论文标题
明确的超伪和强制飞机波概括性的beltrami流动
Explicit superposed and forced plane wave generalized Beltrami flows
论文作者
论文摘要
我们重新访问并为不可压缩的Euler和Navier-Stokes方程提供新的明确解决方案的新线性空间，并在$ \ Mathbb {r}^n $上以及$ \ Mathbb {r}^3 $上的旋转boussinesq方程。我们施放这些解决方案是某些任意振幅的某些线性平面波的叠加，这些线性平面波也通过在波矢量和流动方向上的约束来求解非线性方程。对于$ n \ leq 3 $，这些是通用Beltrami流的明确示例。我们表明，通过常数线性变化强迫相应平面波类型的术语产生显式溶液。我们在Eulerian坐标中工作，并区分消失的两种情况和梯度非线性项，其中非线性项会改变压力。我们引入的方法可以在某些非线性流体模型中找到明确的解决方案，也可以在具有材料衍生物的其他方程中使用。我们的方法从平面波的角度从不同流体模型的已知显式解决方案提供了另一种观点，并提供了不同流量组件之间透明的非线性相互作用。
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on $\mathbb{R}^n$, as well as the rotating Boussinesq equations on $\mathbb{R}^3$. We cast these solutions are superpositions of certain linear plane waves of arbitrary amplitudes that also solve the nonlinear equations by constraints on wave vectors and flow directions. For $n\leq 3$ these are explicit examples for generalized Beltrami flows. We show that forcing terms of corresponding plane wave type yield explicit solutions by linear variation of constants. We work in Eulerian coordinates and distinguish the two situations of vanishing and of gradient nonlinear terms, where the nonlinear terms modify the pressure. The methods, that we introduce to find explicit solutions in some nonlinear fluid models, can also be used in other equations with material derivative. Our approach offers another view on known explicit solutions of different fluid models from a plane wave perspective, and provides transparent nonlinear interactions between different flow components.
