Exploring the convective instability in a shoaling internal solitary wave of depression over gentle slopes*

The shoaling internal solitary wave (ISW) of depression is explored through a high resolution deformed spectral multidomain penalty method flow solver. The ISW becomes convectively unstable while maintaining its symmetric shape and an unstable region develops in the wave interior, characterized by the entrapment of heavier-over-light fluid, in the form of a recirculating core. The convective instability is attributed to the stretching of the near-surface vorticity layer of the baroclinic background current. According to field observations in the South China Sea, this region may drive turbulent-induced mixing, estimated to be up to four times larger than that in the open ocean. Motivated by such observations and recent 2D simulations by the authors, emphasis is placed on the convective breaking that leads to a subsurface core, using 3D simulations, where the ISW propagates in the normal-to-isobath direction and a transitional structure develops in the transverse. As the wave enters the breaking regime, the growth of the gravest lateral instability is compared with the rate of development of convective overturn associated with the core.  As such, a preliminary understanding of the formation of recirculating cores in ISWs is obtained.