اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدModeling Kelvin Wave Cascades in Superfluid Helium
85
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the latter and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in $k$-space via a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and the closeness of the numerics for the higher-order DAM to the analytical predictions for the lower-order DAM .
قيم البحث
اقرأ أيضاً
Both the Kelvin wave and the Kolmogorov turbulence interpretations presented in the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala and M. Soe, arXiv:0905.0159] are misleading, and much more theoretical analysis needs to be done for the
interpretation of the important numerical results obtained by the authors. A way to do this is suggested.
We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum $ESb{LN
}(k)propto k^{-5/3}$ must replace in future theory (e.g. in finding the quantum turbulence decay rate) the previously used spectrum $ESb {KS}(k)propto k^{-7/5}$, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade.
The $A$ phase and the $B$ phase of superfluid He-3 are well studied, both theoretically and experimentally. The decay time scale of the $A$ phase to the $B$ phase of a typical supercooled superfluid $^3$He-A sample is calculated to be $10^{20,000}$ y
ears or longer, yet the actual first-order phase transition of supercooled $A$ phase happens very rapidly (in seconds to minutes) in the laboratory. We propose that this very fast phase transition puzzle can be explained by the resonant tunneling effect in field theory, which generically happens since the degeneracies of both the $A$ and the $B$ phases are lifted by many small interaction effects. This explanation predicts the existence of peaks in the $A to B$ transition rate for certain values of the temperature, pressure, and magnetic field. Away from these peaks, the transition simply will not happen.
We argue that classical transitions can be the key to explaining the long standing puzzle of the fast A-B phase transition observed in superfluid Helium 3 while standard theory expects it to be unobservably slow. Collisions between domain walls are s
hown to be capable of reaching phases inaccessible through homogenous nucleation on the measured timescales. We demonstrate qualitative agreements with prior observations and provide a definite, distinctive prediction that could be verified through future experiments or, perhaps, a specific analysis of existing data.
The Kelvin-Helmholtz instability is well-known in classical hydrodynamics, where it explains the sudden emergence of interfacial surface waves as a function of the velocity of flow parallel to the interface. It can be carried over to the inviscid two
-fluid dynamics of superfluids, to study different types of interfaces and phase boundaries in quantum fluids. We report measurements on the stability of the phase boundary separating the two bulk phases of superfluid 3He in rotating flow, while the boundary is localized with the gradient of the magnetic field to a position perpendicular to the rotation axis. The results demonstrate that the classic stability condition, when modified for the superfluid environment, is obeyed down to 0.4 Tc, if a large fraction of the magnetic polarization of the B-phase is attributed to a parabolic reduction of the interfacial surface tension with increasing magnetic field.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
