Kinetic helicity (hereafter helicity) is defined by the correlation between the velocity and the flow-aligned vorticity. Helicity, as well as energy, is an inviscid invariant of the hydrodynamic equations. In contrast to energy, a measure of the turbulent intensity, turbulent helicity, representing right- and left-handed twist associated with a fluctuating motion, provides a measure of the structural or topological property of the fluctuation. The helicity effect on the turbulent transport can be analytically obtained in the framework of the multiple-scale renormalized perturbation expansion theory through the inclusion of the non-reflectionally-symmetric part for the lowest-order (homogeneous and isotropic) velocity correlation. The physical significance of the helicity-related contribution to the momentum transport is explained. By utilizing the analytical expression of the Reynolds stress, a turbulence model with helicity effect incorporated (helicity model) is constructed. This helicity model is applied to a swirling flow to show its validity in describing the prominent properties of the flow. In addition to the transport suppression, inhomogeneous helicity coupled with a rotation can induce a large-scale flow. The results of direct numerical simulations (DNSs) confirming the global flow generation by helicity will be also reviewed, followed by several possible applications in geo- and astro-physical flow phenomena.
In isotropic helical turbulence, a new single helical model is suggested for large eddy simulation. Based on the Kolmogrov's hypotheses, the helical model is proposed according to the balance of helicity dissipation and the average of helicity flux across the inertial range, and the helical model is a kind of eddy viscosity model. The coefficient of the helical model is constant and can be also determined dynamically. Numerical simulations of forced and decaying isotropic helical turbulence demonstrate that the helical model predicts the energy and helicity evolution well. The statistical char…
For helical isotropic turbulence, an improved two-term helical subgrid-scale (SGS) model is proposed and four types of dynamic methods are given to do large-eddy simulation (LES), which include the standard dynamic procedure, the least quatratic sum dynamic procedure, the dynamic procedure with single con- straint of helicity dissipation and the dynamic one with dual constraints of energy and helicity dissipation. Tested a priori and a posteriori in both steady and decaying helical isotropic turbulence, the four types of dynamic helical models and the dynamic Smogorinsky model are compared wit…
Using results of laboratory experiments, direct numerical simulations, geomagnetic and solar observations, it is shown that high moments of helicity distribution can dominate power spectra of the magnetic field generated by the magnetohydrodynamic (MHD) dynamo in swirling turbulence even for the cases with zero global helicity. The notion of helical distributed chaos has been used for this purpose.
It is shown that the correlation integrals (invariants) play an important, and at certain conditions a dominant, role in helical isotropic homogeneous turbulence both in the inertial and near-dissipation ranges. Results of direct numerical simulations and recent laboratory experiments with multiscale grids have been used for this purpose. A possibility of spontaneous breaking of reflection symmetry has been also briefly discussed in this context.
Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main features, both new and old, as the discovery of bi-directional cascades or the role of helical vortices in the enhancement of large-scale magnetic fields in the dynamo problem. The dynamical contribution in magnetohydrodynamic (MHD) of the cross-correlation between velocity and induction is discussed as well. We consider next how turbulent transport is affected b…
In this paper we study the enstrophy transers in helical turbulence using direct numerical simulation. We observe that the helicity injection does not have significant effects on the inertial-range energy and helicity spectra ($\sim k^{-5/3}$) and fluxes (constants). We also calculate the separate contributions to enstrophy transfers via velocity to vorticity and vorticity to vorticity channels. There are four different enstrophy fluxes associated with the former channel or vorticity stretching, and one flux associated with the latter channel or vorticity advection. In the inertial range, the …
We investigate analytically the amplification of a weak magnetic field in a homogeneous and isotropic turbulent flow lacking reflectional symmetry (helical turbulence). We propose that the spectral distributions of magnetic energy and magnetic helicity can be found as eigenmodes of a self-adjoint, Schrödinger-type system of evolution equations. We argue that large-scale and small-scale magnetic fluctuations cannot be effectively separated, and that the conventional alpha-model is, in general, not an adequate description of the large-scale dynamo mechanism. As a consequence, the correct numeric…
