arXiv subjects

Alexander G. Chefranov

Publications and source records attributed to Alexander G. Chefranov.

12 recordsLinked to original sources

arXiv2025

Revision of the linear stability paradox for known bounded shear flows

The well-known paradox of linear stability for the some bounded shear flows is not solved up to now and is bypassed on the basis of the non-linear mechanisms consideration. We prove that it is arising only due to an idealized assumption of an exact space periodicity for the small hydrodynamic perturbations. When finite non-zero viscosity is taken into account only quasi-periodic boundary conditions must be used. The conditions of linear instability to the Hagen-Poiseuille flow and to the plane Couette flow are obtained.

physics.flu-dyn↗

arXiv2025

Hagen-Poiseuille Flow Linear Stability Paradox Resolving and Viscous Dissipative Mechanism of the Turbulence Emergence in the Boundary Layer

In the linear theory of hydrodynamic stability up to now there exist examples of flows for which there is full quantitative distinction, as for cylindrical Hagen-Poiseuille (HP) flow in a pipe with round section, between theory conclusions and experimental data on the threshold Reynolds number Reth. In the present work, we show that to get a conclusion of linear instability of the HP flow for finite Reynolds numbers Re, it is necessary to abandon the use of traditional 'normal' form of disturbances which assumes an opportunity of separation of variables describing disturbances variability depending on radial and longitudinal (along the pipe axis) coordinates. In the result of the absence of such variables separation, in the suggested linear theory, it is proposed to use Bubnov-Galerkin's approximation method modification that gives an opportunity to account longitudinal variability periods distinctions for different radial modes defined a priori in the result of standard Galerkin-Cantorovich's method to the equation of evolution of extremely small axially symmetric velocity field tangential component disturbances. We found that when considering even two linearly interacting radial modes for the HP flow, linear instability is possible only when there exists mentioned above conditionally periodic longitudinal along the pipe axis disturbance variability when Re_th(p) very sensitively depends on the ratio p of two longitudinal periods each of which describes longitudinal variability for its own radial mode only. Obtained for the HP flow linear instability realization minimal value Re_th=448 (when p=1.527) quantitatively agrees with the Tolmin-Shlihting waves in the boundary layer emergence, where also Re_th=420. We get quantitative agreeing of the phase velocity values of the considered disturbances with experimental data on the fronts of the turbulent 'puffs' spreading in the pipe.

physics.flu-dyn↗

arXiv2023

Investigating the dynamics of point helical vortices on a rotating sphere to model tropical cyclones

A general exact weak solution to the nonlinear equation of the conservation of the absolute vorticity in a thin layer of an incompressible medium on a rotating sphere is proposed. It takes into account the helicity of the point vortices and the non-uniformity of the depth of the layer. This is used to develop a model of the observed interactions of spiral atmospheric vortices. The fusion of two point helical vortices (HVs) on the rotating sphere is considered. We also analyze the prognostic applicability of the dynamics of the HVs for modeling the abrupt changes observed in the trajectories of tropical cyclones and their landfall in comparison with the traditional approach. The analytical condition for chiral symmetry violation related to the direction of the movement of the center of a helical cyclone is obtained.

physics.flu-dyn↗

arXiv2020

Point vortices dynamics on a rotating sphere and modeling of global atmospheric vortices interaction

It is shown that the hydrodynamics equations for a thin spherical liquid layer are satisfied by the stream function of a pair of antipodal vortices-APV, in contrast to the stream function of a single point vortex on a sphere with a background of a uniform opposite sign vorticity. A simple zero solution of the equation of the absolute vorticity conservation is used for bypassing well-known nonlinear problem of a point vortices interaction with regular vorticity field and an exact solution for APVs dynamics problem on a rotating sphere is obtained. Due to this a new stable stationary solution for the dynamics of APV is obtained, which can model the dynamics of the global vortex structures such as atmospheric centers of action.

physics.flu-dyn↗

arXiv2017

The hydrodynamic singular vortex on the sphere and the Dirac monopole

An exact correspondence is established between mathematical description of the single "elementary vortex" (EV)velocity on the sphere (Zermelo,1902;Bogomolov,1977) and the Dirac magnetic monopole (DMM) vector potential (Dirac, 1931). Similar analogy with DMM was noted only for the vortices in quantum fluid He-3A (Blaha,1976;Volovik,Mineev,1976). Singular EV on a sphere is usually considered using compensating vortex field, uniformly distributed over the sphere. It is necessary to meet the Gauss-Kelvin theorem with zero integral vorticity over the sphere. However since Bogomolov (1977)(see also Dritshel,Boatto,2015)uniform vorticity impact on dynamics is neglected when only the velocity field of singular EV is taken into account. It is not true because the hydrodynamic equations do not allow existence of a solution in the form of an isolated EV but allow solutions in the form of the antipodal EV pairs. It is also suggested the possibility of DMM existence only in the form of the point magnetic dipoles, consisting of two DMM with different signs of the magnetic charge.

physics.flu-dyn↗

arXiv2017

Dissipative-centrifugal instability of the Burgers vortex core and cyclone-anticyclone vortex asymmetry

