Decay of a turbulent cascade of capillary waves at the surface of liquid hydrogen

Free decay of a turbulent cascade of capillary waves was experimentally studied at the surface of liquid hydrogen after switching off harmonic pumping. It was found that the cascade starts to decay at the high-frequency side of the frequency spectrum and proceeds in the quasi-stationary regime. The characteristic relaxation time of the whole cascade proves to be close to the viscous-damping time of the wave, whose frequency coincides with the surface-excitation frequency.     

Influence of the size-dependent surface tension of a liquid film on a capillary force in an atomic force microscope

An adsorbed water film always exists between the sample and the probing tip of an atomic force microscope operating at atmospheric conditions. A new expression for the capillary force that acts between the tip and the thin liquid film has been obtained taking into account the size dependence of the surface tension of the liquid described by an exact solution of the Gibbs-Tolman-Koenig-Buff equation. The calculation agrees fairly well with the experimental results.     

Distribution of the probability of oscillations of the surface of liquid hydrogen in the turbulent regime

The probability distribution density of the deviation of the surface of liquid hydrogen from the equilibrium plane state in the system of capillary waves has been analyzed. It has been shown that this probability distribution density for the case of the excitation of the surface oscillations by low-frequency noise in the turbulent regime is well reproduced by a Gaussian. When the oscillations are excited by a low-frequency harmonic force, the stochastization of the waves occurs after several scattering events.     

Evolution of clusters of a floating tracer on the surface of a turbulent fluid

We study the behavior of a cluster of a floating tracer in a two-dimensional turbulent medium in conection with problems of the physics of the atmosphere and ocean. We obtain an asymptotic solution to the equation for the density of a cluster of the floating tracer for a small coefficient of molecular diffusion for the case of a specified velocity field on the fluid surface. The time evolution of the cluster shape and coordinates has been analyzed. N. I. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 4, pp. 357–364, April, 2000.     

Evolution of an asymmetric turbulent shear layer in a thermocline

Large eddy simulations are used to examine the evolution of a shear layer in a thermocline with non-uniform density stratification. Unlike previous studies, the density in the present study is continuously stratified and has stratification in the upper half different from the lower half of the shear layer. The stratification in the upper half is fixed at J_u = 0.05, while the stratification in the lower half is increased to J_d = 0.05, 0.15, 0.25 and 0.35, leading to a progressively stronger asymmetry of the Ri_g profile in the four cases. Here, J is the bulk Richardson number and Ri_g is the gradient Richardson number. The type of shear instability and the properties of the ensuing turbulence are found to depend strongly on the degree of asymmetry in stratification. The shear instability changes from a Kelvin–Helmholtz (KH) mode at J_d = 0.05 to a Holmboe (H) mode at J_d = 0.35 and exhibits characteristics of both KH and H modes at intermediate values of J_d. Differences in the evolution among the cases are quantified using density visualisations and statistics such as mean shear, mean stratification and turbulent kinetic energy.     

Analysis of the force action of a gas jet on the surface of a liquid

The results of theoretical and experimental investigations of the interaction of a gas jet with the surface of a viscous liquid are reported. Relations are derived for calculating the force exerted by the gas jet on the liquid surface. A dependence of the gas jet compression ratio in the nozzle outlet on the pressure in front of the nozzle is revealed. The values of the shape factor for the indentation formed by the gas jet on the surface of the liquid are determined for various diameters of the indentation and the distances between the outlet hole of the nozzle and the liquid surface. The theoretical conclusions formulated here are confirmed by the results of experiments.     

Motion of a liquid droplet in a capillary under the action of static force and an acoustic field

We consider the motion of a liquid droplet inside a capillary of a porous medium under the action of a static force and an acoustic field. We derive the equation of motion of the droplet in the capillary and analyze numerically its solution. We show that the vibration attenuates the influence of the capillary force. Due to the effect of the acoustic field, the droplet motion in a capillary of constant cross-section starts at a lower value of the static force, and the reciprocal velocity of the droplet increases. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 2, pp. 155–161, February 2000.     

