论文标题
Casimir保存二维湍流的光谱
Casimir preserving spectrum of two-dimensional turbulence
论文作者
论文摘要
我们介绍了通过采用结构性构成积分器获得的强制二维湍流的能量谱的预测。特别是，我们在单位球体上构建了Navier-Stokes方程的有限模式近似，该方程在消失的粘度限制的极限下保留了lie-poisson结构。结果，涡度的综合能力在无关的限制中保存。我们获得了存在双能级联的有力证据，包括形成直接级联的惯性范围的-3缩放。我们表明，与传统数值方法相比，这可以在适度的分辨率下实现。
We present predictions of the energy spectrum of forced two-dimensional turbulence obtained by employing a structure-preserving integrator. In particular, we construct a finite-mode approximation of the Navier-Stokes equations on the unit sphere, which, in the limit of vanishing viscosity, preserves the Lie-Poisson structure. As a result, integrated powers of vorticity are conserved in the inviscid limit. We obtain robust evidence for the existence of the double energy cascade, including the formation of the -3 scaling of the inertial range of the direct cascade. We show that this can be achieved at modest resolutions compared to those required by traditional numerical methods.
