Sự khác biệt giữa vật lý và toán học là ở chỗ, vật lý luôn gắn liền với thế giới tự nhiên, trong khi toán học lại biểu diễn các mô hình trừu tượng độc lập với thế giới tự nhiên. Tuy vậy, sự khác biệt không phải lúc nào cũng rõ ràng. | 2 Stability of Quasi Two-Dimensional Vortices 53 such as the pairing of same sign vortices or the creation of vorticity filaments. They should therefore modify the phenomenology of the turbulence. In particular for large Rossby number and small Froude number the pairing of two vortices is unstable to the generalized zigzag instability and while approaching each other the vortices should form thinner and thinner layers resulting in an energy transfer to smaller length scales and not larger scales as in the 2D turbulence. This effect of the zigzag instability would then explain the result of Lindborg 32 who shows processing turbulence data collected during airplane flights and computing third-order moment of the turbulence that the energy cascade in the horizontal energy spectra is direct and not reverse as it was conjectured by Lilly 31 . Appendix Local Approach Along Trajectories In this appendix we investigate the instability of a 2D steady basic flow characterized by a velocity UB and a pressure PB in the inviscid case. The normal vector of the flow field is denoted e2. The 3D perturbations are denoted u p . In a frame rotating at the angular frequency e2 the linearized Euler equation read as d u UB Vu Vp 2Q X u d t V .u 0. Following Lifschitz and Hameiri 33 we consider a rapidly oscillating localized perturbation u exp iệ x t Ệ a t O 8 p exp iệ x t Ệ n t O 8 where Ệ is a small parameter. Substitution in the linearized Euler equations leads to a set of differential equations for the amplitude and the wave vector k VỘ evolving along the trajectories of the basic flow d x dt d k dt LTB k d a dt I Ca UB with LB VUB the velocity gradient tensor the superscript T denoting the transposition I the unity tensor and C the Coriolis tensor 54 . Chomaz et al. 0 -2Q 0 C 2Q 0 0 . 0 0 0 The pressure has been eliminated by applying the operator P k I - kkr iki2 The incompressibility equation yields 0. The .
