论文标题
在2D Navier-Stokes中的最大肠耗散时，粘度消失的极限
On Maximum Enstrophy Dissipation in 2D Navier-Stokes Flows in the Limit of Vanishing Viscosity
论文作者
论文摘要
我们考虑在二维（2D）Navier-Stokes流中腐蚀，并专注于这种数量在消失的粘度中的表现。在回忆了许多先验估计值对此数量的较低和上限提供的估计之后，我们指出了一个优化问题，旨在探测这些估计值作为粘度的功能。更确切地说，此问题的解决方案是具有固定的壁画的初始条件，并具有所得的2D Navier-Stokes流动的属性，从而在给定的时间窗口上局部最大化了肠胃腐败。该问题通过基于伴随的梯度上升方法和解决方案进行数值解决，该问题对于广泛的粘度和时间窗口的长度揭示了局部最大化器的多个分支的存在，每种分支都与囊状扩增的独特机制相关联。最大肠耗散对粘度的依赖性与CAIAMPA，Crippa＆Spirito（2021）引起的估计值相吻合，证明了这种结合的清晰度。
We consider enstrophy dissipation in two-dimensional (2D) Navier-Stokes flows and focus on how this quantity behaves in thelimit of vanishing viscosity. After recalling a number of a priori estimates providing lower and upper bounds on this quantity, we state an optimization problem aimed at probing the sharpness of these estimates as functions of viscosity. More precisely, solutions of this problem are the initial conditions with fixed palinstrophy and possessing the property that the resulting 2D Navier-Stokes flows locally maximize the enstrophy dissipation over a given time window. This problem is solved numerically with an adjoint-based gradient ascent method and solutions obtained for a broad range of viscosities and lengths of the time window reveal the presence of multiple branches of local maximizers, each associated with a distinct mechanism for the amplification of palinstrophy. The dependence of the maximum enstrophy dissipation on viscosity is shown to be in quantitative agreement with the estimate due to Ciampa, Crippa & Spirito (2021), demonstrating the sharpness of this bound.
