Complete band gaps for liquid surface waves propagating over a periodically drilled bottom

¹Surface Physics Laboratory, National Key Lab, Fudan University, Shanghai 200433, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 3, 2004

Summary

Researchers developed a plane-wave expansion method to study liquid surface waves over periodic structures. They discovered complete band gaps in wave propagation for both square and triangular hole lattices, offering insights into wave control.

Area of Science:

Fluid dynamics
Acoustics
Materials science

Background:

The mild-slope equation describes wave propagation in shallow water.
Periodic structures can create band gaps, preventing wave propagation within certain frequency ranges.
Understanding wave behavior in structured media is crucial for various applications.

Purpose of the Study:

To apply a plane-wave expansion approach to the mild-slope equation.
To investigate liquid surface wave propagation over periodically structured bottoms.
To identify and analyze band gaps in these systems.

Main Methods:

Developed a plane-wave expansion method tailored for the mild-slope equation.
Calculated band structures for bottoms with square and triangular lattices of holes.
Analyzed the influence of structural parameters on band gap formation.

Main Results:

Successfully applied the plane-wave expansion method to solve the mild-slope equation.
Identified complete band gaps for liquid surface waves over both square and triangular periodic structures.
Discussed key parameters affecting the existence and characteristics of these band gaps.

Conclusions:

The plane-wave expansion method is effective for analyzing wave phenomena in periodically structured fluids.
Periodic structures, specifically lattices of holes, can effectively control liquid surface wave propagation.
Band gaps offer a mechanism for designing systems that filter or block specific wave frequencies.

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Related Experiment Videos

Complete band gaps for liquid surface waves propagating over a periodically drilled bottom

Area of Science:

Background:

Purpose of the Study:

Main Methods:

Main Results:

Conclusions:

Related Concept Videos

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