Internal waves have recently been shown to be a crucial component of energy transport and mixing in the oceans. A number of mechanisms are known to facilitate the direct cascade of energy from the large scales of internal waves down to small-scale mixing. The parametric subharmonic instability (PSI) is perhaps the most studied mechanism recently, but is only well established for infinite plane waves in the inviscid limit as well as with limited viscosity (Koudella & Staquet 2006). Naturally occurring internal waves are of course finite width, and often of complex-valued envelope profile (Thomas & Stevenson 2006). It has further been shown experimentally (Bourget et al. 2013), and in limiting cases theoretically (Karimi & Akylas 2014), that finite beam width effects are significant for the ability of PSI to extract and transfer energy to smaller scales. Yet we show here that there is little agreement to the extent of this effect.
Thus we present the results of a series of numerical studies investigating the width ef- fects on the threshold amplitude for PSI, and compare these to two independent analyses (Bourget et al. 2014; Karimi & Akylas 2014). Finally, we present an investigation of the effects of mean flow and circulation on PSI and explain the influence on the evolution of the subharmonic daughter frequencies using a time-frequency analysis.
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