We consider various questions about the 2d incompressible Navier-Stokes and Euler equations on a torus when dissipation is removed from or added to some of the Fourier modes.

We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes are forced) via Kolmogorov equation approach.

We prove the strong Feller property and ergodicity for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes are forced) via Galerkin approximation approach.

Recently, the Nash-style convex integration has been becoming main scheme for mathematical study of turbulence, and building block it either Beltrami flow (finite mode) or Mikado (compactly supported in physical side). On other hand, physics, is observed that turbulence composed a hierarchy scale-by-scale vortex stretching. Thus our motivation this to find another type blocks accompanied by str...

We consider transport properties for a class of periodic, Gaussian, stationary, divergence free, random velocity elds in R 2 with a nite number of spatial modes. Full asymptotics of the eeective diiusivity is obtained in the case of short time correlations, on a fully rigorous basis. Existence and uniqueness for a hypoellip-tic partial diierential equation coupling velocity Fourier modes to phy...

TheCORONAS satellite, launched on 1994March 2, carried theDIFOS experiment to observe irradiance fluctuations due to global solar oscillations. The DIFOS experiment was working for almost 50 days near solar activity minimum. We present first results of the Fourier analysis of the full time series. The fine structure of the low-l p-modes is shown and fitted with Lorentzian line profiles. Results...

Fourier modal method based quantitative analysis method of optical power flow and energy loss in general multi-block photonic structures with an internal dipole emitter is described. The analytic expressions of modal power flow and loss are derived for accurate and efficient quantitative analysis. It is revealed that a few dominating excited photonic modes substantially govern the internal ener...

It is well known that Kirchhoff equations admit infinitely many simple modes, i. e. time periodic solutions with only one Fourier component in the space variables. We prove that, for some choices of the nonlinearity, these simple modes are unstable provided that their energy is large enough. This result, stated in an abstract Hilbert space setting, and proved by reducing to a system of two seco...

The gradual transformation of a guided TM00 mode into an ‘‘intermediate’’ double mode by a splitting junction has been investigated with a phase-sensitive photon scanning tunneling microscope. Field profiles and wave vectors of the modes have been directly determined from the phase information. Via a Fourier analysis of the measured phase and amplitude maps the decay of the TM00 mode and buildu...