Hydrodynamic Turbulence Research Articles

Application of water quality indices for evaluating water quality and anthropogenic impact assessment

Influences of different environmental variables are predicted to increase during the next century in association with abrupt changes in water quality. Determining the magnitude of such effects is difficult because variation of environmental variables is generally unpredictable, and thus, available data are rare. In this study, water quality monitoring was conducted based on new operational indicators and multi-metric indices to evaluate water quality status and biological response at temporal and spatial scales in west coastal water of Malaysia. The trophic state index ranged from 6 to 8 in temporal and spatial scales and suggested a highly productive system with a high trophic level, characteristic of a low-quality system. The eutrophication index varied from 0.65 to 4.45 and most of the samples had a bad (49%) or poor (45.5%) water quality, and only 5.3% of the water samples had a moderate productive system with a moderate trophic level. In West Port, anthropogenic sources and natural processes are likely to contribute to increase in nutrient concentrations and trophic level in the water column. During the study period, no secondary symptoms or eutrophication events occurred which could be due to water exchange and hydrodynamic turbulence, which prevented the eutrophication development at this region.

Nuclear Power Plants with Circulating Uranium Hexafluoride Based Fuel. Results of Investigations of Fluid Dynamics and Heat Transfer. Applications, Challenges, and Prospects. An Overview

The propositions of the development of reactor systems using UF6 as the nuclear fuel were put forward in USSR and USA already in the fifties of the last century, while from the beginning of the seventies the UF6-based reactors have become considered as the power sources for spaceborne nuclear power plants (NPP). The application of UF6 circulating in the closed NPP contourmakes it possible to realize the potential advantages of the flow-through design due to the gaseous fuel mobility compared with the existing NPPs with solid cores. At different plant designs, reactor arrangements, and special flow organization in fuel elements the power range from hundreds of kilowatts to tens megawatts can be realized. The areas of application of power plants with circulating UF6 can, in particular, include the spaceborne NPPs of wide power range for electric and plasma rocket engines used in the manned flight to Mars, the reactor-laser with direct pumping of gaseous laser mixtures with nuclear fission products, and the on-ground nuclear electric power plants of new generation with high performance with respect to the fuel cycle and safety. On the basis of an analysis of the results of investigations performed in USSR and USA to the end of the nineties of the last century and presented in this overview it can be concluded that from the standpoint of the physics of working processes and constructional materials resistant in the UF6 environment, there are no insurmountable obstacles for developing the NPPs with circulating UF6. The list of problems, whose solution can favor the further development of this line of research, if it would be implemented, is formulated. In Section 1 the fuel element designs are described and the techniques of flow organization in them are experimentally validated. In Section 2 the computational and experimental support of the programs is presented. It includes the calculations of the fluid dynamics and heat and mass transfer, the thermal and transport properties of uranium hexafluoride, the special properties of uranium hexafluoride as a working body, and the uranium hexafluoride effect on the constructionalmaterials. In Section 3 the projects of spaceborne power plants of closed and open type on a wide power range are reviewed. In Section 4 one of the promising lines in the field of the nuclear energy use, namely, the reactor-laser development, is presented. Section 5 overviews the on-ground plants, where, apart from the electric power plants, of interest are transport power plants, high-temperature engineering systems, in particular, for hydrogen production, the plants for producing high neutron fluxes, and some others. Section 6 presents considerations concerning the realization of rig reactor experiments with uranium hexafluoride circulating in the reactor core, whose criticity is fully ensured by the gaseous UF6. These experiments could be the final stage in corroborating the power source of the new type both under space and on-ground conditions. Section 7 contains an analysis of the available publications on the state of the art of investigations in the United States, which allows one to suppose that in USA a vast program of studies on the use of nuclear reactors with circulating UF6 in the space and on-ground energetics is being systematically performed. In Section 8 some problems which need to be solved in developing the power plants with circulating uranium hexafluoride are listed; they require a vast amount of scientific research. The work on the determination of the design of the power plants with circulating UF6 and hydrodynamic processes occurring in them were conducted in the Keldysh Research Center (before 1976 the Institute of Thermal Processes) under the supervision of A.A. Pavel’ev, who was the author of many ideas in the field of hydrodynamic stability and turbulence realized in experimental setups and computationmethods. In memory of his invaluable contribution into this line of research the authors dedicate to him this overview.

