Mach Wave and Acoustical Wave Structure in Nonequilibrium Gas-Particle Flows

In this Element, the gas-particle flow problem is formulated with momentum and thermal slip that introduces two relaxation times. Starting from acoustical propagation in a medium in equilibrium, the relaxation-wave equation in airfoil coordinates is derived though a Galilean transformation for uniform flow. Steady planar small perturbation supersonic flow is studied in detail according to Whitham's higher-order waves. The signals owing to wall boundary conditions are damped along the frozen-Mach wave, and are both damped and diffusive along an effective-intermediate Mach wave and diffusive along the equilibrium Mach wave where the bulk of the disturbance propagates. The surface pressure coefficient is obtained exactly for small-disturbance theory, but it is considerably simplified for the small particle-to-gas mass loading approximation, equivalent to a simple-wave approximation. Other relaxation-wave problems are discussed. Martian dust-storm properties in terms of gas-particle flow parameters are estimated.

COUPLING OF A UNIFORM FLOW WITH A RADIAL FLOW

The authors consider the problem of conjugation of a uniform turbulent water flow and a radial flow. The solution uses a simple wave, which allowed us to obtain an analytical solution at all points of the flow. The bottom of the channel, into which the flow flows from a rectangular pipe, is assumed to be horizontal and smooth. The article provides a step-by-step calculation algorithm. The method is intended for use by designers of hydraulic structures.

KINEMATIC WAVE EQUATIONS FOR MOVABLE RIVERBEDS

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the “simple” wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement.

A Discrete Huber-braun Neuron Model: From Nodal Properties to Network Performance

Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it’s the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered noise and obstacles as the two important factor which changes the excitability of the neurons in the network. When there is no noise or obstacle, the network display simple wave propagation with highly excitable neurons. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. Now when we consider only noise with no obstacle, for selected noise variances the network supports wave re-entry. By introducing an obstacle in this noisy network, the re-entry soon disappears, and the network soon enters idle state with no resetting. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. This in a two-layer network stimulus play an important role in spatiotemporal dynamics of the network. Similar noise effects like the single layer network are also seen in the two-layer network.

Shear instability of wind drift as the initiation mechanism for the bag-breakup fragmentation of the air-water interface at high winds.

<p>The "bag breakup" fragmentation is the dominant mechanism for generating spray in hurricane winds, which parameters substantially affect the exchange processes between the ocean and the atmosphere and, thereby, the dynamics of the development of sea storms. This fast process can only be studied in lab using sophisticated experimental techniques based on high-speed video filming. In such circumstances, the transfer of laboratory data to field conditions requires a kind of theoretical model that describes how the initiation of disturbances occurs, which then lead to fragmentation events, what is the threshold for fragmentation, what is the volume of liquid, which determines the size of spray droplets, that undergoes fragmentation, and how it depends on wind parameters, etc. The conclusions of the model can be first verified in the laboratory experiment and then applied to field conditions.</p><p>In the present work, such a model is proposed. First of all, a linear theory of small-scale disturbances on the water surface under the action of a strong wind has been built, which makes it possible to describe their structure, dispersion properties and determine the threshold value of the dynamic air flow velocity at which such disturbances become growing. These disturbances comprise small-scale ripples concentrated within the thin surface layer and growing fast due to shear instability of the wind drift flow in the water. The peculiarity of the structure of these disturbances enables one to consider the nonlinear stage of their evolution within the Riemann simple wave equation modified to describe the increasing disturbances. The analytical solution of the obtained equation suggests the scaling of the volume of liquid undergoing the "bag-breakup" fragmentation, to estimate the scale of the formed droplets and the speed of their injection into the atmosphere. The scaling correctly describes the dependencies of these quantities on the wind friction velocity obtained in laboratory experiments.</p><p>The obtained results are applied for the construction of the fetch-dependent spray generation function, which is applicable in the field. Within the Lagrangian stochastic model for the inertial droplets in the marine boundary layer, the momentum, heat, moisture and enthalpy exchange coefficients are calculated. One should notice substantial  feedback effect on the atmosphere caused by the presence of spray in hurricane conditions.</p><p>This work was supported by RFBR grant 19-05-00249 and RSF grant 19-17-00209.</p><p> </p>

