On the interaction of short linear internal waves with internal solitary waves

Abstract

Abstract. We study the interaction of small-scale internal wave packets with a large-scale internal solitary wave using high-resolution direct numerical simulations in two dimensions. A key finding is that for wave packets whose constituent waves are short in comparison to the solitary wave width, the interaction leads to an almost complete destruction of the short waves. For mode-1 short waves in the packet, as the wavelength increases, a cutoff is reached, and for larger wavelengths the waves in the packet are able to maintain their structure after the interaction. This cutoff corresponds to the wavelength at which the phase speed of the short waves upstream of the solitary wave exceeds the maximum current induced by the solitary wave. For mode-2 waves in the packet, however, no corresponding cutoff is found. Analysis based on linear theory suggests that the destruction of short waves occurs primarily due to the velocity shear induced by the solitary wave, which alters the vertical structure of the waves so that significant wave activity is found only above (below) the deformed pycnocline for overtaking (head-on) collisions. The deformation of vertical structure is more significant for waves with a smaller wavelength. Consequently, it is more difficult for these waves to adjust to the new solitary-waveinduced background environment. These results suggest that through the interaction with relatively smaller length scale waves, internal solitary waves can provide a means to decrease the power observed in the short-wave band in the coastal ocean.

Shear-induced breaking of internal gravity waves

“…The propagation and instability of internal waves in such regions, where the background stratification varies strongly, is far different to the case of uniform stratification (Sutherland 2016). Nevertheless, the fundamental mechanism of shear refracting small-scale internal waves seems relevant at sharp density interfaces, at least in situations with large internal solitary waves as considered by Xu & Stastna (2018). Understanding how generic the mixing properties of this shear–wave interaction are for arbitrary is vital for the general application of our results.…”

Analysis of conditions for the propagation of internal waves in a three­layer finite­depth liquid

“…Interaction of small internal wave packets with a large internal wave was studied in [9]. The main result was that the indicated interaction with a single wave leads to a complete destruction of the packet which consists of waves having small length in comparison with the length of single waves.…”

“…According to (9) and (10), the wave motion on the lower and upper contact surfaces can be represented in the first approximation as: (1) (2) 11 11…”