Arbitrary-order Hilbert Spectral Analysis and Intermittency in Solar Wind Density Fluctuations

Abstract The properties of inertial- and kinetic-range solar wind turbulence have been investigated with the arbitrary-order Hilbert spectral analysis method, applied to high-resolution density measurements. Due to the small sample size and to the presence of strong nonstationary behavior and large-scale structures, the classical analysis in terms of structure functions may prove to be unsuccessful in detecting the power-law behavior in the inertial range, and may underestimate the scaling exponents. However, the Hilbert spectral method provides an optimal estimation of the scaling exponents, which have been found to be close to those for velocity fluctuations in fully developed hydrodynamic turbulence. At smaller scales, below the proton gyroscale, the system loses its intermittent multiscaling properties and converges to a monofractal process. The resulting scaling exponents, obtained at small scales, are in good agreement with those of classical fractional Brownian motion, indicating a long-term memory in the process, and the absence of correlations around the spectral-break scale. These results provide important constraints on models of kinetic-range turbulence in the solar wind.

Droplets behavior of subcooled dispersed phase under nucleate boiling of continuous phase of liquid emulsion

The paper considers the influence of the dispersed phase of the emulsion upon the nature of heat and mass transfer in systems of immiscible liquids. In particular, is studied the interfacial interaction and breakage of subcooled drops of the dispersed phase during bubble boiling of the continuous phase of the emulsion. They predetermine the complex nature of the joint behavior of hydrodynamic and thermal processes. It is known that the controlled conditions for dispersion of emulsions in MQCL method under the minimum amount of cooling lubrication be able to improve the quality of metal processing by 10–18% (Maruda et al., 2017). Phase changes liquid generate in it a special kind of pulsation motion: «hot» turbulence of the superheated continuous phase. She is generated by process formation of nuclei and growth of steam bubbles accompanying by the pressure pulsations. Thus heat energy is converted into mechanical energy of the perturbed by the movement of vapor bubbles in evaporating liquid. The formula for the evaluating perturbations of the continuous phase of the emulsion under the influence of vapor bubbles is proposed. The behavior of these fluctuations depends on the frequency of the viable vapor phase nuclei formation related to the heat flow density. The dependence, obtained by Labuntsov (2000) for boiling homogeneous liquid, is used as a characteristic of the thermal velocity.Taking into account the character of the boiling of the continuous phase of emulsion, the generalization of the Kolmogorov-Hinze model has been performed for breakage drops in isothermal flow of emulsion under the influence of turbulent fluctuations of velocity. A correlation model of “thermal” breakup is proposed, which is complementary to the physical representations of the breakup for subcooled drops during the liquid emulsion boiling. Using dimensionless criteria was justified the form of the correlation for the maximum stable droplet size and thermal velocity fluctuations. This makes it possible to relate mechanisms hydrodynamic and thermal processes at use of usual computer tools used in practice for engineering calculations. The correlation for the maximum stable droplet size and thermal velocity fluctuations was developed in a dimensionless form. The results of the model studies were evaluated using the experimental data on the breakup of drops of oil in coolant “oil-water” (Januszkiewicz et al., 2004). They were obtained under conditions of creeping flow in a narrow channel, eliminating the creation of ordinary hydrodynamic turbulence. A good agreement with experimental data indicates that the present model would be promising for the extension of model representations about the breakup of droplets in complex processes of heat and mass transfer in liquid emulsions.

