Adiabatic approximation (AP) combined with perturbation theory gives a fast normal-mode solution of temporal coherence for sound field in a two-dimensional deep water with time-varying random internal waves. Internal waves induced mode changes are deduced using the first-order perturbation theory [C. T. Tindle, L. M. O’Driscoll and C. J. Higham, Coupled mode perturbation theory of range dependence, J. Acoust. Soc. Am. 108(1) (2000) 76–83]. And mode perturbations in amplitude are neglected by the adiabatic method with wavenumber perturbations in phase merely considered. The AP expression of temporal coherence function is theoretically identical to the adiabatic transport equation theory [J. A. Colosi, T. K. Chandrayadula, A. G. Voronovich and V. E. Ostashev, Coupled mode transport theory for sound transmission through an ocean with random sound speed perturbations: Coherence in deep water environments, J. Acoust. Soc. Am. 134(4) (2013) 3119–3133]. Numerical results of the adiabatic temporal coherence function for several low frequencies and ranges up to 1000[Formula: see text]km are calculated. Then the coherence time scales obtained from the calculations are examined by a one-way coupled theory considering forward scattering [A. G. Voronovich, V. E. Ostashev and J. A. Colosi, Temporal coherence of acoustic signals in a fluctuating ocean, J. Acoust. Soc. Am. 129(6) (2011) 3590–3597]. Comparisons demonstrate that the range and frequency dependence of coherence time for both methods are quite close. And this shows good agreement with the well-known inverse frequency and inverse square root range laws. In addition, the internal wave energy dependence of coherence time is also studied.

中文翻译：

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绝热扰动模式下波动深水声传输的时间相干性

绝热逼近 (AP) 结合微扰理论给出了具有时变随机内波的二维深水中声场时间相干性的快速正模解。使用一阶微扰理论推导出内波引起的模式变化 [CT Tindle、LM O'Driscoll 和 CJ Higham，距离依赖性的耦合模式微扰理论，J. Acoust。社会党。是。108（1）（2000）76-83]。并且仅考虑相位中的波数扰动的绝热方法忽略了幅度上的模式扰动。时间相干函数的 AP 表达式在理论上与绝热输运方程理论相同 [JA Colosi, TK Chandrayadula, AG Voronovich 和 VE Ostashev, 具有随机声速扰动的海洋中声音传输的耦合模式传输理论：深水环境中的相干性，J. Acoust。社会党。是。134（4）（2013）3119-3133]。计算了几个低频和范围高达1000[公式：见正文]km的绝热时间相干函数的数值结果。然后通过考虑前向散射的单向耦合理论检查从计算中获得的相干时间尺度 [AG Voronovich、VE Ostashev 和 JA Colosi，波动海洋中声学信号的时间相干性，J. Acoust。社会党。是。129（6）（2011）3590-3597]。比较表明，两种方法的相干时间的范围和频率依赖性非常接近。这与众所周知的反频率和反平方根范围定律非常吻合。