Vertically Propagating Internal Waves in a Tropical Reservoir

Abstract:

The classical interpretation of coherent oscillations in closed basins has been based on the decomposition onto its natural standing modes. However, as first hypothesized by Thorpe (1998) and later demonstrated by Henderson and Deemer (2012) (HD2012), lakes with particular geometries cannot develop such modes for certain frequencies due to the absorption of the wave rays in specific areas of the basin resulting from supercritical reflection. In this work, we present evidence of the consequent vertical propagation of the internal waves in a tropical reservoir. This work supports HD2012 findings and, by incorporating numerical modeling, validates some of their considerations and extend their results by proving standing modes preclusion for more general settings, analyzing further the effect of the sloping bottom and of the stratification on the vertical propagation.

The study site is La Fe reservoir, a tropical Colombian reservoir. The main measurements were obtained from a thermistor chain located in the deepest zone of the lake. Phase analysis of the measured and simulated (AEM3D) lake temperatures revealed a gradual phase shifting along the water column for diurnal oscillations, which according to HD2012 is the signature of vertical propagation. The modeled velocities adjusted well to WKB theory of propagating internal waves.

We performed numerical experiments of periodically forced wedge-shaped basins varying the bottom slope and considering stratifications with thin and thick metalimnions, typical of summer temperate and tropical lakes, respectively. For subcritical slopes, standing seiches develop accordingly to the classical picture with phase shifts of π radians. For supercritical slopes, less energy reflects upwards to conform the standing seiche resulting in a net downward energy propagation, whose signature is the gradual upward phase shift. The signature of such effect is more evident for a wide metalimnion.

Henderson, S. M., and Deemer, B. R. (2012), Vertical propagation of lakewide internal waves, Geophys. Res. Lett., 39, L06405

Thorpe, S.A. (2013), Some Dynamical Effects of Internal Waves and the Sloping Sides of Lakes, in Physical Processes in Lakes and Oceans, Coastal Estuarine Stud., vol 54, edited by J. Imberger, pp 441-460