Relating quantum mechanics with hydrodynamic turbulence

In this letter we attempt to trace back the origin of quantum uncertainty. We show that the Schrödinger equation can be mapped into the inviscid Favre-Reynolds turbulence equations of classical compressible fluids, albeit in zero temperature. Under this mapping the probability density function becomes the Reynolds time mean density of the fluid, the real and the imaginary parts of the momentum become the mean and turbulent root-mean-square velocities, respectively, where the latter obeys the first Fick law of diffusion and saturates the lower bound of the uncertainty principle. The mean pressure is proportional to the divergence of the turbulent mass flux and is the source for stochasticity. The roles of the pressure gradient force and the Reynolds stress tensor convergence, under this mapping, are illustrated in two well-known systems, namely, the 1s orbital hydrogen atom and the 1D dynamic Gaussian wavepacket. Finally, we analyze within an independent part of the letter, a conjecture according to which this pressure results from vacuum fluctuations at the zero-point energy, mediated by random collisions of the particle with virtual photons. This suggests that the typical turbulent eddy is of the size of the Compton wavelength corresponding to a Reynolds averaging time scale which is twice the Zitterbewegung period. Moreover, according to this interpretation the quantized characteristics of the particle result from interactions with virtual photons.

Energy-Dynamics Resulting in Turbulent and Acoustic Phenomena in an Underexpanded Jet

Underexpanded jets exhibit interactions between turbulent shear layers and shock-cell trains that yield complex phenomena that are absent in the more commonly studied perfectly expanded jets. We quantitatively analyze these mechanisms by considering the interplay between hydrodynamic (turbulence) and acoustic modes, using a validated large-eddy simulation. Using momentum potential theory (MPT) to achieve energy segregation, the following observations are made. The sharp gradients in fluctuations introduced by the shock-cell structure are captured mostly in the hydrodynamic mode, whose amplitude is an order of magnitude larger than the acoustic mode. The acoustic mode has a relatively smoother distribution, exhibiting a compact wavepacket form. Proper orthogonal decomposition (POD) identifies the third-to-sixth cells as the most dynamic structures. The imprint of shock cells is discernible in the nearfield of the acoustic mode, primarily along the sideline direction. Energy interactions that feed the acoustic mode remain compact in nature, facilitating a simple propagation technique for farfield noise prediction. The farfield sound spectra show peak directivity at 30 ∘ to the downstream axis. The POD modes of the acoustic component also identify two main energetic components in the wavepacket: one representative of the periodic internal structure and the other of intermittent downstream lobes. The latter component occurs at exactly the same frequency as, and displays high correlation with, the farfield peak noise spectra, making the acoustic mode a better predictor of the dynamics than velocity fluctuations.

Issues in Eulerian–Lagrangian modeling of sediment transport under saltation regime

The saltation regime is very important for understanding the sediment transport mechanism. However, there is no consensus on a model for the saltation regime. This study answers several questions raised with respect to the Eulerian–Lagrangian modeling of sediment transport. The first question is why the previous saltation models that use different combinations of hydrodynamic forces yielded acceptable results? The second question is which shear lift model (i.e. a shear lift expression and its coefficient) is more appropriate? Another important question is which hydrodynamic forces have greater contributions to the saltation characteristics of a sediment particle? The last question is what are the contributions of the turbulence fluctuations as well as effects of using two- and three-dimensional (2D and 3D) models on the simulation results? In order to fairly answer these questions, a systematic study was done by considering different scenarios. The current study is the first attempt to clearly discuss these issues. A comprehensive 3D saltation model for non-cohesive sediment was developed that includes all the hydrodynamic forces acting on the particle. The random nature of sediment transport was included using turbulent flow and bed-particle collision models. The eddy interaction model was applied to generate a 3D turbulent flow field. Bed-particle collisions were considered using the concept of a contact zone and a corresponding contact point. The validation of the model was done using the available experimental data for a wide range of sediment size (0.03 to 4.8 cm). For the first question, the results indicated that some of the hydrodynamic effects show opposing trends and some have negligible effects. With these opposing effects it is possible to adjust the coefficients of different models to achieve acceptable agreement with the same experimental data while omitting some aspects of the physics of the process. A suitable model for the shear lift force was developed by linking the lift coefficient to the drag coefficient and the contributions of the hydrodynamic forces and turbulence fluctuations as well as the consequences of using of 2D and 3D models were studied. The results indicate that the shear lift force and turbulent flow fluctuations are important factors for the saltation of both sand and gravel, and they cannot be ignored.

Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalises the often-used cartesian shearing box model. The numerical method is an overall second order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localise the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of "bursty" dynamics such as the superhump phenomenon.

Interacting Multiscale Acoustic Vortices as Coherent Excitations in Dust Acoustic Wave Turbulence.

In this work, using three-dimensional intermittent dust acoustic wave turbulence in a dusty plasma as a platform and multidimensional empirical mode decomposition into different-scale modes in the 2+1D spatiotemporal space, we demonstrate the experimental observation of the interacting multiscale acoustic vortices, winding around wormlike amplitude hole filaments coinciding with defect filaments, as the basic coherent excitations for acoustic-type wave turbulence. For different decomposed modes, the self-similar rescaled stretched exponential lifetime histograms of amplitude hole filaments, and the self-similar power spectra of dust density fluctuations, indicate that similar dynamical rules are followed over a wide range of scales. In addition to the intermode acoustic vortex pair generation, propagation, or annihilation, the intra- and intermode interactions of acoustic vortices with the same or opposite helicity, their entanglement and synchronization, are found to be the key dynamical processes in acoustic wave turbulence, akin to the interacting multiscale vortices around wormlike cores observed in hydrodynamic turbulence.

Complexity of viscous dissipation in turbulent thermal convection

Using direct numerical simulations of turbulent thermal convection for the Rayleigh number between 106 and 108 and unit Prandtl number, we derive scaling relations for viscous dissipation in the bulk and in the boundary layers. We show that contrary to the general belief, the total viscous dissipation in the bulk is larger, albeit marginally, than that in the boundary layers. The bulk dissipation rate is similar to that in hydrodynamic turbulence with log-normal distribution, but it differs from (U3/d) by a factor of Ra−0.18. Viscous dissipation in the boundary layers is rarer but more intense with a stretched-exponential distribution.

Turbulent statistics and intermittency enhancement in coflowing superfluidHe4

The large scale turbulent statistics of mechanically driven superfluid $^4$He was shown experimentally to follow the classical counterpart. In this paper we use direct numerical simulations to study the whole range of scales in a range of temperatures $T \in[1.3,2.1]$K. The numerics employ self-consistent and non-linearly coupled normal and superfluid components. The main results are that (i) the velocity fluctuations of normal and super components are well-correlated in the inertial range of scales, but decorrelate at small scales. (ii) The energy transfer by mutual friction between components is particularly efficient in the temperature range between 1.8K and 2K, leading to enhancement of small scales intermittency for these temperatures. (iii) At low $T$ and close to $T_{\lambda}$ the scaling properties of the energy spectra and structure functions of the two components are approaching those of classical hydrodynamic turbulence.

Exact result in strong wave turbulence of thin elastic plates.

An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5-Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛℓ, where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

The decay of isotropic magnetohydrodynamics turbulence and the effects of cross-helicity

Decaying homogeneous and isotropic magnetohydrodynamics (MHD) turbulence is investigated numerically at large Reynolds numbers thanks to the eddy-damped quasi-normal Markovian (EDQNM) approximation. Without any background mean magnetic field, the total energy spectrum $E$ scales as $k^{-3/2}$ in the inertial range as a consequence of the modelling. Moreover, the total energy is shown, both analytically and numerically, to decay at the same rate as kinetic energy in hydrodynamic isotropic turbulence: this differs from a previous prediction, and thus physical arguments are proposed to reconcile both results. Afterwards, the MHD turbulence is made imbalanced by an initial non-zero cross-helicity. A spectral modelling is developed for the velocity–magnetic correlation in a general homogeneous framework, which reveals that cross-helicity can contain subtle anisotropic effects. In the inertial range, as the Reynolds number increases, the slope of the cross-helical spectrum becomes closer to $k^{-5/3}$ than $k^{-2}$. Furthermore, the Elsässer spectra deviate from $k^{-3/2}$ with cross-helicity at large Reynolds numbers. Regarding the pressure spectrum $E_{P}$, its kinetic and magnetic parts are found to scale with $k^{-2}$ in the inertial range, whereas the part due to cross-helicity rather scales in $k^{-7/3}$. Finally, the two $4/3$rd laws for the total energy and cross-helicity are assessed numerically at large Reynolds numbers.

