The seasonal evolution of wind/internal wave resonance in Lake Kinneret

Data from a thermistor chain and wind sensor collected over an annual stratification cycle in Lake Kinneret (Israel) during 2000 were used to investigate the seasonal evolution of wind/internal wave resonance. Internal wave periods determined from an analytical model were compared with observations, and we show that resonance during 2000 occurred during three distinct times of the year—at the onset of stratification (March), during the heating phase (June), and during the cooling phase (November). In all cases, resonance was between the wind and the dominant radial, azimuthal, and vertical mode-one cyclonic (Kelvin) wave previously observed in Lake Kinneret. Internal waves are a ubiquitous feature of lakes, existing because of wind forcing acting on a stratified water column, where the stratification is generally due to temperature. Wind applied to the surface can cause a surface setup of water at the downwind end. This pressure force is balanced by a tilting of the metalimnion in the opposite sense—that is, downward at the downwind end (Spigel and Imberger 1980). When the wind forcing relaxes, the water surface oscillates (a barotropic wave), as does the metalimnion (a baroclinic wave). The two motions can effectively be considered to be decoupled (Monismith 1985), because they form orthogonal solutions to the wave equation. It is the internal (baroclinic) waves that are of interest in the present study, because they provide much of the energy and motion for biogeochemical processes in lakes. In large lakes, the picture becomes complicated, because the effects of the Earth’s rotation begin to influence the frequency and structure of the internal waves. Internal gravity waves in large lakes take the form of cyclonic (Kelvin and/ or Poincaré) or anticyclonic (Poincaré) waves (Antenucci et al. 2000; Antenucci and Imberger 2001), where the wave crests rotate around the perimeter of the lake basin. Antenucci and Imberger (2001) showed that the frequency, as well as the ratio of potential : kinetic energy, of internal gravity waves in approximately circular or elliptic lakes was dependent on the aspect ratio, radial mode, azimuthal mode, and Burger number. The Burger number is defined as c/Lf, where c is the phase speed of internal waves in a nonrotating system, L is some length scale characterizing the basin width, and f is the Coriolis parameter. For a small Burger number, rotation dominates over gravity, and waves approach the oceanic case (known as inertial oscillations) in which the motion is dominated by the kinetic energy signal. For a large Acknowledgments We acknowledge the field support and technical staff from the Kinneret Limnological Laboratory (KLL) for providing assistance, particularly Tzahi Rosenberg for maintaining the lake station and helping in the transfer of data from KLL to the Centre for Water Research, and Peter Yeates, who provided the time series of the lake number. The field component of this project was funded by the Israeli Water Commission. This is Centre for Water Research reference ED-1276-JA. Burger number, gravity dominates over rotation, and waves approach the nonrotating case of equal partitioning between potential and kinetic energy. Using the Burger number classification, Antenucci and Imberger (2001) were able to describe the characteristics of the dominant internal waves in Lake Kinneret, Israel. Wind forcing of lakes is typically periodic in some sense because of periodicity in weather patterns. The wind over Lake Kinneret has a dominant wind-forcing return period of 24 h (Neumann and Stanhill 1978), Lake Lugano has a period of 60–90 h (Mysak et al. 1985), and Loch Ness has a period of ;50 h (Thorpe 1974). The internal waves in these systems have periods of similar magnitude, which raises the possibility of resonant forcing of the internal waves by the wind. Both Mysak et al. (1985) and Thorpe (1974) discussed the possibility of this resonant interaction between the wind and internal wave field; however, the spectral peaks in the wind field were not sufficiently sharp or the theoretical model not sufficiently complete to conclude that resonance was occurring. Antenucci et al. (2000) presented evidence of the resonant forcing of the dominant vertical, radial, and azimuthal mode-one cyclonic (Kelvin) wave in Lake Kinneret, which during the time of their measurements had a period of ;24 h. The objective of the present article is to trace the seasonal evolution of wind and internal wave resonance in Lake Kinneret, using the Burger number classification of Antenucci and Imberger (2001). Field data were analyzed using a wavelet transform (Torrence and Compo 1998) to determine the seasonal evolution of the nonrotating phase speed, c, and hence the evolution of the Burger number. This was used to determine the natural frequencies of the lake and to show how these frequencies coincide with forcing frequencies at several times during the year. The internal wave response was determined via wavelet transforms of thermistor chain data and are presented both as an amplitude and energy response. The implications of wind/internal wave resonance for water quality are also discussed.