Finite-amplitude gravity waves in the atmosphere: travelling wave solutions
Finite-amplitude gravity waves in the atmosphere: travelling wave solutions
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大气中的有限振幅重力波：行波解
DOI：
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发表时间：
2017
影响因子：
3.7
通讯作者：
U. Achatz
中科院分区：
文献类型：
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作者：
M. Schlutow;R. Klein;U. Achatz
Wentzel-Kramers-Brillouin理论由Grimshaw(地球物理)采用。流体动力学，第6卷，1974年，第131-148页)和Achat z等人。(《流体力学》，第210卷，2010年，第120-147页)，以推导大气中非静力内重力波包的调制方程。这一理论允许波包的垂直范围与压力标尺高度相当，以及波幅较大，波浪诱导的平均流速与局部脉动速度相当。文中给出了这些非线性调制方程的两类精确行波解。第一类涉及叠加在相当一般的背景状态上的水平传播的波包。在共同移动的参照系中，这类例子的结构类似于静止的山背风波。数值模拟证实了伪不可压缩模型下附近行波解的存在，并显示出比预期更好的关于渐近展开参数的收敛。第二类行波解也具有群速度的垂直分量，但仅存在于等温背景层结下。这些波包括一个有趣的非线性波-均流相互作用过程：水平周期波包垂直传播，同时从高空的平均风中抽走能量。在这个过程中，它降低了低层风的速度。结果表明，在大的水平波长范围内，调制方程同样适用于静水波。除了这些具有直接物理意义的结果外，新的非线性行波解还为后续研究非线性内波不稳定性和设计数值流动解算器的精细测试实例提供了坚实的基础。
Wentzel–Kramers–Brillouin theory was employed by Grimshaw (Geophys. Fluid Dyn., vol. 6, 1974, pp. 131–148) and Achatz et al. (J. Fluid Mech., vol. 210, 2010, pp. 120–147) to derive modulation equations for non-hydrostatic internal gravity wave packets in the atmosphere. This theory allows for wave packet envelopes with vertical extent comparable to the pressure scale height and for large wave amplitudes with wave-induced mean-flow speeds comparable to the local fluctuation velocities. Two classes of exact travelling wave solutions to these nonlinear modulation equations are derived here. The first class involves horizontally propagating wave packets superimposed over rather general background states. In a co-moving frame of reference, examples from this class have a structure akin to stationary mountain lee waves. Numerical simulations corroborate the existence of nearby travelling wave solutions under the pseudo-incompressible model and reveal better than expected convergence with respect to the asymptotic expansion parameter. Travelling wave solutions of the second class also feature a vertical component of their group velocity but exist under isothermal background stratification only. These waves include an interesting nonlinear wave–mean-flow interaction process: a horizontally periodic wave packet propagates vertically while draining energy from the mean wind aloft. In the process it decelerates the lower-level wind. It is shown that the modulation equations apply equally to hydrostatic waves in the limit of large horizontal wavelengths. Aside from these results of direct physical interest, the new nonlinear travelling wave solutions provide a firm basis for subsequent studies of nonlinear internal wave instability and for the design of subtle test cases for numerical flow solvers.