Modelling the impact of hydrodynamic turbulence on the competition between Microcystis and Chlorella for light

Intensified hydrodynamic turbulence through artificial mixing has been widely used to suppress toxic Microcystis blooms. In contrast, attenuations of turbulent mixing by reservoir impoundment would lead to the shift from Chlorella to Microcystis. However, the intervention mechanisms of the turbulence on the competitions between buoyant Microcystis and sinking Chlorella are still unclear. In this study, we develop a mathematical model between Microcystis and Chlorella competing for light by incorporating the buoyancy regulation of Microcystis with different sizes. The results from numerical simulations indicate that a better vertical distribution help competing algae win the competition. Most of buoyant Microcystis float upwards into the upper layer to have fully photosynthesis and dominate while most of sinking Chlorella stay in the lower layer in relatively calm water. However, faster-growing Chlorella dominates in the relatively turbulent water because both coexisting species are distributed uniformly over depth. In addition, the competitive advantage pictures reveal that water turbulence together with water depth reflect the dominant algae when nutrients are rich and water temperature is suitable.

An improved SPH model for turbulent hydrodynamics of a 2D oscillating water chamber

An improved smoothed particle hydrodynamic (SPH) model is developed to study the complex hydrodynamic behaviour of an onshore oscillating water chamber. The improvements include adding a diffusive term to the continuity equation and incorporating the corrective smoothed particle method (CSPM). A modified boundary condition is implemented to better simulate the pressure field near the solid boundary. The SPH model is first verified by comparing the numerical results with analytical solutions and the available experimental data. The verified model is then applied to study the hydrodynamic behaviour of an onshore oscillating water chamber. The free surface elevations inside the water chamber and the total forces acting on the front wall of the water chamber are studied for different wave conditions. The turbulence energy distribution and the sloshing phenomenon in the water chamber are also investigated.

Turbulent hydrodynamics experiments in high energy density plasmas: scientific case and preliminary results of the TurboHEDP project

The physics of compressible turbulence in high energy density (HED) plasmas is an unchartered experimental area. Simulations of compressible and radiative flows relevant for astrophysics rely mainly on subscale parameters. Therefore, we plan to perform turbulent hydrodynamics experiments in HED plasmas (TurboHEDP) in order to improve our understanding of such important phenomena for interest in both communities: laser plasma physics and astrophysics. We will focus on the physics of supernovae remnants which are complex structures subject to fluid instabilities such as the Rayleigh–Taylor and Kelvin–Helmholtz instabilities. The advent of megajoule laser facilities, like the National Ignition Facility and the Laser Megajoule, creates novel opportunities in laboratory astrophysics, as it provides unique platforms to study turbulent mixing flows in HED plasmas. Indeed, the physics requires accelerating targets over larger distances and longer time periods than previously achieved. In a preparatory phase, scaling from experiments at lower laser energies is used to guarantee the performance of future MJ experiments. This subscale experiments allow us to develop experimental skills and numerical tools in this new field of research, and are stepping stones to achieve our objectives on larger laser facilities. We review first in this paper recent advances in high energy density experiments devoted to laboratory astrophysics. Then we describe the necessary steps forward to commission an experimental platform devoted to turbulent hydrodynamics on a megajoule laser facility. Recent novel experimental results acquired on LULI2000, as well as supporting radiative hydrodynamics simulations, are presented. Together with the development of LiF detectors as transformative X-ray diagnostics, these preliminary results are promising on the way to achieve micrometric spatial resolution in turbulent HED physics experiments in the near future.

