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A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This phenomenon...

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Related Experiment Video

Updated: Jul 4, 2026

Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons

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Published on: July 21, 2018

Necessary conditions for mode interactions in parametrically excited waves.

T Epstein¹, J Fineberg

¹The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel.

Physical Review Letters

|June 4, 2008

Summary

Nonlinear wave interactions in Faraday instability are observed only when spatial modes peak simultaneously. The temporal dynamics of these waves follow Hill

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Area of Science:

Fluid dynamics
Nonlinear physics
Wave phenomena

Background:

The Faraday instability describes parametrically excited waves on a fluid surface.
Understanding nonlinear states is crucial for fluid dynamics.
Previous studies have explored various regimes of this instability.

Purpose of the Study:

To investigate the spatial and temporal structure of nonlinear states in the Faraday instability.
To analyze the conditions for three-wave interactions between spatial modes.
To characterize the temporal behavior of individual wave modes.

Main Methods:

Studying short-time dynamics of parametrically excited waves.
Analyzing spatial mode interactions.
Describing temporal structures using functional forms.

Main Results:

Three-wave interactions between spatial modes occur exclusively when their peak values are simultaneous.
The temporal structure of each mode is consistently described by Hill's equation.
Dominant nonlinear interaction type does not influence the temporal structure of individual modes.

Conclusions:

Simultaneity of spatial mode peaks is a key condition for nonlinear interactions in this regime.
Hill's equation accurately models the temporal dynamics of wave modes.
The findings provide insights into the complex behavior of nonlinear fluid waves.