Fig 1 - uploaded by Galina Levina
Content may be subject to copyright.
Isoline maps for the stationary free convection flow at Re =0, P r=1 and Ra=3000: (a) stream function, (b) temperature ; r=0 corresponds to the axis of symmetry location.
Source publication
A numerical approach is substantiated for searching for the large-scale alpha-like instability in thermoconvective turbulence. The main idea of the search strategy is the application of a forcing function which can have a physical interpretation. The forcing simulates the influence of small-scale helical turbulence generated in a rotating fluid wit...
Similar publications
A b s t r a c t The supertree and supermatrix frameworks have been cast as mutually exclusive approaches toward the prob-lem of large-scale phylogenetic inference. Despite often coming under severe criticism, the supertree approach has proven superior to date at deriving comprehensive phylogenetic estimates for many groups (e. g., mammals as a whol...
Induction of recursive theories in the normal ILP setting is a complex task because of the non-monotonicity of the consistency property. In this paper we propose computational solutions to some relevant issues raised by the multiple predicate learning problem. A separate-and-parallel-conquer search strategy is adopted to interleave the learning of...
This paper presents a novel extended dynamic programming approach for energy
minimization (EDP) to solve the correspondence problem for stereo and motion. A
significant speedup is achieved using a recursive minimum search strategy
(RMS). The mentioned speedup is particularly important if the disparity space
is 2D as well as 3D. The proposed RMS can...
In this paper we consider the problem of optimal search strategies on multi-linked networks, i.e. graphs whose nodes are endowed with several independent sets of links. We focus preliminarily on agents randomly hopping along the links of a graph, with the additional possibility of performing non-local hops to randomly chosen nodes with a given prob...
Citations
... The study of the helical nature of tropical cyclogenesis began with the verification of the basic hypothesis and, at the same time, the necessary conditions for the implementation of the vortex dynamo mechanism, namely, the existence of helical atmospheric turbulence, which is characterized by a non-zero mean helicity. For this purpose, approaches and results of two series of numerical experiments, Levina and Burylov (2006) and Montgomery et al. (2006), were brought together. ...
... The first of them, by Levina and Burylov (2006), was undertaken to examine a mathematical model of the turbulent vortex dynamo that was formulated in terms of mean-field hydrodynamics (Krause and Rädler, 1980) as the mean-field equations, which describe the dynamo-effect in a non-uniformly heated medium (Moiseev et al., 1988). This allowed the development of numerical methods for analysis of helical features of the velocity field and resulted in the diagnostic approach for detection of the large-scale helical-vortex instability. ...
... The scenario of a "vortical hot tower (VHT) route" showed many similarities with an upscale organization through the vortex dynamo (Levina and Burylov, 2006) and was chosen as a superb basis to introduce and examine the helical features of the threedimensional convective atmospheric turbulence. The diagnostic approach by Levina and Burylov (2006) was applied for analysis of data from atmospheric modeling (Montgomery et al., 2006). ...
In this paper, the concept of helical cyclogenesis is discussed, allowing for a unified interpretation of the existence of intense large-scale long-lived vortices in the atmosphere through the transfer of energy from cloud-scale motions. In 2022, the first evidence of such a phenomenon was found at Jovian high latitudes. The theory introduces ideas about large-scale threshold instabilities in turbulence with broken mirror symmetry. Such turbulence, called helical turbulence, occurs in a rotating, stratified, moist atmosphere. The present publication emphasizes the problem of tropical cyclogenesis in the Earth’s atmosphere. In the case of tropical cyclones, these ideas allowed, for the first time, the development of a procedure for the exact diagnosis of the emergence of large-scale helical-vortex instability and interpretation of this event as the birth of a tropical cyclone. Our very simple diagnostics and lucid quantitative criterion of the tropical cyclogenesis are discussed in the context of their successful application to two distinct idealized genesis scenarios and three observed tropical cyclones. In all cases, a nascent vortex became energy-self-sustaining and intensifying dozens of hours before the formation of a tropical depression. The pivotal role of rotating cumulonimbus clouds, known as vortical hot towers (VHTs), is highlighted. They are a necessary element both to provide and to diagnose the instability. These main actors of the helical cyclogenesis are illustrated by authors’ photos, satellite imagery, and animation from idealized atmospheric modeling. New fundamental and applied interpretations are offered. The hypothesis on the two-scale vortex dynamo-effect is put forward, which suggests the energy transfer from the VHTs scale, 10–30 km, directly to the mesoscales, hundreds km, of the system circulation of a tropical cyclone. Based on the results of the applied new diagnostics, we propose a definition of tropical cyclogenesis: interpret the onset of helical-vortex instability as the beginning of the genesis stage while considering the formation of a tropical depression as this stage completion. The diagnostics is best suited as a fundamental basis for detecting the “Potential Tropical Cyclone” stage introduced by the U.S. National Weather Service for operational forecasting purposes. Prospects are discussed.
