论文标题
非线性浅水动力学和奇怪的粘度
Non-linear shallow water dynamics with odd viscosity
论文作者
论文摘要
在这封信中，我们得出了对应于较浅的粘度（$ν_O$）的浅深度（$ h $）的浅深度（$ H $）的表面动力学的Korteweg-de Vries（KDV）方程，该方程在长波长弱的非线性限制下具有奇数粘度（$ν_O$）。在长波长极限中，奇数粘度项扮演着表面张力的作用，尽管在左右移动器中具有相反的迹象。我们表明，在KDV动力学的适用性内，存在两个机制，我们称之为弱$（|ν_O| <\ sqrt {gh^3}/6）$和strong $（| v_o |> \ sqrt {gh^3}/6）$ parity-parity-parity-parity-party-prime-prime-prime-pright obkin-unbure-pright-unbure-akenting neking neking neking neking nisting neking nisting neking nisting。尽管“弱”平价破坏制度导致右手和左推动者之间的孤子振幅和速度的较小定性差异，但手势部门之一的抑郁症（负振幅）的相反结果，“强”平价破坏了方案。
In this letter, we derive the Korteweg-de Vries (KdV) equation corresponding to the surface dynamics of a shallow depth ($h$) two-dimensional fluid with odd viscosity ($ν_o$) subject to gravity ($g$) in the long wavelength weakly nonlinear limit. In the long wavelength limit, the odd viscosity term plays the role of surface tension albeit with opposite signs for the right and left movers. We show that there exists two regimes with a sharp transition point within the applicability of the KdV dynamics, which we refer to as weak $(|ν_o|< \sqrt{gh^3}/6)$ and strong $(|ν_o|> \sqrt{gh^3}/6)$ parity-breaking regimes. While the `weak' parity breaking regime results in minor qualitative differences in the soliton amplitude and velocity between the right and left movers, the `strong' parity breaking regime on the contrary results in solitons of depression (negative amplitude) in one of the chiral sectors.