The role of the different helical components of the magnetic and velocity fields in the inverse spectral transfer of magnetic helicity is investigated through Fourier shell-to-shell transfer analysis. Both magnetic helicity and energetic transfer analysis are performed on chosen data from direct numerical simulations of homogeneous isothermal compressible magnetohydrodynamic turbulence, subject to both a large-scale mechanical forcing and a small-scale helical electromotive driving. The root mean square Mach number of the hydrodynamic turbulent steady-state taken as initial condition varies fr…
Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations in Fourier space [F. Waleffe, Phys. Fluids A 4, 350 (1992)] we introduce a modified version of helical shell models for turbulence with non-local triadic interactions. By using both an analytical argument and numerical simulation, we show that there exists a class of models, with a specific helical structure, that exhibits a statistically stable inverse energy cascade, in close analogy with that predicted for the Navier-Stokes equations restricted to the same helical interactions. We further support th…
Decaying three-dimensional (3D) turbulence is studied via direct numerical simulations (DNS) for an isotropic non-rotating flow and for rotating flows with and without helicity. We analyze the cases of moderate Rossby number and large Reynolds number focusing on the behavior of the energy spectrum at large scales and studying its effect on the time evolution of the energy and integral scales for $E(k) \sim k^4$ initial conditions. In the non-rotating case we observe the classical energy decay rate $t^{-10/7}$ and a growth of the integral length proportional to $t^{2/7}$ in agreement with the p…
The principles of restricted superposition of circularly polarized arbitrary-amplitude waves for several hydrodynamic type models are illustrated systematically with helical representation in a unified sense. It is shown that the only general modes satisfying arbitrary-amplitude superposition to kill the generic nonlinearity are the mono-wavelength homochiral Beltrami mode and the one-dimensional-two-component stratified vorticity mode, which we call the XYz flow/wave; while, there are other special superposition principles for some specific cases. We try to remark on the possible connections …
To elucidate the influence of shear flow on the generation of magnetic field (the dynamo effect), we study the kinematic limit where the magnetic field does not backreact on the velocity field. By non-perturbatively incorporating the effect of shear in a helically forced turbulence, we show that turbulence intensity and turbulent transport coefficients (turbulent viscosity, $α$ and $β$ effect) are enhanced by a weak shear while strongly suppressed for strong shear. In particular, $β$ is shown to be much more strongly suppressed than $α$ effect. We discuss its important implications for dynamo …
We show that helical turbulence produced during a first-order phase transition generates circularly polarized cosmological gravitational waves (GWs). The characteristic frequency of these GWs for an extreme case of the phase transition model is around $10^{-3}$ --- $10^{-2}$ Hz with an energy density parameter as high as $10^{-12}$ --- $10^{-11}$. The possibility of detection is briefly discussed.
We solve the Navier-Stokes equations with two simultaneous forcings. One forcing is applied at a given large-scale and it injects energy. The other forcing is applied at all scales belonging to the inertial range and it injects helicity. In this way we can vary the degree of turbulence helicity from non helical to maximally helical. We find that increasing the rate of helicity injection does not change the energy flux. On the other hand the level of total energy is strongly increased and the energy spectrum gets steeper. The energy spectrum spans from a Kolmogorov scaling law $k^{-5/3}$ for a …
While in classical turbulence helicity depletes nonlinearity and can alter the evolution of turbulent flows, in quantum turbulence its role is not fully understood. We present numerical simulations of the free decay of a helical quantum turbulent flow using the Gross-Pitaevskii equation at high spatial resolution. The evolution has remarkable similarities with classical flows, which go as far as displaying a dual transfer of incompressible kinetic energy and helicity to small scales. Spatio-temporal analysis indicates that both quantities are dissipated at small scales through non-linear excit…
Using direct numerical simulation of hydrodynamic turbulence with helicity forcing applied at all scales, a near-maximum helical turbulent state is obtained, with an inverse energy cascade at scales larger than the energy forcing scale and a forward helicity cascade at scales smaller than the energy forcing scale. In contrast to previous studies using decimated triads, our simulations contain all possible triads. By computing the shell-to-shell energy fluxes, we show that the inverse energy cascade results from weakly non-local interactions among homochiral triads. Varying the helicity injecti…
We study the evolution of kinetic and magnetic energy spectra in magnetohydrodynamic flows in the presence of strong cross helicity. For forced turbulence, we find weak inverse transfer of kinetic energy toward the smallest wavenumber. This is plausibly explained by the finiteness of scale separation between the injection wavenumber and the smallest wavenumber of the domain, which here is a factor of 15. In the decaying case, there is a slight increase at the smallest wavenumber, which is probably explained by the dominance of kinetic energy over magnetic energy at the smallest wavenumbers. Wi…