... A helical structure, a unique feature of convective vortices, is formed by developing primary tangential and vertical secondary circulation, providing moisture and heat supply from the ocean surface. The merging of helical convective cells increases the horizontal scale of vortices, which is associated with a sharp increase in kinetic energy and a significant increase in heat transfer (Levina & Burylov, 2006). Their study pointed out that heat flux enhancement through a layer has been observed with an increase in the mean helicity value of a flow. ...
The development of large‐scale vortex dynamo during tropical cyclogenesis through the mutual intensification of primary and secondary circulation in terms of helical evolution is well studied. However, the influence of atmospheric helicity on ocean surface heat and moisture fluxes associated with tropical cyclone (TC) evolution is yet to be understood. At its development stage, the heat and moisture flux from the ocean surface increases with the increase in intensity of the TC. This time, TC‐Ocean interaction works in a positive feedback mechanism. However, after a particular stage, the very intense wind of the TC causes strong turbulent mixing in the underlying ocean. Hence, the upper ocean layer temperature starts decreasing, leading to a decrease in heat and moisture flux exchange to the TC. We have analyzed the emergence of vortex helical structure in TC and the role of helicity in modulating surface heat and moisture fluxes. The result shows that helical development is associated with the axisymetrization of the vertical velocity and diabatic heating at the middle and upper troposphere. There is no definite TC intensity at which the initiation of negative feedback of TC‐upper ocean interaction occurs. However, the increase in helicity above 200 × 10⁻² ms⁻² reversed the TC‐ocean interaction trend. Therefore, TC helicity evolution and upper ocean interaction are essential to understand TC evolution.
... [1][2][3] The studies on the helical force effect were discussed by Levina and her collaborators. [4][5][6][7] Rutkevich 8 derived an averaged equation that describes the production of large-scale structures in an anisotropic turbulent medium with the Coriolis effect. Essoun and Chabi Orou 9 studied the helical force effect and Coriolis on rotating convection and showed how the helical force affects the Pr Ta − parameter space which divides into steady and overstable instability regions. ...
Linear and weakly nonlinear stability analyses of thermosolutal convection in a couple‐stress fluid with effects of helical force and rotation are performed. The governing nondimensional equations are solved using the normal modes. We have shown the effect of the helical force parameter, solutal Rayleigh number, Couple stress parameter, Lewis number, Taylor number, and Prandtl number on stationary and oscillatory convection regions and presented graphically. Solutal Rayleigh number, Couple stress parameter, Lewis number, and Taylor number have a stabilizing effect on the system whereas the helical force parameter has a destabilizing effect on the system. To study heat transport by convection we have derived the Ginzburg–Landau equation.
... This discovery fostered the development of the magneto-hydrodynamic (MHD) theory. The publications on the hydrodynamic alpha effect have been made by Levina et al. [41,42,43] following by many others works [44][45][46][47][48]. ...
We used linear stability theory based on the normal mode decomposition technique to study the criterion of appearance of the stationary convection and the oscillatory convection in a binary viscoelastic fluid mixture in a porous medium under the effect of helical force. Nonlinear stability theory based on the minimum representation of double Fourier series is used to study the rate of heat and mass transfer. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. Expressions for heat and mass transfer rates are determined as a function of Nusselt and Sherwood number, respectively. The transient behaviors of the Nusselt number and the Sherwood number are studied by solving the finite amplitude equations using the Runge - Kutta method. Then, the effect of each dimensionless parameter on the system is studied pointed out interesting results.
