arXiv subjects

R. Hänninen

Publications and source records attributed to R. Hänninen.

At least 19 recordsLinked to original sources

arXiv2022

Rotating quantum wave turbulence

Rotating turbulence is ubiquitous in nature. Previous works suggest that such turbulence could be described as an ensemble of interacting inertial waves across a wide range of length scales. For turbulence in macroscopic quantum condensates, the nature of the transition between the quasiclassical dynamics at large scales and the corresponding dynamics at small scales, where the quantization of vorticity is essential, remains an outstanding unresolved question. Here we expand the paradigm of wave-driven turbulence to rotating quantum fluids where the spectrum of waves extends to microscopic scales as Kelvin waves on quantized vortices. We excite inertial waves at the largest scale by periodic modulation of the angular velocity and observe dissipation-independent transfer of energy to smaller scales and the eventual onset of the elusive Kelvin-wave cascade at the lowest temperatures. We further find that energy is pumped to the system through a boundary layer distinct from the classical Ekman layer and support our observations with numerical simulations. Our experiments demonstrate a new regime of turbulent motion in quantum fluids where the role of vortex reconnections can be neglected, thus stripping the transition between the classical and the quantum regimes of turbulence down to its bare bones.

physics.flu-dyn↗

arXiv2016

Leapfrogging Kelvin waves

Two vortex rings can form a localized configuration whereby they continually pass through one another in an alternating fashion. This phenomenon is called leapfrogging. Using parameters suitable for superfluid helium-4, we describe a recurrence phenomenon that is similar to leapfrogging, which occurs for two coaxial straight vortex filaments with the same Kelvin wave mode. For small-amplitude Kelvin waves we demonstrate that our full Biot-Savart simulations closely follow predictions obtained from a simpified model that provides an analytical approximation developed for nearly parallel vortices. Our results are also relevant to thin-cored helical vortices in classical fluids.

physics.flu-dyn↗

arXiv2016

Helicity within the vortex filament model

Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its key attribute as a quadratic invariant. By defining a spanwise vector to the vortex through the use of a Seifert framing, we are able to introduce twist and henceforth recover the key properties of helicity. We present several examples for calculating internal twist to illustrate why the centreline helicity alone will lead to ambiguous results if a twist contribution is not introduced. Our choice of the spanwise vector can be expressed in terms of the tangential component of velocity along the filament. Since the tangential velocity does not alter the configuration of the vortex at later times, we are able to recover a similar equation for the internal twist angle for classical vortex tubes. Our results allow us to explain how a quasi-classical limit of helicity emerges from helicity considerations for individual superfluid vortex filaments.

physics.flu-dyn↗

arXiv2015

Kelvin waves from vortex reconnection in superfluid helium at low temperatures

We report on the analysis of the root mean square curvature as a function of the numerical resolution for a single reconnection of two quantized vortex rings in superfluid helium. We find a similar scaling relation as reported in the case of decaying thermal counterflow simulations by L. Kondaurova et al. There the scaling was related to the existence of a Kelvin-wave cascade which was suggested to support the L'vov-Nazarenko spectrum. Here we provide an alternative explanation that does not involve the Kelvin-wave cascade but is due to the sharp cusp generated by a reconnection event in a situation where the maximum curvature is limited by the computational resolution. We also suggest a method for identifying the Kelvin spectrum based on the decay of the rms curvature by mutual friction. Our vortex filament simulation calculations show that the spectrum of Kelvin waves after the reconnection is not simply $n(k) \propto k^{-η}$ with constant $η$. At large scales the spectrum seems to be close to the Vinen prediction with $η$ = 3 but becomes steeper at smaller scales.

cond-mat.other↗

arXiv2015

Comment on "Reconnection of quantized vortex filaments and the Kolmogorov spectrum"

In this Comment we would like to emphasize that in Phys. Rev. B 90, 104506 (2014) the calculated energy spectrum takes into account only the small interaction (cross) term and, additionally, this term is only calculated at the instant when the two vortices reconnect. The majority of the kinetic energy is contained in the self-energy term which has a characteristic spectrum of $1/k$. If this, and the additional average over time, is taken into account the suggested Kolmogorov type $k^{-5/3}$ spectrum is likely not visible in the kinetic energy spectrum which contains both terms. Therefore, we find the suggestion misleading that the Kolmogorov spectrum in superfluids arises from the reconnection of vortices.

cond-mat.other↗

arXiv2014

Breakdown of Potential Flow to Turbulence around a Sphere Oscillating in Superfluid He-4 above the Critical Velocity

