论文标题
水平磁场中铁氟烷表面的波湍流的数值模拟
Numerical simulation of the wave turbulence on the surface of a ferrofluid in a horizontal magnetic field
论文作者
论文摘要
在一维弱非线性模型的框架中考虑了在水平磁场中具有高渗透性的铁氟烷表面毛细管的湍流。在强磁场的极限下，研究的表面波可以在外部场的方向上或靠在外部磁场方向上传播，即类似于完美传导的流体中的Alfvén波。反向传播非线性波的相互作用导致液体表面上的波湍流的发展。计算数据表明，湍流的光谱分为两个部分：低频分散区域，磁力主导和高频分散剂，其中毛细作用力的影响变得显着。在第一个区域，地面高程的光谱在$ k $和$ω$域中具有相同的指数，并且其值接近$ -3.5 $，这与从弱涡轮电源的尺寸分析获得的估计中达成了很好的一致性。在高频下，表面波的计算空间频谱接近$ k^{ - 5/2} $，在频率方面对应于$ω^{ - 5/3} $。该光谱与纯毛细血管波获得的Zakharov-Filonenko光谱不一致。对这一事实的可能解释是在较弱的分散媒体中通常引起的相干结构（例如冲击波）的影响。
The turbulence of capillary waves on the surface of a ferrofluid with a high permeability in a horizontal magnetic field is considered in the framework of a one-dimensional weakly nonlinear model. In the limit of a strong magnetic field, the surface waves under study can propagate without distortions along or against the direction of external field, i.e., similar to Alfvén waves in a perfectly conducting fluid. The interaction of counter-propagating nonlinear waves leads to the development of wave turbulence on the surface of the liquid. The computational data show that the spectrum of turbulence is divided into two parts: a low-frequency dispersionless region, where the magnetic forces dominate and a high-frequency dispersive one, in which the influence of capillary forces becomes significant. In the first region, the spectrum of the surface elevation has the same exponent in $k$ and $ω$ domains and its value is close to $-3.5$, what is in a good agreement with the estimation obtained from the dimensional analysis of the weak turbulence spectra. At the high frequencies, the computed spatial spectrum of the surface waves is close to $k^{-5/2}$ which corresponds to $ω^{-5/3}$ in terms of the frequency. This spectrum does not coincide with the Zakharov-Filonenko spectrum obtained for pure capillary waves. A possible explanation of this fact is in the influence of coherent structures (like shock waves) usually arising in media with weak dispersion.
