Oleksii Rudenko

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.

Universal Model of Finite Reynolds Number Turbulent Flow in Channels and Pipes

In this Letter, we suggest a simple and physically transparent analytical model of pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model provides an accurate quantitative description of the profiles of the mean-velocity and Reynolds stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe, for a wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von Kàrmàn and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.

Analytic model of the universal structure of turbulent boundary layers

Turbulent boundary layers exhibit a universal structure that nevertheless is rather complex and is composed of a viscous sublayer, a buffer zone, and a turbulent log-law region. In this letter, we present a simple analytic model of turbulent boundary layers that culminates in explicit formulas for the profiles of the mean velocity, the kinetic energy, and the Reynolds stress as a function of the distance from the wall. The resulting profiles are in close quantitative agreement with measurements over the entire structure of the boundary layer without any need of refitting in the different zones.

Onset of Flow Induced Tonal Noise in Corrugated Pipe Segments

Corrugated pipes combine small-scale rigidity and large-scale flexibility, which make them very useful in industrial applications. The flow through such a pipe can induce strong undesirable tonal noise (whistling) and even drive integrity threatening structural vibrations. Placing a corrugated segment along a smooth pipe reduces the whistling, while this composite pipe still retains some global flexibility. The whistling is reduced by thermoviscous damping in the smooth pipe segment. For a given corrugated segment and flow velocity, one would like to predict the smooth pipe length just sufficient to avoid tonal noise: the onset of whistling. A linear model based on empirical data is proposed that predicts the conditions at the onset of whistling for a composite pipe at moderately high Reynolds numbers, Re: 3000 < Re < 100; 000. Experimental results for corrugated pipes of eight different corrugation geometries are presented revealing fair agreement with the theory. Based on these results, a universal qualitative prediction tool is obtained valid for corrugated pipe segments long compared to the acoustic wave-length.

Energy conservation and second-order statistics in stably stratified turbulent boundary layers

We address the dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the atmospheric boundary layer with a stable temperature stratification in mind. Traditional approaches to this problem, based on the profiles of mean quantities, velocity second-order correlations, and dimensional estimates of the turbulent thermal flux run into a well-known difficulty, predicting the suppression of turbulence at a small critical value of the Richardson number, in contradiction with observations. Phenomenological attempts to overcome this problem suffer from various theoretical inconsistencies. Here we present a closure approach taking into full account all the second-order statistics, which allows us to respect the conservation of total mechanical energy. The analysis culminates in an analytic solution of the profiles of all mean quantities and all second-order correlations removing the unphysical predictions of previous theories. We propose that the approach taken here is sufficient to describe the lower parts of the atmospheric boundary layer, as long as the Richardson number does not exceed an order of unity. For much higher Richardson numbers the physics may change qualitatively, requiring careful consideration of the potential Kelvin-Helmoholtz waves and their interaction with the vortical turbulence.

Corrugated pipe segment with anechoic termination: critical Mach number for whistling

Corrugated pipes combine local stiffness with global flexibility, which makes them very useful. A drawback of corrugated pipes is the whistling, which results from coupling of vortex shedding with acoustic plane waves due to the flow through the pipe. We consider the possibility to reduce whistling by placing a short corrugated pipe segment along a long smooth pipe. A linear model is proposed in which the magnitude of the dipolar sound source is determined empirically. The model allows to estimate the critical Mach number of the flow through the pipe above which the whistling will always occur even for anechoic pipe terminations.

Analytical modeling for heat transfer in sheared flows of nanofluids

We developed a model for the enhancement of the heat flux by spherical and elongated nanoparticles in sheared laminar flows of nanofluids. Besides the heat flux carried by the nanoparticles, the model accounts for the contribution of their rotation to the heat flux inside and outside the particles. The rotation of the nanoparticles has a twofold effect: it induces a fluid advection around the particle and it strongly influences the statistical distribution of particle orientations. These dynamical effects, which were not included in existing thermal models, are responsible for changing the thermal properties of flowing fluids as compared to quiescent fluids. The proposed model is strongly supported by extensive numerical simulations, demonstrating a potential increase of the heat flux far beyond the Maxwell-Garnett limit for the spherical nanoparticles. The road ahead, which should lead toward robust predictive models of heat flux enhancement, is discussed.

Hydrodynamic interaction between whistling axisymmetric cavities in the presence of a coupling longitudinal standing wave

An axisymmetric cavity along a pipe is a commonly encountered construction in industrial applications, which can also be considered as a unit element of a corrugated pipe. At critical conditions such a configuration causes severe noise problems, called whistling. Whistling is a self-sustained oscillation, driven by a flow-acoustic interaction. In the current study, the hydrodynamic interaction between two such cavities is addressed in the presence of a coupling standing wave along the pipe. The phenomenon is investigated both experimentally and numerically. The hydrodynamic interaction has a strong effect both for the amplitude and for the Strouhal number of the whistling, which depends critically on the separation distance between two adjacent cavities.

Velocity and energy profiles in two- versus three-dimensional channels : effects of an inverse- versus a direct-energy cascade

In light of some recent experiments on quasi two-dimensional (2D) turbulent channel flow we provide here a model of the ideal case, for the sake of comparison. The ideal 2D channel flow differs from its three-dimensional (3D) counterpart by having a second quadratic conserved variable in addition to the energy and the latter has an inverse rather than a direct cascade. The resulting qualitative differences in profiles of velocity V and energy K as a function of the distance from the wall are highlighted and explained. The most glaring difference is that the 2D channel is much more energetic, with K in wall units increasing logarithmically with the Reynolds number Re_{tau} instead of being Re_{tau} independent in 3D channels.