Saturation of the Inverse Cascade in Surface Gravity-Wave Turbulence

Area of Science:

• Fluid dynamics
• Wave turbulence

Background:

• Surface gravity-wave turbulence typically involves energy transfer to smaller scales (downscale transfer).
• Weak turbulence theory predicts an inverse cascade, transferring energy to larger scales.

Purpose of the Study:

• To observe and analyze surface gravity-wave turbulence at scales larger than the forcing scales.
• To investigate the occurrence and implications of an upscale energy transfer in wave turbulence.

Main Methods:

• Experimental observation of surface gravity-wave turbulence in a large basin.
• Analysis of energy transfer mechanisms, including both downscale and upscale cascades.

Main Results:

• Observed surface gravity-wave turbulence at scales exceeding the forcing scales.
• Identified an upscale energy transfer, consistent with the inverse cascade of weak turbulence theory.
• A steady state was reached due to the inverse cascade saturation, influenced by wave steepness and nonlinear dissipative structures like sharp-crested waves.

Conclusions:

• Surface gravity-wave turbulence can exhibit an inverse cascade, leading to energy transfer to larger scales.
• The saturation of this inverse cascade is linked to nonlinear effects and the formation of dissipative structures.
• Experimental findings support theoretical predictions of inverse cascades in weakly turbulent systems.