Problems when using Mode-sum replacing the FFT to generate perturbation for turbulence

[YaoguangPei]

Hi all,
Recently I wanna use turb with AMR, however due to FFT is not compatible with AMR, and turb needs FFT to generate perturbation, so I wanna use new method to replace FFT, thus I found a method called Mode-sum to replace. Here is the main equation for Mode-sum,

where A is the amplitude, e is the vector for shearing. The distribution of A is controlled by the parameter expo. Moreover FFT controls the power spectrum of the whole region, and Mode-sum controls the spectrum of cell, to maintain continuity, for all A I times 1/(nxnynz). As u can see, perturbation rely on the position of each cell, so it is naturally compatible with AMR.
But when I run the sim for both method under the same condition with no AMR, the velocity of FFT will be 1 km/s, and KE will be 70,
for Mode-sum, the velocity will be much higher like thousands of km/s, and KE will be that level too.
So I debug the parameter s and dv_mean just before the injection part, I found the order of s and dv_mean for both method is near the same, so I do not know where it's the problem.
To have a clear view, I also give u the debug info at the beginning of the sim.


If you have any ideas for this problem or u wanna more info, please fell free to contact me.
Best regards,
Yaoguang Pei