Turbulent capillary cascade near the edge of the inertial range on the surface of a quantum liquid

In the dissipative range at frequencies above the inertial frequency range, the turbulent cascade of capillary waves on the surface of liquid helium and hydrogen decays according to an exponential law. The characteristic frequency of the quasi-Planck distribution is determined by the spectral characteristic of an exciting force. In the case of harmonic pumping on the surface of superfluid helium in the discrete turbulence regime, energy condensation is observed near the high-frequency edge of the inertial range. The effect is due to the influence of discreteness in the spectrum of the eigenfrequencies of surface excitations and in the turbulence distribution on the energy transfer through the cascade.     

On the turbulent thermal conductivity of a gas in the field of an external force

The kinetic relation defining turbulent thermal conductivity in the field of an external force is derived using the entropy evolution equation applied to an ideal one-component turbulent gas under the assumption of fluctuation polytropism.     

On the characteristic time for the realization of instability on a flat charged liquid surface

A nonlinear integral equation that describes the time evolution of the amplitude of a nonlinear unstable wave on the flat uniform charged surface of an ideal incompressible liquid has been derived and solved. The characteristic time for the realization of instability is found to be determined by the initial amplitude of a virtual wave initiating the instability and the supercritical increment in the Tonks-Frenkel parameter. At a zero supercritical increment, the characteristic time for the realization of instability is only determined by the initial amplitude and can be rather long (up to eight hours). This effect is characteristic of a flat charged liquid surface and does not occur in charged drops.     

Formation of an energy cascade in a system of vortices on the surface of water

The formation of an energy cascade in a system of vortices generated by perpendicular standing waves with a frequency of 6 Hz on the water surface has been experimentally studied. It has been found that peaks appear on the energy distribution over wave vectors E(k) after switching on pumping. These peaks are transformed with time because of the energy redistribution over scales. The stationary distribution E(k) established 300 s after switching on pumping can be described by a power-law function of the wave vector E(k) ～ k^1.75. It has been shown that waves with frequencies of about 18, 15, 12, 9, and 3 Hz appear on the surface of water owing to the nonlinear interaction at the excitation of a 6-Hz wave. It is assumed that the energy cascade of the turbulent motion in the wave vector range of 0.3–5 cm^?1 is formed by the nonlinear interaction between vortices generated by all waves propagating on the surface and direct energy fluxes toward high wave vectors dominate.     

Capillary turbulence at the surface of liquid hydrogen

The results of studying the nonlinear capillary waves at a charged surface of liquid hydrogen are reported. Spectral density is experimentally determined for the surface elevations excited by spectrally narrow low-frequency pumping. It is shown that the spectral density in the range 100 Hz–5 kHz obeys the power-law dependence constω^m (scaling). The m exponent is close to ?3, indicating that the capillary turbulence regime is established.     

Stationary soliton on a charged surface of liquid helium and hydrogen films

A change in the shape of a charged surface of liquid hydrogen and helium — the formation of a solitary wave (a positively charged hump for hydrogen and a negatively charged dimple for helium)-is observed in an electric field exceeding a critical value under conditions of total compensation of the applied field by the surface charge. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 547–552 (10 April 1997)     

Effect of VGs on a turbulent hydrogen jet

The aim of this study is to investigate numerically the effects of four vortices on the dynamic, scalar, and turbulent fields of the hydrogen jet. These vortices, which appear in the vicinities of the nozzle, are created by the vortex generators (VGs), and they are assembled with periodicity or symmetry in order, respectively, to give four vortices of the same or opposite direction. A second-order Reynolds stress model is used to investigate asymmetric turbulent jet. The results indicate that the presence of the vortex near the emission jet section noticeably enhances mixing to ensure a good combustion.     

The turbulence of capillary waves on the surface of liquid hydrogen

It is experimentally demonstrated that the surface excitation of liquid hydrogen at a low frequency results in the turbulent mode in a system of capillary waves. The experimental results are in good agreement with the theory of weak wave turbulence. The pair correlation function of the surface deviations is described by the exponential function ω^m. The exponent m decreases in magnitude from m=?3.7±0.3 to ?2.8±0.2 when the pumping at a single resonant frequency changes to broadband noise excitation. Measurements are made of the dependence of the boundary frequency ω_b of the upper edge of the inertial range in which the Kolmogorov spectrum is formed on the wave amplitude η_p at the pumping frequency. It is demonstrated that the obtained data are well described by a function of the form ω_b∝η _p ^4/3 ω _p ^23/9 .     

