When atmospheric storms pass over the ocean, they resonantly force near-inertial waves (NIWs); internal waves with a frequency close to the local Coriolis frequency $f$. It has long been recognised that the evolution of NIWs is modulated by the ocean's mesoscale eddy field. This can result in NIWs being concentrated into anticyclones and provide an efficient pathway for their propagation to depth. Whether mesoscale eddies are effective at modulating the behaviour of NIWs depends on the wave dispersiveness $\varepsilon^2 = fλ^2/Ψ$, where $λ$ is the deformation radius and $Ψ$ is a scaling for the eddy streamfunction. If $\varepsilon\gg1$, NIWs are strongly dispersive, and the waves are only weakly affected by the eddies. We calculate the perturbations away from a uniform wave field and the frequency shift away from $f$. If $\varepsilon\ll1$, NIWs are weakly dispersive, and the wave evolution is strongly modulated by the eddy field. In this weakly dispersive limit, ray-tracing emerges as a valid description of the NIW evolution even if the large-scale atmospheric forcing apparently violates the requisite assumption of a scale separation between the waves and the eddies. The large-scale forcing excites many wave modes, each of which varies on a short spatial scale and is amenable to asymptotic analysis analogous to the semi-classical analysis of quantum systems. The strong modulation of weakly dispersive NIWs by eddies has the potential to modulate the energy input into NIWs from the wind, but under oceanic conditions, this effect should be small.
Refraction and straining of wind-generated near-inertial waves by barotropic eddies
本文分析了定常和非定常正压准地转涡旋对风生近慣性波的畸变，重点研究了中尺度应变和折射作用下水平波矢量$\boldsymbol{k}$的演变。该模型初始化与水平均匀（$\boldsymbol{k}=0$）的表面限制的近慣性波，然后根据Young和Ben Jelloul的相位平均模型的演变。首先考虑定常正压涡偶极子。当波浪能向下传播并向反气旋方向传播时，急流区出现近单色剪切带。由于折射作用，水平和垂直波数都随着$t$产生后经过的时间线性增长，因此它们的比值，即波段的斜率，是与时间无关的。与被动标量动力学的类比表明，应变应导致$|\boldsymbol{k}|$的指数生长。相反，应变不仅在射流中心无效，而且在其汇合和分流区域也无效。低波模在反气旋核心下方迅速逃逸，使得弱色散的高波模在混合层中占主导地位。在弱色散极限下，$\boldsymbol{k}=- t \nabla ζ(x,y,t)/2$假设：（i）涡动垂直涡度$ζ$根据正压准地转方程演变;（ii）$\boldsymbol{k}=0$初始，如通常假设的大尺度大气风暴产生的近慣性波。在稳定流中，应变是无效的，因为$\boldsymbol{k}$总是垂直于流动。在非定常流中，应变改变了涡度梯度，因此也改变了$\boldsymbol{k}$，并可解释显著的能量转移。
Parametrisation of the wave-zonal flow interactions taking into account the full Coriolis acceleration. The necessity of going beyond the traditional approximation in the sub-inertial regime and in weakly stratified regions
Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学，巴黎西岱大学，法国原子能和替代能源委员会，法国国家科学研究中心，天体物理学与分子星际介质实验室）