The present paper deals with the study of spectral properties of the helical mode of uniform isotropic turbulence in the presence and in the absence of mean helicity. It is shown that even in the absence of mean helicity, the helicity of individual helical modes affects the spectral behavior of turbulence. Besides, it is shown that both in the presence and in the absence of mean helicity, intermediate characteristic scales connected with the presence of helicity in helical modes should exist. The existence of these scales makes it possible to solve the problem of helicity dissipation divergenc…
The role of the moments of helicity distribution in rotating turbulence has been studied using the notion of helical distributed chaos. Results of the direct numerical simulations, laboratory experiments and geophysical observations have been used in this investigation. It is shown, in particular, that even for the cases when the global helicity is equal to zero at least even moments are usually non-zero (due to the appearance of the local spatial regions with strong negative and positive helicity) and can play a significant role in the rotating turbulence as adiabatic invariants. Rotating buo…
Turbulent ship wake conservation at a long distance is one of unsolved problems at present. It is well known that wakes have a rotational structure and slowly expand with distance. Nevertheless, experimental data on their structure and properties are not sufficient. On the other hand, these experimental data show that the divergence of wakes does not change according to the law 1/5, as predicted by the theory. In our work we study the effect of helicity on the parameters of a turbulent ship wake. Taking into account the helical nature of the wake, we can clarify the difference between turbulen…
We investigate magnetic field amplification in a turbulent velocity field with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan model. We present the numerical solution of the model for the practically important case of Kolmogorov distribution of velocity fluctuations, with a large magnetic Reynolds number. We find that in contrast to the nonhelical case where growing magnetic fields are described by a few bound eigenmodes concentrated inside the inertial interval of the velocity field, in the helical case the number of bound eigenmodes considerably increases; moreover, …
We perform a study on the evolution of helical quantum turbulence at different temperatures by solving numerically the Gross-Pitaevskii and the Stochastic Ginzburg-Landau equations, using up to $4096^3$ grid points with a pseudospectral method. We show that for temperatures close to the critical the fluid described by these equations can act as a classical viscous flow, with the decay of the incompressible kinetic energy and the helicity becoming exponential. The transition from this behavior to the one observed at zero temperature is smooth as a function of temperature. Moreover, the presence…
We study the intermittency properties of the energy and helicity cascades in two 1536^3 direct numerical simulations of helical rotating turbulence. Symmetric and anti-symmetric velocity increments are examined, as well as probability density functions of the velocity field and of the helicity density. It is found that the direct cascade of energy to small scales is scale invariant and non-intermittent, whereas the direct cascade of helicity is highly intermittent. Furthermore, the study of structure functions of different orders allows us to identify a recovery of isotropy of strong events at…
A decomposition of the energy and helicity fluxes in a turbulent hydrodynamic flow is proposed. The decomposition is based on the projection of the flow to a helical basis that allows to investigate separately the role of interactions among modes of different helicity. The proposed formalism is then applied in large scale numerical simulations of a non-helical and a helical flow, where the decomposed fluxes are explicitly calculated. It is shown that the total energy flux can be split in to three fluxes that independently remain constant in the inertial range. One of these fluxes that correspo…
We show that in decaying hydromagnetic turbulence with initial kinetic helicity, a weak magnetic field eventually becomes fully helical. The sign of magnetic helicity is opposite to that of the kinetic helicity - regardless of whether or not the initial magnetic field was helical. The magnetic field undergoes inverse cascading with the magnetic energy decaying approximately like t^{-1/2}. This is even slower than in the fully helical case, where it decays like t^{-2/3}. In this parameter range, the product of magnetic energy and correlation length raised to a certain power slightly larger than…
