We present an experimental study of resonant generation of superharmonic internal waves as a result of interaction between horizontally propagating vertical internal wave modes $m$ and $n$ at frequency ${\omega }_0$ in a uniformly stratified finite-depth fluid. Thorpe (J. Fluid Mech. 24 , 737, 1966) has shown theoretically that modes $m$ and $n$ at frequency ${\omega }_0$ and mode-$p=|m-n|$ at frequency $2{\omega }_0$ are in triadic resonance at specific values of ${\omega }_0$. We demonstrate the occurrence of this triadic resonance by forcing a primary wave field of modes $m$ and $n$ at various ${\omega }_0$ using a novel internal wave generator, and observing the spontaneous growth (or lack thereof) of the superharmonic mode-$p=|m-n|$ at frequency $2{\omega }_0$. A superharmonic wave field with a predominantly mode-$p=|m-n|$ structure is observed over a finite range of frequency ($\Delta {\omega }_0\simeq 0.03N$) around the resonant value, where $N$ is the uniform buoyancy frequency. The spatial growth of the superharmonic wave field is then quantitatively measured, to subsequently compare with the predictions from amplitude evolution equations at resonance at various forcing amplitudes, thereby validating this model. It is furthermore shown that a large scale spatial evolution of the wave field is more suited to describe our experiments than the slow temporal evolution approach. The paper concludes with a brief discussion of viscous effects.

中文翻译：

---

内部波模之间的共振相互作用产生超谐波波的实验研究

由于水平传播的垂直内部波模式之间的相互作用，我们提出了共振产生超谐波内部波的实验研究 $米$ 和 $ñ$ 在频率上 ${\omega }_0$在均匀分层的有限深度流体中。索普（J. Fluid Mech。24，737，1966）理论上表明$米$ 和 $ñ$ 在频率上 ${\omega }_0$ 和模式-$p=|米-ñ|$ 在频率上 $2{\omega }_0$ 在特定值下处于三重共振 ${\omega }_0$。我们通过强迫模的主波场来证明这种三重共振的发生$米$ 和 $ñ$ 在各种 ${\omega }_0$ 使用新型的内部波发生器，并观察超谐波模式的自发增长（或缺乏）$p=|米-ñ|$ 在频率上 $2{\omega }_0$。主要是模式的超谐波波场$p=|米-ñ|$ 在有限的频率范围内观察到结构（$\Delta {\omega }_0\simeq 0.03ñ$）在谐振值附近，其中 $ñ$是均匀的浮力频率。然后，对超谐波波场的空间增长进行定量测量，以与在各种强迫振幅下共振时振幅演化方程的预测值进行比较，从而验证该模型。此外还表明，与缓慢的时间演化方法相比，波场的大规模空间演化更适合描述我们的实验。本文最后简要讨论了粘性效应。