A new exact solution of the hydrodynamic equations is obtained in the form of the Burgers vortex generalization (BVG)accounting for the medium rotation as a whole and linear uniform friction. The nonlinear dissipative-centrifugal instability(DCI)condition, associated with some superthreshold rotation angular velocity and nonzero friction, for solid-body rotating core of BVG is obtained. The new effect of cyclone-anticyclone vortex asymmetry, arising during DCI of BVG vortex core, is shown to be similar to that observed for the atmospheres of high speed rotating planets and laboratory experiments.

physics.flu-dyn↗

arXiv2015

Linear Instability of the Plane Couette and Plane Poiseuille Flows

We show possibility of the Plane Couette (PC) flow instability for Reynolds number Re>Reth=140. This new result of the linear hydrodynamic stability theory is obtained on the base of refusal from the traditionally used assumption on longitudinal periodicity of the disturbances along the direction of the fluid flow. We found that earlier existing understanding on the linear stability of this flow for any arbitrary large Reynolds number is directly related with an assumption on the separation of the variables of the spatial variability for the disturbance field and their periodicity in linear theory of stability. By the refusal from the pointed assumptions also for the Plane Poiseuille (PP) flow, we get a new threshold Reynolds value Reth=1040 that with 4% accuracy agrees with the experiment contrary to more than 500% discrepancy for the earlier known estimate Reth=5772 obtained in the frame of the linear theory but when using the "normal" disturbance form (S. A. Orszag, 1971).

physics.flu-dyn↗

arXiv2013

Countering Wrapping Attack on XML Signature in SOAP Message for Cloud Computing

It is known that the exchange of information between web applications is done by means of the SOAP protocol. Securing this protocol is obviously a vital issue for any computer network. However, when it comes to cloud computing systems, the sensitivity of this issue rises, as the clients of system, release their data to the cloud. XML signature is employed to secure SOAP messages. However, there are also some weak points that have been identified, named as XML signature wrapping attacks, which have been categorized into four major groups; Simple Ancestry Context Attack, Optional element context attacks, Sibling Value Context Attack, Sibling Order Context. In this paper, two existing methods, for referencing the signed part of SOAP Message, named as ID referencing and XPath method, are analyzed and examined. In addition, a new method is proposed and tested, to secure the SOAP message. In the new method, the XML any signature wrapping attack is prevented by employing the concept of XML digital signature on the SOAP message. The results of conducted experiments show that the proposed method is approximately three times faster than the XPath method and even a little faster than ID.

cs.CR↗

arXiv2013

Parametric Excitation of Internal Gravity Waves in Ocean and Atmosphere as Precursors of Strong Earthquakes and Tsunami

The condition of internal gravity waves (IGW) parametric excitation in the rotating fluid layer heated from above, with the layer vibration along the vertical axis or with periodic modulation in time of the vertical temperature distribution, is obtained. We show the dual role of the molecular dissipative effects that may lead not only to the wave oscillations damping, but also to emergence of hydrodynamic dissipative instability (DI) in some frequency band of IGW. This DI also may take place for the localized in horizontal plane tornado-like disturbances, horizontal scale of which does not exceed the character vertical scale for the fluid layer of the finite depth. Investigated parametric resonance mechanism of IGW generation in ocean and atmosphere during and before earthquakes allows monitoring of such waves (with double period with respect to the period of vibration or temperature gradient modulation) as precursors of these devastating phenomena.

physics.flu-dyn↗

arXiv2012

Interaction of Global-Scale Atmospheric Vortices: Modeling Based on Hamiltonian System for Antipodal Vortices on Rotating Sphere

It is shown for the first time that only an antipodal vortex pair (APV) is the elementary singular vortex object on the sphere compatible with the hydrodynamic equations. The exact weak solution of the absolute vorticity equation on the rotating sphere is obtained in the form of Hamiltonian dynamic system for interacting APVs. This is the first model describing interaction of Barrett vortices corresponding to atmospheric centers of action (ACA). In particular, new steady-state conditions for N=2 are obtained. These analytical conditions are used for the analysis of coupled cyclone-anticyclone ACAs over oceans in the Northern Hemisphere.

physics.flu-dyn↗

arXiv2012

Investigation of Hill Cipher Modifications Based on Permutation and Iteration

Two recent Hill cipher modifications which iteratively use interweaving and interlacing are considered. We show that strength of these ciphers is due to non-linear transformation used in them (bit-level permutations). Impact of number of iterations on the avalanche effect is investigated. We propose two Hill cipher modifications using column swapping and arbitrary permutation with significantly less computational complexity (2 iterations are used versus 16). The proposed modifications decrease encryption time while keeping the strength of the ciphers. Numerical experiments for two proposed ciphers indicate that they can provide a substantial avalanche effect.

cs.CR↗

arXiv2010

Linear Exponential Instability of the Hagen-Poiseuille Flow with Respect to Synchronous Bi-Periodic Disturbances

For Gagen-Poiseuille flow, we show that exponential instability (to extremely small, axially symmetric disturbances represented by Galerkin's approximation) is possible only if there exists bi-periodic variability of the disturbances along the pipe axis when the threshold Reynolds number depends on the ratio of two longitudinal periods. Absolute minimum (for) is obtained that corresponds to the observed conditions of transition from the laminar resistance law to the turbulent one and Tollmien-Schlichting waves exciting in the boundary layer.

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