streaks are extracted, including quasi-streamwise vortex and reversed horseshoe vortex (head pointing upstream), most inclining at about 10 to 20 degrees. Quasi-streamwise vortices are the dominant structure, and both high- and low-speed streaks are fringed with such vortices; they adjoin the surface streaks as counter-rotating arrays in either staggered or side-by-side spatial arrangement. The length of quasi-streamwise vortices, however, are significantly shorter than the corresponding surface streaks, only 10% of the extracted quasi-streamwise vortices are longer than 150 wall units. Reversed horseshoe vortices, associated with downwelling motions and surface convergence, are located beneath the high-speed streaks. In contrast to the turbulent boundary layer next to a flat wall, typical forward horseshoe vortices (head pointing downstream) associated with upwelling motions are barely found within the free-surface turbulent shear flow.</p><p>This work was supported by the Taiwan Ministry of Science and Technology (MOST 107-2611-M-002 -014 -MY3).</p>

The spacing of streaks in wind waves from low to high wind

<p>Quasi-streamwise vortices within aqueous shear layer beneath wind waves are found to contribute significantly to the scalar transfer across the air-water interface. These streamwise vortices manifest themselves by inducing distinct elongated high-speed streaks on the interface. The density of these streaks, which can be quantified by the transverse spacing of streaks, thus characterizes the interfacial scalar transfer contributed by the quasi-streamwise vortices. Thermal imageries of laboratory wind waves and flow fields obtained from numerical simulations of turbulent shear flows bounded by stress-driven flat boundary and wavy surface are utilized to study the characteristics of streak spacings and their dependence on wind speed. Consistent with previous studies, analyses of the thermal imageries of laboratory wind waves confirm that the streak spacings conform closely to a lognormal distribution, and the mean streak spacing <em>d</em> decreases as the wind speed increases. Revisiting the nondimensional mean spacing scaled by the viscous length, <em>d<sup>+</sup>=du<sup>*</sup></em>/<em>ν</em>, where <em>u<sup>*</sup></em> is the shear velocity of water and ν is the kinematic viscosity of water, however, reveals the different interpretations from the previous studies. For low to immediate wind-speed range,<em>u<sup>*</sup></em>< 0.5 cm/s, the nondimensional mean spacing does not follow the scaling of <em>d<sup>+</sup></em>≈ 100 observed in the turbulent wall layer; the scaled mean spacing <em>d<sup>+</sup></em>< 100. This is also observed in numerical simulation of turbulent shear flow bounded by a stress-driven flat surface. For immediate wind-speed range, 0.5 cm/s < <em>u<sup>*</sup></em>< 1.2 cm/s, within which surface waves become significant, the nondimensional mean streak spacings derived from the thermal imageries of wind waves remain to be less than the universal value of 100. The scaled mean streak spacing of simulated turbulent shear layer next to a stress-driven plane boundary, however, increases with the wind speed and approaches the value of 100 at this immediate wind-speed range. Imposing surface waves on the simulated turbulent shear flow significantly reduces the nondimensional streak spacing as observed on the wind-wave surfaces. Such reduction of streak spacings in finite-amplitude wind waves can be attributed to the additional wave stress arising in the oscillatory boundary layer, and the turning and stretching of turbulent vortices by the Lagrangian drift of progressive waves. At high wind speeds, <em>u<sup>*</sup> ></em> 1.2 cm/s, despite the occurrence of wave breaking, the scaled mean spacing approaches the universal value of 100 observed in the turbulent wall layer. This work was supported by the Taiwan Ministry of Science and Technology (MOST 107-2611-M-002 -014 -MY3).</p>