Evolution of turbulent kinetic energy in a perturbed turbulent boundary layer

The paper considers the evolution of turbulent kinetic energy in a turbulent boundary layer perturbed by suction. The results show that the boundary layer equilibrium is altered in a non-linear manner due to suppression of the structures near the wall. The behavior, however, suggests that the wavelength of alteration of the equilibrium of the layer is unaffected by a change in Reynolds number and suction rate.     

声表面波介质表面受力条件下的波速变化研究

为了计算力负载直接作用在声表面波传播表面时波速的变化特性,通过有效材料系数将负载引入,并用广义Green函数计算声速,得到了数值计算的结果,并用声表面波谐振器进行了实验.实验结果表明,将力负载直接加载在声表面波的传播表面时,波速变化量和力负载大小近似为线性关系,该加载方式下,实验中声表面波谐振器的谐振频率对外加质量负载有较高的灵敏度,可达1900 Hz/g.     

Impulse characteristic as a response of a liquid sensor based on shear-horizontal surface acoustic waves

The feasibility of using the impulse response of a liquid sensor based on shear-horizontal surface acoustic waves to identify liquids is justified. Identification of some liquid analytes with a single-channel sensor is experimentally demonstrated. The sensor is built around a delay line based on shear-horizontal surface acoustic waves that are excited in a 36°YX LiTaO₃-Al film-SiO₂ film-molecularly imprinted polymer film layered structure. By way of example, the concentration of the morpholine impurity (molecules of which are used as a template in synthesis of this molecularly imprinted polymer) in the liquids is measured. Impulse characteristics are derived by applying the fast inverse Fourier transformation to the amplitude-frequency responses of the sensor taken in a 60-MHz wide band at a center frequency of 105 MHz. The reproducibility of results obtained using such a technique and its application are discussed.     

Extraction of the acoustic component of a turbulent flow exciting a plate by inverting the vibration problem

An improvement of the Force Analysis Technique (FAT), an inverse method of vibration, is proposed to identify the low wavenumbers including the acoustic component of a turbulent flow that excites a plate. This method is a significant progress since the usual techniques of measurements with flush-mounted sensors are not able to separate the acoustic and the aerodynamic energies of the excitation because the aerodynamic component is too high. Moreover, the main cause of vibration or acoustic radiation of the structure might be due to the acoustic part by a phenomenon of spatial coincidence between the acoustic wavelengths and those of the plate. This underlines the need to extract the acoustic part. In this work, numerical experiments are performed to solve both the direct and inverse problems of vibration. The excitation is a turbulent boundary layer and combines the pressure field of the Corcos model and a diffuse acoustic field. These pressures are obtained by a synthesis method based on the Cholesky decomposition of the cross-spectra matrices and are used to excite a plate. Thus, the application of the inverse problem FAT that requires only the vibration data shows that the method is able to identify and to isolate the acoustic part of the excitation. Indeed, the discretization of the inverse operator (motion equation of the plate) acts as a low-pass wavenumber filter. In addition, this method is simple to implement because it can be applied locally (no need to know the boundary conditions), and measurements can be carried out on the opposite side of the plate without affecting the flow. Finally, an improvement of FAT is proposed. It regularizes optimally and automatically the inverse problem by analyzing the mean quadratic pressure of the reconstructed force distribution. This optimized FAT, in the case of the turbulent flow, has the advantage of measuring the acoustic component up to higher frequencies even in the presence of noise.     

Quasiadiabatic decay of capillary turbulence on the charged surface of liquid hydrogen

We study the free decay of capillary turbulence on the charged surface of liquid hydrogen. We find that decay begins from the high frequency end of the spectral range, while most of the energy remains localized at low frequencies. The apparent discrepancy with the self-similar theory of nonstationary wave turbulent processes is accounted for in terms of a quasiadiabatic decay wherein fast nonlinear wave interactions redistribute energy between frequency scales in the presence of finite damping at all frequencies. Numerical calculations based on this idea agree well with experimental data.