On the Semi-Analytical Solutions in Hydrodynamics of Ideal Fluid Flows Governed by Large-Scale Coherent Structures of Spiral-Type

We have presented here a clearly formulated algorithm or semi-analytical solving procedure for obtaining or tracing approximate hydrodynamical fields of flows (and thus, videlicet, their trajectories) for ideal incompressible fluids governed by external large-scale coherent structures of spiral-type, which can be recognized as special invariant at symmetry reduction. Examples of such structures are widely presented in nature in “wind-water-coastline” interactions during a long-time period. Our suggested mathematical approach has obvious practical meaning as tracing process of formation of the paths or trajectories for material flows of fallout descending near ocean coastlines which are forming its geometry or bottom surface of the ocean. In our presentation, we explore (as first approximation) the case of non-stationary flows of Euler equations for incompressible fluids, which should conserve the Bernoulli-function as being invariant for the aforementioned system. The current research assumes approximated solution (with numerical findings), which stems from presenting the Euler equations in a special form with a partial type of approximated components of vortex field in a fluid. Conditions and restrictions for the existence of the 2D and 3D non-stationary solutions of the aforementioned type have been formulated as well.

Monte Carlo method for solving the problem of predicting the computer network resistance against DoS attacks

The application of the Monte Carlo method to solving the problem of identifying and assessing the protection against DDoS attacks of weak nodes is considered. The field of research is of practical and theoretical interest, since the methods developed by the classical theory of reliability are focused on simple, stationary flows. Under the conditions of DDoS attacks, the flow of attacking requests is not stationary, so the known analytical models give an unacceptable error. For the reliability of the results, the freedom to choose the distribution function, the moments of arrival of the attacking requests, their duration and the response of the attacked node is required. The method is applicable for modelling a computer network when organizing an information security audit.

Foundations of Engineering Mathematics Applied for Fluid Flows

Based on a brief historical excursion, a list of principles is formulated which substantiates the choice of axioms and methods for studying nature. The axiomatics of fluid flows are based on conservation laws in the frames of engineering mathematics and technical physics. In the theory of fluid flows within the continuous medium model, a key role for the total energy is distinguished. To describe a fluid flow, a system of fundamental equations is chosen, supplemented by the equations of the state for the Gibbs potential and the medium density. The system is supplemented by the physically based initial and boundary conditions and analyzed, taking into account the compatibility condition. The complete solutions constructed describe both the structure and dynamics of non-stationary flows. The classification of structural components, including waves, ligaments, and vortices, is given on the basis of the complete solutions of the linearized system. The results of compatible theoretical and experimental studies are compared for the cases of potential and actual homogeneous and stratified fluid flow past an arbitrarily oriented plate. The importance of studying the transfer and transformation processes of energy components is illustrated by the description of the fine structures of flows formed by a free-falling drop coalescing with a target fluid at rest.

Nonhomogeneous Dispersive Water Waves and Painlev\'{e} equations

In this letter we consider three nonhomogeneous deformations of Dispersive Water Wave (DWW) soliton equation and prove that their stationary flows are equivalent to three famous Painlev\'{e} equations, i.e. $P_{II}$, $P_{III}$ and $P_{IV},$ respectively. Comment: 6 pages

3-D visualization of transparent fluid flows from snapshot light field data

This paper presents the use of light field data, recorded in a snapshot from a single plenoptic camera, for 3-D visualization of transparent fluid flows. We demonstrate the transfer of light field deconvolution, a method so far used only in microscopy, to macroscopic scales with a photographic setup. This technique is suitable for optically thin media without any additional particles or tracers and allows volumetric investigation of non-stationary flows with a simple single camera setup. An experimental technique for the determination of the shift-variant point spread functions is presented, which is a key for applications using a photographic optical system. The paper shows results from different test cases with increasing complexity. Reconstruction of the 3-D positions of randomly distributed light points demonstrates the achievable high accuracy of the technique. Gas flames and droplets of a fluorescent liquid show the feasibility of the proposed method for the visualization of transparent, luminous flows. The visualizations exhibit high quality and resolution in low-contrast flows, where standard plenoptic software based on computer vision fails. Axial resolution depends on the data and is about an order of magnitude lower than the lateral resolution for simple point objects. The technique also allows the time-resolved analysis of flow structures and the generation of 3D3C-velocity fields from a sequence of exposures. Graphical Abstract

Deriving the full turbulent stress tensor from paired ADCP measurements: application to under-ice convection

<p>The Reynolds stress tensor (RST) is the key characteristic of turbulence describing the paths of turbulent kinetic energy transfer and its anisotropy. Despite recent technical advances in application of multi-beam acoustic Doppler current profilers (ADCPs) to in situ acquiring of the RST components, derivation of the full Reynolds tensor from raw flow measurements remains a challenging problem. We present a method for derivation of the full set of turbulent stresses, based on combined use of two ADCPs with two beams from adjacent devices crossing at some point.  In the proposed framework, two 3-beam ADCPs with vertically aligned axes constitute the minimum configuration sufficient to derive 6 equations for all 6 RST components. <br>The method was applied to studying turbulence in a convectively mixed layer in ice-covered Lake Kilpisjärvi. The calculated dynamics of all six stress components revealed diurnal periodicity along with the variations with the periods of a few hours. The pulsations intensities (diagonal components of RST) remained positive except short outliers; less than 5% of cases did not meet the so-called realizability requirements (positive definiteness of the stress matrix). The off-diagonal stresses demonstrated sign-changing dynamics, mirroring the inter-component energy transfer.<br>The ratio of pulsation intensities along vertical and horizontal axes varied in the range from 0.02 to 0.25. The r.m.s. values of horizontal and vertical pulsations reached diurnal maximums of 4 and 1 mm/s correspondingly, the latter being close to 1/3 of the convective velocity w*, in accordance with the previous studies on free convection. <br>The new approach provides an immediate insight into the internal structure of the turbulent boundary mixing, especially relevant to anisotropic non-stationary flows, like buoyancy-driven convection. The preliminary results on under-ice convection elucidate strong anisotropy of the convective flow — a key to understanding the heat and mass transport in ice-covered waters.</p>