This paper provides the numerical investigation of two-dimensional stochastic Navier-Stokes equation driven by additive white noises. The vorticity-stream function method is presented to calculate the incompressible fluid flow. In order to solve the formulation of steam function equation, we propose a Crank-Nicolson Fourier pseudo-spectral method. Numerical results obviously show that the presence of stochastic forcing can have an impact upon the shapes of vortex in fluid flow. To a certain extent, the phenomenon of eddy shedding and the formation of some new vortex in a random medium can be observed, which make it possible for us to conduct optimal control experiments in the development of vortex structures.

Ion beam-assisted deposition (IBAD) has been proposed as a promising texturing technology that uses film epitaxy method to obtain biaxial texture on a non-textured metal or compound substrate. Magnesium oxide (MgO) is the most well explored texturing material. In order to obtain the optimal biaxial texture, the actual thickness of the IBAD-MgO film must be controlled within 12 nm. Due to the bombardment of ion beams, IBAD-MgO has large lattice deformation, poor texture and many defects in the films. In this work, an additional homogeneous epitaxy MgO (epi-MgO) layer has been deposited on the IBAD-MgO layer by electron-beam evaporation. The biaxial texture can be optimized by the deposition of additional epi-MgO layer. The effects of growth temperature, film thickness, deposition rate and oxygen flux on the texture and morphology of the epi-MgO film were systematically studied. After the research of epi-MgO process, the best full width at half maximum (FWHM) values were 2.2 for the out-of-plane texture and 4.8° for the in-plane texture, respectively. Subsequently, the LaMnO3 cap layer and YBa2Cu3O7-x (YBCO) functional layer was deposited on the epi-MgO layer to test the quality of MgO layer. Finally, the critical current density of YBCO films is 6MA/cm2 (77K, 500nm, self-field), indicating that this research provides a high-quality MgO substrate for the YBCO layer.