In an experiment in the Institute of Continuous Media Mechanics in Perm (Russia) an non--stationary screw dynamo is intended to be realized with a helical flow of liquid sodium in a torus. The flow is necessarily turbulent, that is, may be considered as a mean flow and a superimposed turbulence. In this paper the induction processes of the turbulence are investigated within the framework of mean--field electrodynamics. They imply of course a part which leads to an enhanced dissipation of the mean magnetic field. As a consequence of the helical mean flow there are also helical structures in the…
We study the effect of large-scale spectral forcing on the scale-dependent anisotropy of the velocity field in direct numerical simulations of homogeneous incompressible turbulence. Two forcing methods are considered: the steady ABC single wavenumber scheme and the unsteady non-helical or helical Euler scheme. The results are also compared with high resolution data obtained with the negative viscosity scheme. A fine-grained characterization of anisotropy, consisting in measuring some quantities related to the two-point velocity correlations, is used: we perform a modal decomposition of the spe…
We present results from two 1536^3 direct numerical simulations of rotating turbulence where both energy and helicity are injected into the flow by an external forcing. The dual cascade of energy and helicity towards smaller scales observed in isotropic and homogeneous turbulence is broken in the presence of rotation, with the development of an inverse cascade of energy now coexisting with direct cascades of energy and helicity. In the direct cascade range, the flux of helicity dominates over that of energy at low Rossby number. These cascades have several consequences for the statistics of th…
Recent numerical simulations have shown the strong impact of helicity on \ADD{homogeneous} rotating hydrodynamic turbulence. The main effect can be summarized through the following law, $n+\tilde n = -4$, where $n$ and $\tilde n$ are respectively the power law indices of the one-dimensional energy and helicity spectra. We investigate this rotating turbulence problem in the small Rossby number limit by using the asymptotic weak turbulence theory derived previously. We show that the empirical law is an exact solution of the helicity equation where the power law indices correspond to perpendicula…
The conventional approach to the turbulent energy cascade, based on Richardson-Kolmogorov phenomenology, ignores the topology of emerging vortices, which is related to the helicity of the turbulent flow. It is generally believed that helicity can play a significant role in turbulent systems, e.g., supporting the generation of large-scale magnetic fields, but its impact on the energy cascade to small scales has never been observed. We suggest for the first time a generalized phenomenology for isotropic turbulence with an arbitrary spectral distribution of the helicity. We discuss various scenar…
Spectral transfer processes in magnetohydrodynamic (MHD) turbulence are investigated analytically by decomposition of the velocity and magnetic fields in Fourier space into helical modes. Steady solutions of the dynamical system which governs the evolution of the helical modes are determined, and a stability analysis of these solutions is carried out. The interpretation of the analysis is that unstable solutions lead to energy transfer between the interacting modes while stable solutions do not. From this, a dependence of possible interscale energy and helicity transfers on the helicities of t…
We present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami (ABC) forcing, creating helical flow. The Zeman scale $\ell_Ω$ at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy $E$ and helicity $H$, and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of $3072^3$ points, with Ro…
We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions and turbulent transport coefficients of passive scalars in turbulent rotating helical and non-helical flows. We show that helicity affects the inertial range scaling of the velocity and of the passive scalar when rotation is present, with a spectral law consistent with $\sim k_{\perp}^{-1.4}$ for the passive scalar variance spectrum. This scaling law is consistent with the phenomenological argument presented in \cite{imazio2011} for rotating non-helical flows, wich states that i…
We present a study of spectral laws for helical turbulence in the presence of solid body rotation up to Reynolds numbers Re~1*10^5 and down to Rossby numbers Ro~3*10^-3. The forcing function is a fully helical flow that can also be viewed as mimicking the effect of atmospheric convective motions. We test in the helical case variants of a model developed previously (Baerenzung et al. 2008a) against direct numerical simulations (DNS), using data from a run on a grid of 15363 points; we also contrast its efficiency against a spectral Large Eddy Simulation (LES) (Chollet and Lesieur 1981) as well …
Ideas and theories of turbulence based on modifying the Navier-Stokes equation, to obtain equilibrium and non-equilibrium time-reversible dynamical ensembles relevant to helical turbulence, are presented. Discussions of controlling helicity to control the aerodynamic force, heat and noise are presented, together with the compressible turbulence relevant statistical mechanics analysis. A helical time-reversible system for nonequilibrium dynamical ensemble is constructed. Applications are also remarked.
