Nonlinear Dynamics and Chaos in the Sea and Land Breeze

Yizhak Feliks Department of Mathematics, Israel Institute for Biological Research, Ness-Ziona, Israel

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Abstract

In this work the evolution of the sea and land breeze is studied using a nonlinear model under calm synoptic conditions and diurnal periodic forcing of ground temperature. The breeze is examined as a function of the strength of the heating amplitude of ground temperature θ0. For θ0 ≤ 6°C, the solution is quasi-periodic with two incommensurate oscillations of 24 and 22.6 h; the last is the inertial oscillation at latitude 32°N. A very low frequency oscillation (VLFO) of 16 days, which is the linear combination of the two incommensurate oscillations, is also obtained. For θ0 = 7°C, the solution becomes nonperiodic. For θ0 ≥ 10°C, chaotic solutions are obtained. In the chaotic regime the prominent oscillations can be divided into two classes. One class includes short-time-scale oscillations, such as the 24-h oscillation, the 22.4-h slightly modified inertial oscillation, and their harmonics. The second class incorporates time scales that are larger than a week, such as 15 days, which is a linear combination of the 24- and 22.4-h oscillations. The flow in the second class is in geostrophic balance. The kinetic energy, which manifests spells of very large energy fluctuations, is examined. During these spells the amplitude of the VLFO is large, and the amplitude of the 24-h oscillation is small compared to the spells where the fluctuations in the kinetic energy are small.

Analyses of the wind observations in the central coast of Israel in the summer months show great similarity to the model simulation in the chaotic regime. A VLFO of 10 days, which is prominent in its parallel to the shore component, is interpreted to be the result of the nonlinear interaction between the inertial oscillation at the central latitude of the eastern Mediterranean, 33.5°N, and the 24-h oscillation as obtained in the present model.

Corresponding author address: Y. Feliks, Dept. of Mathematics, Israel Institute for Biological Research, P.O.B. 19 Ness-Ziona, Israel. Email: feliks@iibr.gov.il

Abstract

In this work the evolution of the sea and land breeze is studied using a nonlinear model under calm synoptic conditions and diurnal periodic forcing of ground temperature. The breeze is examined as a function of the strength of the heating amplitude of ground temperature θ0. For θ0 ≤ 6°C, the solution is quasi-periodic with two incommensurate oscillations of 24 and 22.6 h; the last is the inertial oscillation at latitude 32°N. A very low frequency oscillation (VLFO) of 16 days, which is the linear combination of the two incommensurate oscillations, is also obtained. For θ0 = 7°C, the solution becomes nonperiodic. For θ0 ≥ 10°C, chaotic solutions are obtained. In the chaotic regime the prominent oscillations can be divided into two classes. One class includes short-time-scale oscillations, such as the 24-h oscillation, the 22.4-h slightly modified inertial oscillation, and their harmonics. The second class incorporates time scales that are larger than a week, such as 15 days, which is a linear combination of the 24- and 22.4-h oscillations. The flow in the second class is in geostrophic balance. The kinetic energy, which manifests spells of very large energy fluctuations, is examined. During these spells the amplitude of the VLFO is large, and the amplitude of the 24-h oscillation is small compared to the spells where the fluctuations in the kinetic energy are small.

Analyses of the wind observations in the central coast of Israel in the summer months show great similarity to the model simulation in the chaotic regime. A VLFO of 10 days, which is prominent in its parallel to the shore component, is interpreted to be the result of the nonlinear interaction between the inertial oscillation at the central latitude of the eastern Mediterranean, 33.5°N, and the 24-h oscillation as obtained in the present model.

Corresponding author address: Y. Feliks, Dept. of Mathematics, Israel Institute for Biological Research, P.O.B. 19 Ness-Ziona, Israel. Email: feliks@iibr.gov.il

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