... This discovery encouraged the development of the MHD theory. The publications on the hydrodynamic alpha effect were made by Levina et al. [23][24][25][26]. In a convective system, it has been shown that the force responsible for helical turbulence is pseudo-vector in nature, called the helical force. ...
This work studies the simultaneous effects of helical force, rotation and porosity on the appearance of stationary convection in a binary mixture of a ferrofluid and on the size of convection cells. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. The effect of each parameter on the system is studied. The consideration of the simultaneous effect of the basic characteristics made it possible to determine the evolution of the convection threshold in the ferrofluid and then the size of convection cells. The analyzes of the various results obtained allowed us to deduce whether the convection sets in quickly or with a delay when the various effects taken into account in the study are considered simultaneously.
... The author's experience gained in numerical examination of the mathematical model of the turbulent vortex dynamo in a convectively unstable rotating fluid [10][11][12] was used to elaborate on a procedure for the exact diagnosis of TC genesis. ...
... The numerical examination of the vortex dynamo model confirmed [10][11][12] that the first sign of the hypothesized large-scale helical-vortex instability should be the generation of the linkage of tangential and transverse circulation on the system scale, and resulting in positive feedback that makes the forming large-scale vortex energy self-sustaining. Such feedback was expected to reveal itself in mutual intensification of both circulations. ...
... For diagnosis of the large-scale helical-vortex instability during TC formation [3,4,14], we should analyze the evolution of kinetic energy divided into two parts: the energy of primary, EP, and secondary, ES, circulation, similar to that which was performed in [10][11][12] ...
In the present work, we explore in detail the crucial role of special convective coherent structures of cloud scales—vortical hot towers (VHTs)—in the formation and maintenance of the secondary circulation and, therefore, of the whole mesoscale vortex system. On this basis, we propose how the onset of large-scale instability, i.e., the beginning of TC genesis, can be diagnosed exactly and distantly with VHTs patterns in the field of temperature (satellite data) and vertical helicity (cloud-resolving numerical analysis). The present research is intended to contribute to a recently initiated development of operational diagnosis of the beginning of TC genesis based on GOES Imagery and supported by cloud-resolving numerical modeling.
... This discovery favored the development of MHD theory. The publications on the hydrodynamic alpha effect were made by Levina and her collaborators [29][30][31][32]. In a convective system, it has been shown that the force responsible for helical turbulence is pseudo -vector in nature, called helical force. ...
... where A 1 , A 2 , A 3 and A 4 are constants. Substituting (32) in (27)-(30), we obtain: ...
In this paper we studied the onset of instability in a horizontal layer of a rotating ferrofluid in the presence of the helical force. The analytical expression of the Rayleigh number of the system is determined as a function of the dimensionless numbers obtained. Then, the effect of each dimensionless parameter is studied. The helical force, the binary parameter ψ then the magnetic parameters M1, M3 and ψm accelerate the onset of stationary convection so rotation and the magnetic parameter M2 delay it. Also all the magnetic parameters, the binary parameter and the rotation cause the convection rolls to shrink while only the helical force increases the size of these structures.
... In geophysical or astrophysical contexts, as well as in laboratory experiments, flows are often accompanied by rotation and consequently they are usually helical. Helicity arises in convection [10,11] and turbulence [12]. Participation of helicity in generation of a dipolar magnetic field in a geodynamo model involving convection in a rapidly rotating spherical shell was explored in [13]. ...
... When the α-effect is absent (A = 0), the leading term in the expansion of the eigenvalue is ε 2 λ 2 , where λ 2 is an eigenvalue of the magnetic eddy diffusivity operator [see (21)]. We have calculated the eigenvalues λ 2 (23) associated with the harmonic eigenfunctions (10). (To the best of our knowledge, the relations (13) and (23) were so far unavailable in the literature; however, see Sec. 9.3 in [31].) ...
We introduce six families of three-dimensional space-periodic steady solenoidal flows, whose kinetic helicity density is zero at any point. Four families are analytically defined. Flows in four families have zero helicity spectrum. Sample flows from five families are used to demonstrate numerically that neither zero kinetic helicity density nor zero helicity spectrum prohibit generation of large-scale magnetic field by the two most prominent dynamo mechanisms: the magnetic α-effect and negative eddy diffusivity. Our computations also attest that such flows often generate small-scale field for sufficiently small magnetic molecular diffusivity. These findings indicate that kinetic helicity and helicity spectrum are not the quantities controlling the dynamo properties of a flow regardless of whether scale separation is present or not.
