不可压缩波Turbulence的能量谱
Incompressible Energy Spectrum from Wave Turbulence
摘要：
具有超流性的玻色-爱因斯坦凝聚体提供了一种与经典流体类似的有趣的现象。由于均匀湍流的柯尔莫哥洛夫谱，不可压缩速度场的统计数据引起了人们极大的兴趣，但在超流体中，从宏观波函数获得速度场的统计数据是一项复杂的任务;因此，迄今为止的大部分工作本质上都是数值的。我们利用弱波湍流（WWT）理论，它提供了宏观波函数的统计数据，以获得统计的速度场，这使我们能够产生一个半解析的过程中提取的WWT制度的不可压缩的能量谱。这是通过引入一个辅助波函数，保留相关的统计和流体力学性质的冷凝物，但具有均匀的密度，从而允许一个简单的描述的速度场。
英文摘要：
Bose-Einstein condensates with their superfluidity property provide an interesting parallel to classical fluids. Due to the Kolmogorov spectrum of homogeneous turbulence the statistics of the incompressible velocity field is of great interest, but in superfluids obtaining quantities such as the statistics of the velocity field from the macroscopic wavefunction turns out be a complicated task; therefore, most of the work up to now has been numerical in nature. We made use of the Weak Wave Turbulence (WWT) theory, which provides the statistics of the macroscopic wavefunction, to obtain the statistics of the velocity field, which allowed us to produce a semi analytical procedure for extracting the incompressible energy spectrum in the WWT regime. This is done by introducing an auxiliary wavefunction that preserves the relevant statistical and hydrodynamical properties of the condensate but with a homogeneous density thus allowing for a simpler description of the velocity field.
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