On the Path from the Turbulent Vortex Dynamo Theory to Diagnosis of Tropical Cyclogenesis

An overview of researches is presented, which was focused on application of a theoretical hypothesis on the turbulent vortex dynamo to the study of tropical cyclogenesis. The dynamo effect is related to the special properties of small-scale helical turbulence with the broken mirror symmetry and was hypothesized to result in large-scale vortices generation in both hydrodynamic and atmospheric turbulence. To introduce this abstract theory into tropical cyclone research, a recent discovery of vortical moist convection in the tropics is emphasized. Based on this finding, we discuss and substantiate the crucial role of rotating cumulonimbus clouds, known as vortical hot towers (VHTs), as a necessary element to provide the dynamo effect. An analogy is traced between the role of interaction “moist convection—vertical wind shear” in creating the vortex dynamo in the atmosphere and the role of the mean electromotive force providing the MHD dynamo in electrically conducting medium. Throughout the review of novel results, a pivotal role of the Russian-American collaboration on examining a helical self-organization of moist convective atmospheric turbulence under tropical cyclone formation by use of cloud-resolving numerical simulation is accented. The efforts resulted in application of the vortex dynamo theory to diagnose a time when cyclogenesis commences in a favorable tropical environment. This may help elaborate a universally accepted definition of tropical cyclogenesis that currently does not exist and contribute to practical purposes of diagnosis and forecasting.

How tracer particles sample the complexity of turbulence

On their roller coaster ride through turbulence, tracer particles sample the fluctuations of the underlying fields in space and time. Quantitatively relating particle and field statistics remains a fundamental challenge in a large variety of turbulent flows. We quantify how tracer particles sample turbulence by expressing their temporal velocity fluctuations in terms of an effective probabilistic sampling of spatial velocity field fluctuations. To corroborate our theory, we investigate an extensive suite of direct numerical simulations of hydrodynamic turbulence covering a Taylor-scale Reynolds number range from 150 to 430. Our approach allows the assessment of particle statistics from the knowledge of flow field statistics only, therefore opening avenues to a new generation of models for transport in complex flows.

Decaying turbulence for the fractional subcritical Burgers equation

We consider the fractional unforced Burgers equation in the one-dimensional space-periodic setting: \begin{document}$\begin{equation} \nonumber\frac{\partial u}{\partial t}+(f(u))_x +ν Λ^{α} u = 0, t ≥ 0,\ \ \ \ {\bf{x}} ∈ {\mathbb{T}}^d = ({\mathbb{R}}/{\mathbb{Z}})^d.\end{equation}$ \end{document} Here $ f$ is strongly convex and satisfies a growth condition, $ Λ = \sqrt{-Δ}, \ ν$ is small and positive, while $ α ∈ (1,\ 2)$ is a constant in the subcritical range.For solutions $ u$ of this equation, we generalise the results obtained for the case $ α = 2$ (i.e. when $ -Λ^{α}$ is the Laplacian) in [12]. We obtain sharp estimates for the time-averaged Sobolev norms of $ u$ as a function of $ ν$. These results yield sharp $ν$-independent estimates for natural analogues of quantities characterising the hydrodynamical turbulence, namely the averages of the increments and of the energy spectrum. In the inertial range, these quantities behave as a power of the norm of the relevant parameter, which is respectively the separation $ \ell$ in the physical space and the wavenumber $ \bf{k}$ in the Fourier space. The form of all estimates is the same as in the case $ α = 2$; the only thing which changes is that $ ν$ is replaced by $ ν^{1/(α-1)}$.

Dynamics of vortex line density and heat transfer processes in superfluid helium

Three dynamics equations for vortex line density are analyzed. It is shown that the Vinen equation gives the values of vortex tangle development time in the case of a constant counterflow more accurately than other alternative equations. Within the system of equations of superfluid turbulence hydrodynamics, obtained using a phenomenological approach, helium boiling times as a function of heat flux density are found, using alternative dynamics equations of vortex tangle density. Unlike the experiments in which different dependences of boiling time tboil on the heat flux density Q (tboil ∝ Qn, −4 ≤ n ≤ −2) are observed, in this case we get only a power-law dependence with an exponent of n = −4. We obtain a velocity distribution of the normal component along the channel, and the temperature dependence of the time near the heater. We conduct a comparison against the numerical and experimental results that were previously obtained in literature.