BASIC PROVISIONS IN MODEL DEVELOPMENT IN THE CURRENT OF OPEN WATER STREAMS

For the design of hydraulic structures, it is necessary to use special methods for calculating the water flow to determine the kinetic energy acting on the structures. A mathematical model of a two-dimensional in terms of stationary open water flow and boundary conditions in the problem of free spreading are formulated. The main solved and to be solved problems of determining the flow parameters are determined, its reduction to a dimensionless form by various transformations of coordinates and flow parameters. The method proposed by I.A. Sherenkov. The solution of the problem is described, which depends on the dimensionless parameter - the Froude criterion at the outlet of the flow from the pipe. With Froude numbers exceeding one or close to it, it is required to build a series of graphs or develop a unified theory, an algorithm for solving the problem. The general conclusions on the work are as follows: - the need for further research has been proven theoretically and experimentally. - tasks are formulated that must be performed, solved in order to obtain a result adequate to the real process of solving the problem of free spreading of a turbulent flow to the entire spectrum of parameters. - substantiated the need to continue research to determine the entire spectrum of parameters of a stationary open two-dimensional potential flow in terms of its outflow from a free-flow pipe into a wide horizontal smooth channel. - the requirements for the model taking into account the conjugation of a uniform flow with a radial flow in the form of a simple wave are determined The work was written with a critical assessment of existing methods for solving the problem and to substantiate the relevance of further scientific research.

Fourier analysis: the simplification of a complex waveform into simple component sine waves of different amplitudes and frequencies

Fourier analysis is the simplification of a complex waveform into simple component sine waves of different amplitudes and frequencies. A discussion on Fourier analysis necessitates reiteration of the physics of waves. A wave is a series of repeating disturbances that propagate in space and time. Frequency: the number of oscillations, or cycles per second. It is measured in Hertz and denoted as 1/time or s-1. Fundamental frequency: the lowest frequency wave in a series. It is also known as the first harmonic. Every other wave in the series is an exact multiple of the fundamental frequency. Harmonic: whole number multiples of the fundamental frequency. Amplitude: the maximum disturbance or displacement from zero caused by the wave. This is the height of the wave. Period: time to complete one oscillation. Wavelength: physical length of one complete cycle. This can be between two crests or two troughs. The higher the frequency, the shorter the wavelength. Velocity: frequency x wavelength. Phase: displacement of one wave compared to another, described as 0°–360°. A sine wave is a simple wave. It can be depicted as the path of a point travelling round a circle at a constant speed, defined by the equation ‘y = sinx’. Combining sine waves of different frequency, amplitude and phase can yield any waveform, and, conversely, any wave can be simplified into its component sine waves. Fourier analysis is a mathematical method of analysing a complex periodic waveform to find its constituent frequencies (as sine waves). Complex waveforms can be analysed, with very simple results. Usually, few sine and cosine waves combine to create reasonably accurate representations of most waves. Fourier analysis finds its anaesthetic applications in invasive blood pressure, electrocardiogram (ECG) and electroencephalogram (EEG) signals, which are all periodic waveforms. It enables monitors to display accurate representations of these biological waveforms. Fourier analysis was developed by Joseph Fourier, a mathematician who analysed and altered periodic waveforms. It is done by computer programmes that plot the results of the analysis as a spectrum of frequencies with amplitude on the y-axis and frequency on the x-axis.

Recording of the Cavitation Phenomena when Modeling Flows in the Trunk Pipelines

In the article, it is proposed to use a numerical method based on the approach of S.K. Godunov to simulate boiling in a pipeline. The paper presents a statement of the real problem of modeling a water hammer, considering possible boiling of the transported liquid on a real object — an oil pipeline. When solving the problem, two variants of flow modeling when closing the valve installed at the end of the pipeline were carried out. In the first Наука и техника 14 Безопасность Труда в Промышленности • Occupational Safety in Industry • № 11'2020 • www.safety.ru case, the possibility of liquid boiling was not considered. In the second case, this opportunity was considered. The performed numerical simulation showed that in the pipeline in emergency situations, liquid columns can be formed, separated by the cavitation zones and oscillating in different phases, respectively, at the collapse of the cavitation zones, which serve as a kind of pressure dampers, the collisions of liquid columns occur, which can lead, depending on the ratio of velocities, to hydraulic shocks that occur not on the valves, but on the linear part of the pipeline (local hydraulic shocks). The waves from these collapses, interacting with each other, create the new pressure peaks that do not coincide with the pattern of simple wave circulation, which are predicted in the simulations that do not consider possible liquid boiling. As a resul t, the pressures reached in the pipeline during fluid hammer is significantly different from what it would be in the absence of boiling. When boiling is considered, the maximum reached pressures are 40 % higher. Moreover, this excess is repeated. The detailed analysis of the pressure profile in the pipeline is given in the article. Based on the results of solving this problem, it is concluded that when modeling pre–emergency and emergency situations in the pipeline, it is necessary to consider the process of possible liquid boiling, since sometimes, as in the presented case, the values of the pressure surges can be higher than the values of the pressure surges in the liquid without considering boiling, which increases the likelihood of emergency depressurization.