Surface cooling as an internal wave generator in high latitudes.

Heat-forced convection is a phenomenon observed frequently in high-latitude oceans. An inherent part of the Global Ocean Conveyor, it affects the global climate state over a wide range of spatial and temporal scales while being fundamentally tied to the diurnal cycle. Despite the importance of convective phenomena, most ocean general circulation models do not fully resolve it, instead parametrizing convection with adjustment schemes that remove static instability in the water by mixing vertically adjacent grid cells. However, the mixed layer response to daily-averaged fluxes is not necessarily the same as the average response to the diurnal cycle. Neglecting the diurnal cycle replaces periodic nightly convective pulses with chronic mixing that does not reach as deep. (Soloviev and Klinger, 2008).

Furthermore, the current understanding of upper-layer processes does not elucidate the consequences of the oscillatory behavior of the diurnal convection at the boundaries of the mixed layer. To address this issue, we devised a numerical experiment to investigate whether an upward heat flux is enough to generate internal waves capable of propagation despite their original forcing having a non-propagating period (~24 hours).   

To reproduce the surface cooling-induced convection and the consequent internal wave generation, we formulated a 2-D model incorporating non-hydrostatic dynamics. Although pressure is the most computationally intensive term to calculate in such models, we could exclude it from our calculation by employing the Navier-Stokes equation with a rigid-lid, incompressible, and Boussinesq approximation, and cross-differentiating the equation system to reach a single equation defined in terms of vorticity and stream function. The model was set with a 60s time step, implemented using a leap-frog scheme, constant step Δx=200m for the horizontal and Δz=5m for the vertical axis, over a 40000 x 2000 m domain. The bottom and lateral boundaries were respectively set to a reflective non-slip and a cyclic boundary. The inertial period for the domain was set at 13.81h, simulating the 60°S latitude. The experiment started from a stratified condition and was forced using a sinusoidal heat-flux function at the middle of the domain with a diurnal period and varying amplitudes.

Our experiment indicates that internal waves are generated at the boundary of the mixed layer by nonlinear wave-wave interactions of the diurnal and inertial periods. The enhancement of the near-inertial period was observed as well as the generation of higher frequency waves of 8, 6 and 4 hours. These waves travel far beyond their generation site and propagate down to 2000 m deep, as deep as the vertical domain allows.

The internal waves observed in the numerical experiment might play an important role in enhancing mixing in the ocean interior at high latitudes, especially during the winter. This mechanism could also help to explain deep and bottom ocean variability and establish a pathway for the upper layer and deep ocean interaction.