... Pr, Ra, and Ta are the dimensionless Prandtl, Rayleigh, and Taylor numbers, e the unit vector directed vertically upward, A the uniform temperature gradient between the horizontal boundaries of the layer, g the gravity acceleration, β the coefficient of thermal expansion, h the layer height. The dimen-Open Journal of Fluid Dynamics sionless parameter C characterizing the small-scale turbulence is related in a rather complicated manner to the turbulence characteristics such as the most energetic scale λ and characteristic time τ of the turbulent velocity correlation [19] [26] [27], and is proportional to the angular velocity of a fluid layer rotation Ω, and the power of internal heat sources Λ. ...
... Here it is important to note that, as applied to tropical cyclones, this would imply an immediate positive feedback between the tangential and overturning circulation. This feedback, being generated by special properties of small-scale helical turbulence and, therefore, named the helical feedback [13] [26] [27], is maintained only through the parameter C, whose explicit form was first given in [19] and discussed in detail in the above works. ...
... The vortex dynamo should operate by linking the poloidal and toroidal component of the velocity field. In mathematical model (3), C-terms responsible for the positive feedback can also be represented as a force of some kind [13] [26] G. Levina Open Journal of Fluid Dynamics [27], which, by analogy, could be called the "vortex-motive" force ...
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.
... Under such conditions, the velocity field can be de-stabilized at large scales analogous to the dynamo α effect resulting in the generation of mean flows and thereby also vorticity;Frisch et al. (1987)called this effect the anisotropic kinetic α effect, later referred to as the AKA-effect. So far it has been detected only in rather simple and idealised models, requiring specialized forcing functions in direct numerical simulations (see e.g.Brandenburg & von Rekowski 2001;Levina & Burylov 2006), although it has been verified using mean-field models in realistic setups (see e.g. vonRekowski et al. 1995). ...
Context. The forcing of interstellar turbulence, driven mainly by supernova (SN) explosions, is irrotational in nature, but the development of significant amounts of vorticity and helicity, accompanied by large-scale dynamo action, has been reported.
Aim. Several earlier investigations examined vorticity production in simpler systems; here all the relevant processes can be considered simultaneously. We also investigate the mechanisms for the generation of net helicity and large-scale flow in the system.
Methods. We use a three-dimensional, stratified, rotating and shearing local simulation domain of the size 1 × 1 × 2 kpc ³ , forced with SN explosions occurring at a rate typical of the solar neighbourhood in the Milky Way. In addition to the nominal simulation run with realistic Milky Way parameters, we vary the rotation and shear rates, but keep the absolute value of their ratio fixed. Reversing the sign of shear vs. rotation allows us to separate the rotation- and shear-generated contributions.
Results. As in earlier studies, we find the generation of significant amounts of vorticity, the rotational flow comprising on average 65% of the total flow. The vorticity production can be related to the baroclinicity of the flow, especially in the regions of hot, dilute clustered supernova bubbles. In these regions, the vortex stretching acts as a sink of vorticity. In denser, compressed regions, the vortex stretching amplifies vorticity, but remains sub-dominant to baroclinicity. The net helicities produced by rotation and shear are of opposite signs for physically motivated rotation laws, with the solar neighbourhood parameters resulting in the near cancellation of the total net helicity. We also find the excitation of oscillatory mean flows, the strength and oscillation period of which depend on the Coriolis and shear parameters; we interpret these as signatures of the anisotropic-kinetic- α (AKA) effect. We use the method of moments to fit for the turbulent transport coefficients, and find α AKA values of the order 3–5 km s ⁻¹ .
Conclusions. Even in a weakly rotationally and shear-influenced system, small-scale anisotropies can lead to significant effects at large scales. Here we report on two consequences of such effects, namely on the generation of net helicity and on the emergence of large-scale flows by the AKA effect, the latter detected for the first time in a direct numerical simulation of a realistic astrophysical system.
