Seasonal evolution of the basin‐scale internal wave field in a large stratified lake

Abstract

The response of the water column to varying conditions of stratification and wind forcing was investigated in Lake Kinneret (Israel) using data collected from thermistor chains and acoustic Doppler current profilers during 1997 and 1998. The strong daily sea breeze was found to generate a vertical mode 1 internal Kelvin wave and basin-scale internal Poincaré waves of vertical modes 1, 2, and 3. The Kelvin wave, the dominant component of the internal wave field, was responsible for alongshore velocities in the nearshore regions. In the upwind nearshore regions, velocities were dominated by the forced response to the wind and were cross-shore in nature. In the lake interior, the Kelvin wave effect on the horizontal velocity field was minor compared to the higher vertical mode Poincaré waves. The Kelvin wave is shown to exist in resonant and nonforced states with the wind, whereas the vertical mode 1 Poincaré wave energy remained relatively constant, despite large variability in the forcing conditions. The energy in the higher mode Poincaré waves varied greatly, both on daily and seasonal timescales. The results demonstrate that the wind energy forces multiple basin-scale internal wave modes and that prior motion in the water column must be considered when determining the subsequent internal wave response in periodically forced systems.

Spatial structure of the dominant basin-scale internal waves in Lake Kinneret

“…Power spectral density (PSD; Bendat and Piersol 1986) of the wind speed ( Fig. 2c) reveals that, in addition to the dominant 24-h periodicity, the wind signal contained a secondary 12-h periodic component that had also been identified by Ou and Bennett (1979) and Antenucci and Imberger (2003) in previous field campaigns. The spatial variability of the wind field during the 2001 field experiment was documented by Laval et al (2003b); the effects of the daily variations in the wind pattern are discussed below.…”

“…6c), but the oscillations were almost in phase at stations Tg and T7. This suggests that this oscillation did not correspond to a monocellular anticyclonic wave of the first azimuthal mode filling the entire basin, as postulated by Antenucci et al (2000). It is possible that wave crests propagated along the transect T9-Tf-Tg while crests at T7 followed a disconnected path.…”

“…The proximity to the periods observed in the field led them to suggest that these two waves were the dominant modes in the lake. In a later article, Antenucci and Imberger (2003) showed how these modes moved in and out of resonance with the 24-h wind forcing as the stratification changed over a seasonal time scale (we refer to resonance as the amplification of the motion that occurs when the period and spatial structure of the forcing coincide with those of one of the natural modes of the system, and not in the sense used by Maas and Lam [1995], who called a resonance the condition in which all wave rays close upon themselves after multiple reflections at the boundaries of the domain). The numerical simulations of Hodges et al (2000) confirmed the rotational character of the 24-h component, but they attributed the 12-h component to a seiche across the east-west axis of the lake with a small north-south component.…”

“…Analytical solutions for these functions have not been found for general bathymetries and only approximate solutions exist. Models with simple horizontal geometries (e.g., rectangular, circular, elliptical) and flat bottoms reproduce the periods well and give indications of the horizontal structure of the natural modes for layered (Heaps and Ramsbottom 1966;Csanady 1967;Antenucci and Imberger 2001) or for continuous stratifications (Csanady 1972;Turner 1973;Monismith 1987), but reveal little as to the effect of an irregular basin shape or a sloping bottom.…”

“…Ou and Bennett (1979) described the 24-h-period oscillation as a vertical and horizontal mode 1 (V1H1) Kelvin wave, and suggested that the 12-h-period motion was a nonrotating V1H1 seiche with a nodal line in the north-south direction. With the circular flatbottom basin model approximation (Csanady 1967), Antenucci et al (2000) estimated the period of the natural internal modes in Lake Kinneret to be 22.5 and 12.2 h and interpreted these as V1H1 cyclonic Kelvin and anticyclonic Poincaré waves, respectively. The proximity to the periods observed in the field led them to suggest that these two waves were the dominant modes in the lake.…”