Experimental Observation of Dark Solitons on the Surface of Water

We present the first ever observation of dark solitons on the surface of water. It takes the form of an amplitude drop of the carrier wave which does not change shape in propagation. The shape and width of the soliton depend on the water depth, carrier frequency, and the amplitude of the background wave. The experimental data taken in a water tank show an excellent agreement with the theory. These results may improve our understanding of the nonlinear dynamics of water waves at finite depths.

Figure 1

Dark soliton solution showing the carrier wave amplitude drop to zero at $X=0$.

Figure 2

Wave channel used in the experiments.

Figure 3

Evolution of the dark soliton along the tank with the water depth $h=0.4\mathrm{m}$. The carrier amplitude is $a=0.04\mathrm{m}$, while $kh=1.2$. Seven panels from top to bottom correspond to experimental records of seven gauges from 1 to 7, respectively, shifted in time to keep zero amplitude at the same position. The envelope over the experimental curves computed using the first-order Fourier analysis is in good agreement with theoretical dark soliton shape.

Figure 4

Evolution of the dark soliton along the tank with the water depth $h=0.25\mathrm{m}$. The carrier amplitude is $a=0.02\mathrm{m}$, while $kh=1.0$. Seven panels from top to bottom correspond to experimental records of seven gauges from 1 to 7, respectively, shifted in time to keep zero amplitude at the same position. The envelope over the experimental curves computed using the first-order Fourier analysis is in good agreement with theoretical dark soliton shape.

Figure 5

The number of modulated waves within the dark soltion versus steepness $ak$. The former is defined with the threshold amplitude of $0.9a$ for the corresponding depth. The triangles correspond the values obtained from the first gauge. The stars correspond the values obtained from the last gauge. Solid lines are obtained from theoretical calculations.

Figure 6

The number of modulated waves within the soliton versus $kh$. The former is defined for the threshold amplitude $0.9a$ for the corresponding depth. The triangles correspond the values obtained from the first gauge. The stars correspond the values obtained from the last gauge. Solid lines are obtained from theoretical calculations.