The onset of turbulent flow around an oscillating sphere in superfluid $^4$He is known to occur at a critical velocity $v_c \sim \sqrt{κω}$ where $κ$ is the circulation quantum and $ω$ is the oscillation frequency. But it is also well known that initially in a first up-sweep of the oscillation amplitude, $v_c$ can be considerably exceeded before the transition occurs, thus leading to a strong hysteresis in the velocity sweeps. The velocity amplitude $v_c^* > v_c$ where the transition finally occurs is related to the density $L_0$ of the remanent vortices in the superfluid. Moreover, at temperatures below ca. 0.5 K and in a small interval of velocity amplitudes between $v_c$ and a velocity that is about 2% larger, the flow pattern is found to be unstable, switching intermittently between potential flow and turbulence. From time series recorded at constant temperature and driving force the distribution of the excess velocities $Δv = v_c^* - v_c$ is obtained and from that the failure rate. Below 0.1 K we also can determine the distribution of the lifetimes of the phases of potential flow. Finally, the frequency dependence of these results is discussed.

cond-mat.other↗

arXiv2013

Dissipation enhancement from a single vortex reconnection in superfluid helium

We investigate a single vortex reconnection event in superfluid helium at finite temperatures using the vortex filament model. The reconnection induces Kelvin waves which strongly increase energy dissipation. We evaluate the mutual friction dissipation from the reconnection and show that the dissipation power has universal form, which is seen by scaling both time (measured from the reconnection event) and power by the mutual friction parameter alpha. This observation allows us to conclude that the Kelvin-wave cascade is not important in the energy dissipation process within the range alpha > 0.001. Rather, the energy is directly transferred from Kelvin waves to the normal component. Moreover, while the excited Kelvin waves greatly enhance energy dissipation, no similar change is seen in angular momentum from the reconnection event. This result has similarities with recent 3He-B measurements. Our results also confirm another earlier observation that the minimum distance between vortices scales approximately as d ~ sqrt(|t-trec|), both before and after the reconnection event.

cond-mat.other↗

arXiv2013

Asymptotic motion of a single vortex in a rotating cylinder

We study numerically the behavior of a single quantized vortex in a rotating cylinder. We study in particular the spiraling motion of a vortex in a cylinder that is parallel to the rotation axis. We determine the asymptotic form of the vortex and its axial and azimuthal propagation velocities under a wide range of parameters. We also study the stability of the vortex line and the effect of tilting the cylinder from the rotation axis.

cond-mat.other↗

arXiv2013

Energy and angular momentum balance in wall-bounded superfluid turbulence

A superfluid in the absence of the viscous normal component should be the best realization of an ideal inviscid Euler fluid. As expressed by d'Alembert's famous paradox, an ideal fluid does not exert drag on bodies past which it flows, or in other words, it does not exchange momentum with them. Also, the flow of an ideal fluid does not dissipate kinetic energy. We study experimentally whether these properties apply to the flow of superfluid 3He-B in a rotating cylinder at low temperatures. It is found that ideal behavior is broken by quantum turbulence, which leads to substantial energy dissipation, as observed also earlier. Here we show that remarkably, nearly ideal behavior is preserved with respect to the angular-momentum exchange between the superfluid and its container, i.e., the drag almost disappears in the zero-temperature limit. This mismatch between energy and angular-momentum transfer results in a new physical situation where the proper description of wall-bounded quantum turbulence requires two effective friction parameters, one for energy dissipation and another for momentum coupling, which become substantially different at very low temperatures.

cond-mat.other↗

arXiv2012

Identification of Kelvin waves: numerical challenges

Kelvin waves are expected to play an essential role in the energy dissipation for quantized vortices. However, the identification of these helical distortions is not straightforward, especially in case of vortex tangle. Here we review several numerical methods that have been used to identify Kelvin waves within the vortex filament model. We test their validity using several examples and estimate whether these methods are accurate enough to verify the correct Kelvin spectrum. We also illustrate how the correlation dimension is related to different Kelvin spectra and remind that the 3D energy spectrum E(k) takes the form 1/k in the high-k region, even in the presence of Kelvin waves.

cond-mat.other↗

arXiv2012

Steady-state spectrum of Kelvin waves on a quantized vortex at finite temperatures

We determine numerically the steady-state spectrum for Kelvin waves on a superfluid 4He vortex that is driven by shaking its end points and damped by mutual friction. The relaxation rate towards a steady state is determined by the mutual friction. We have reached the zero temperature limit where the steady-state spectrum and the vortex length become independent of the temperature. Our drive with pointlike pinning sites produces a characteristic spectrum with $|w_m|\propto m^{-η}$, where $η\approx$ 1.88. The spatially sharply peaked drive and the fact that we are fixing the oscillation amplitude, not the power, causes that there exists no high k cutoff from mutual friction even when mutual friction is large. This spectrum is generic to the pinned boundary conditions used. Without pinning the spectrum is sensitive to the drive. The spectrum even depends on the amplitude of the initial spectrum if vortex is allowed to relax on its own. Therefore, in real systems the Kelvin spectrum is not unique and depends on external conditions.

cond-mat.other↗

arXiv2011

Dynamical scaling of the critical velocity for the onset of turbulence in oscillatory superflows