The motion of a rotating helical body in a viscoelastic fluid is considered. In the case of force-free swimming, the introduction of viscoelasticity can either enhance or retard the swimming speed and locomotive efficiency, depending on the body geometry, fluid properties, and the body rotation rate. Numerical solutions of the Oldroyd-B equations show how previous theoretical predictions break down with increasing helical radius or with decreasing filament thickness. Helices of large pitch angle show an increase in swimming speed to a local maximum at a Deborah number of order unity. The numer…
Shell models of turbulence have a finite-time blowup in the inviscid limit, i.e., the enstrophy diverges while the single-shell velocities stay finite. The signature of this blowup is represented by self-similar instantonic structures traveling coherently through the inertial range. These solutions might influence the energy transfer and the anomalous scaling properties empirically observed for the forced and viscous models. In this paper we present a study of the instantonic solutions for a set of four shell models of turbulence based on the exact decomposition of the Navier-Stokes equations …
We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. We demonstrate that such turbulence is governed by the reconnection of magnetic structures, and not by ideal dynamics, as has previously been assumed. We obtain predictions for the magnetic-energy decay laws by proposing that turbulence decays on reconnection timescales, while respecting the conservation of certain integral invariants representing topological constraints satisfied by the reconnecting magnetic field. As is well known, the magnetic helicity is such an inva…
The dynamics of two-dimensional three-component (2D3C) flows is relevant to describe the long-time evolution of strongly rotating flows and/or of conducting fluids with a strong mean magnetic field. We show that in the presence of a strong helical forcing, the out-of-plane component ceases to behave as a passive advected quantity and develops a nontrivial dynamics which deeply changes its large-scale properties. We show that a small-scale helicity injection correlates the input on the 2D component with the one on the out-of-plane component. As a result, the third component develops a non-trivi…
The distributed chaos driven by Levich-Tsinober (helicity) integral: $I=\int \langle h({\bf x},t)~h({\bf x}+{\bf r}, t)\rangle d{\bf r}$ has been studied. It is shown that the helical distributed chaos can be considered as basis for complex turbulent flows with interplay between large-scale coherent structures and small-scale turbulence, such as Cuette-Taylor flow, wake behind cylinder and turbulent flow in the Large Plasma Device (LAPD) with inserted limiters. In the last case appearance of the helical distributed chaos, caused by the limiters, results in improvement of radial particle confin…
We perform direct numerical simulations to compute the net circular polarization of gravitational waves from helical (chiral) turbulent sources in the early Universe for a variety of initial conditions, including driven (stationary) and decaying turbulence. We investigate the resulting gravitational wave signal assuming different turbulent geneses such as magnetically or kinetically driven cases. Under realistic physical conditions in the early Universe we compute numerically the wave number-dependent polarization degree of the gravitational waves. We find that the spectral polarization degree…
Invariance properties of physical systems govern their behavior: energy conservation in turbulence drives a wide distribution of energy among modes, observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of helicity conservation (correlation between velocity and its curl, measuring departures from mirror symmetry) remains unclear since it does not alter the energy spectrum. However, with solid body rotation, significant differences emerge between helical and non-helical flows. We first outline several results, like the energy and helicity spectral distribution and the…
Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the ratio of kinetic-to-magnetic energy dissipation always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of the energy conversion from ki…
Swimming microorganisms often have to propel in complex, non-Newtonian fluids. We carry out experiments with self-propelling helical swimmers driven by an externally rotating magnetic field in shear-thinning, inelastic fluids. Similarly to swimming in a Newtonian fluid, we obtain for each fluid a locomotion speed which scales linearly with the rotation frequency of the swimmer, but with a prefactor which depends on the power index of the fluid. The fluid is seen to always increase the swimming speed of the helix, up to 50% faster and thus the strongest of such type reported to date. The maximu…