The critical velocity v_c for the onset of turbulence in oscillatory flows of superfluid helium is known to depend on the oscillation frequency omega, namely v_c ~ sqrt(kappa*omega) where kappa is the circulation quantum. Only the numerical prefactor may have some geometry dependence. This universal behaviour was described earlier qualitatively either by employing the superfluid Reynolds number or by extending known dc vortex dynamics to ac flow. In our present work we emphasize that v_c(omega) ~ sqrt(omega) can also be derived rigorously by means of dynamical scaling of equations of vortex dynamics as pointed out by Kotsubo and Swift already two decades ago.

cond-mat.other↗

arXiv2009

Universal onset of quantum turbulence in oscillating flows and crossover to steady flows

The critical velocity v_c for the onset of quantum turbulence in oscillatory flows of superfluid helium is universal and scales as v_c \sim \sqrt{κω}, where κis the circulation quantum and ωis the oscillation frequency. This result can be derived from a general argument based on the "superfluid Reynolds number". Only the numerical prefactor may depend somewhat on the geometry of the oscillating object because the flow velocity at the surface of the object may differ from the velocity amplitude of the body. A more detailed analysis derived from the dynamics of the turbulent state gives v_c \approx \sqrt{8κω/β}, where β\sim 1 depends on the mutual friction parameters. This universality is compared with the recently discovered universality of classical oscillatory flows. We also discuss the effect of remanent vorticity on the onset of quantum turbulence. Finally, by employing the "superfluid Reynolds number" again, we argue how v_c changes when the steady case ω= 0 is approached. In that case v_c scales as κ/R, where R is the size of the object.

cond-mat.other↗

arXiv2009

Rotating inclined cylinder and the effect of the tilt angle on vortices

We study numerically some possible vortex configurations in a rotating cylinder that is tilted with respect to the rotation axis and where different numbers of vortices can be present at given rotation velocity. In a long cylinder at small tilt angles the vortices tend to align along the cylinder axis and not along the rotation axis. We also show that the axial flow along the cylinder axis, caused by the tilt, will result in the Ostermeier-Glaberson instability above some critical tilt angle. When the vortices become unstable the final state often appears to be a dynamical steady state, which may contain turbulent regions where new vortices are constantly created. These new vortices push other vortices in regions with laminar flow towards the top and bottom ends of the cylinder where they finally annihilate. Experimentally the inclined cylinder could be a convenient environment to create long lasting turbulence with a polarization which can be adjusted with the tilt angle.

cond-mat.other↗

arXiv2008

Universal Critical Velocity for the Onset of Turbulence of Oscillatory Superfluid Flow

The critical velocity vc for the onset of turbulent drag of small spheres oscillating in superfluid 4He is frequency dependent (omega/2pi from 100 Hz to 700 Hz) and is described by vc = 2.6sqrt(kappa*omega), where kappa is the circulation quantum. A qualitative analysis based on a recent theory of the onset of superfluid turbulence gives vc = sqrt(8*kappa*omega/beta), where beta is of order 1 and depends on the coefficients of mutual friction. This agrees well with the data and implies that vc is a universal critical velocity that is independent of geometry, size, and surface properties of the oscillating body. This is confirmed by comparing our data on spheres with vc obtained with other oscillating structures by other groups. Numerical simulations indicate somewhat larger critical velocity, above which a rapid increase in vortex length is observed.

cond-mat.other↗

arXiv2008

Frequency Dependence of the Critical Velocity of a Sphere Oscillating in Superfluid Helium-4

It is shown that the critical velocity of a small sphere oscillating in superfluid helium increases with the square root of the oscillation frequency. This behavior can be described by a simple dimensional argument. The size of the sphere and the temperature of the superfluid are found to have no or only very little effect. Surface properties of the sphere and remanent vorticity may have an influence but have not been under systematic investigation in these measurements

cond-mat.other↗

arXiv2006

Anomalous translational velocity of vortex ring with finite-amplitude Kelvin waves

We consider finite-amplitude Kelvin waves on an inviscid vortex assuming that the vortex core has infinitesimal thickness. By numerically solving the governing Biot-Savart equation of motion, we study how the frequency of the Kelvin waves and the velocity of the perturbed ring depend on the Kelvin wave amplitude. In particular, we show that, if the amplitude of the Kelvin waves is sufficiently large, the perturbed vortex ring moves backwards.

physics.flu-dyn↗

arXiv2006

The Generation of Turbulence by Oscillating Structures in Superfluid Helium at Very Low Temperatures

The paper is concerned with the interpretation of many experiments that have been reported recently on the production of quantum turbulence by oscillating spheres, wires and grids in both 4He and 3He-B at temperatures so low that there is a negligible fraction of normal fluid. The experimental results are compared with those obtained in analogous experiments with classical fluids and with preliminary simulations of the quantum turbulence. Particular attention is paid to observed values of drag coefficients and to the very different critical velocities observed in 4He and 3He. It is tentatively concluded that in the case of 4He behaviour may well be similar to that observed in the classical analogues, with relatively small changes when the characteristic size of the oscillating structure is not large compared with the quantized vortex spacing, but that in the case of 3He behaviour is very different and due perhaps to very rapid intrinsic nucleation of the quantized vortices.

cond-mat.soft↗