The excitation and further sustenance of large-scale magnetic fields in rotating astrophysical systems, including planets, stars and galaxies, is generally thought to involve a fluid magnetic dynamo effect driven by helical magnetohydrodynamic turbulence. While this scenario is appealing on general grounds, it however currently remains largely unconstrained, notably because a fundamental understanding of the nonlinear asymptotic behaviour of large-scale fluid magnetism in the astrophysically-relevant but treacherous regime of large magnetic Reynolds number $Rm$ is still lacking. We explore thi…
In this paper, we study a new type of large-scale instability in obliquely rotating stratified fluids with small scale non-helical turbulence. The small-scale turbulence is generated by the external force with zero helicity and low Reynolds number. The theory uses the method of multiscale asymptotic developments. The nonlinear equations for large scale motions are obtained in the third order of the perturbation theory. In this paper, we consider the linear instability and the stationary nonlinear modes. We obtain solutions in the form of nonlinear Beltrami waves and localized vortex structures…
The buildup of small-scale magnetic helicity which accompanies the oppositely signed growth on large scales is central to conventional dynamical quenching theories of mean-field dynamos. However, the conventional formalism presumes isotropic turbulence and thereby excludes part of the magnetic Lorentz back-reaction. This renders it insufficient to predict the full quenching for general anisotropic flows. To overcome this deficiency, we derive a new generalized quenching formalism that includes the full back-reacting Lorentz force, and a new "selective-damping-$τ$" closure which conserves magne…
The free decay of MHD turbulence at large Reynolds numbers is studied numerically using a shell model. We study the statistical properties based on representative sample of realisations (128 realisations for each type of initial conditions) over the period of $10^5$ large-scale turnover times. The performed simulations show that the force-free non-helical MHD turbulence can demonstrate two different scenarios of evolution in spite of similar initial conditions. Within the first scenario, the cross-helicity accumulation is so fast that the energy cascade vanishes before significant magnetic ene…
Drift of interfaces in forced stably-stratified turbulence and the role of vertically-sheared helical structures
Department of Physics & INFN, University of Rome “Tor Vergata”（罗马第二大学物理系及意大利国家核物理研究所）；INFN Sezione di Lecce（意大利国家核物理研究所莱切分部）；CNR NANOTEC（意大利国家研究委员会纳米技术研究所）
We investigate the effects of helical swimmer shape (i.e., helical pitch angle and tail thickness) on swimming dynamics in a constant viscosity viscoelastic (Boger) fluid via a combination of particle tracking velocimetry, particle image velocimetry and 3D simulations of the FENE-P model. The 3D printed helical swimmer is actuated in a magnetic field using a custom-built rotating Helmholtz coil. Our results indicate that increasing the swimmer tail thickness and pitch angle enhances the normalized swimming speed (i.e., ratio of swimming speed in the Boger fluid to that of the Newtonian fluid).…
We present direct numerical simulations and alpha-model simulations of four familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects: selective decay, dynamic alignment, inverse cascade of magnetic helicity, and the helical dynamo effect. The MHD alpha-model is shown to capture the long-wavelength spectra in all these problems, allowing for a significant reduction of computer time and memory at the same kinetic and magnetic Reynolds numbers. In the helical dynamo, not only does the alpha-model correctly reproduce the growth rate of magnetic energy during the kinematic regime, bu…
The effects of large scale mechanical forcing on the dynamics of rotating turbulent flows are studied by means of numerical simulations, varying systematically the nature of the mechanical force in time. We demonstrate that the statistically stationary solutions of these flows depend on the nature of the forcing mechanism. Rapidly enough rotating flows with a forcing that has a persistent direction relatively to the axis of rotation bifurcate from a non-helical state to a helical state despite the fact that the forcing is non-helical. We find that the nature of the mechanical force in time and…
We study the linear stability of elastic collapsible tubes conveying fluid, when the equilibrium configuration of the tube is helical. A particular case of such tubes, commonly encountered in applications, is represented by quarter- or semi-circular tubular joints used at pipe's turning points. The stability theory for pipes with non-straight equilibrium configurations, especially for collapsible tubes, allowing dynamical change of the cross-section, has been elusive as it is difficult to accurately develop the dynamic description via traditional methods. We develop a methodology for studying …
