Generation of focused waves using Second Order Wave Theory


The test cases provide generation and evolution of focused waves in intermediate water depth generated using piston type wave-maker theory with second order correction. Generation of focused waves using superimposition of linear paddle displacements leads to generation of spurious free sub and super harmonics, which can influence the shape and energy distribution over frequency. This is particularly important while studying interaction with structures and wave-breaking. The second order solution for the boundary value problem is provided by Schaffer (1996) to suppress spurious free waves. This dataset provides a validation for focused wave spectrum with three different bandwidths.

Experimental Set-up

The experiments were performed using a wave tank in the Franzius-Institute Laboratory, Hannover, Germany. The tank is 110.0m long, 2.2m wide, and 2.0m deep with a computer-controlled hydraulically driven piston type wave-maker at one end of the tank. The tank was filled with fresh water to a working depth (d) of 0.7m. Temporal variations of the free surface elevation at desired locations in the wave flume were recorded by six capacitance wave gauges. One wave gauge was fixed at 4.835m distance from the wave paddle, whereas the other five wave gauges were mounted on a movable trolley at a spacing of 0.2m. Relying on the high repeatability of the experiments surface elevation measurements a minimum of 15 stations along the wave tank could be achieved for each of the test cases, by moving the trolley to different positions and repeating the experiment. The repeatability of the experiments was confirmed by comparing the surface elevation measurements at the fixed wave gauge location (i.e. at 4.835m). The differences in surface elevations for every run were within a range of ±1.5%.

Experimental Test Program

For this study the theoretical location of the focussing point is set to 21m from the wave paddle. However the actual focussing location will be after the theoretical location as explained in Sriram (2015). The central frequency (fc) for all the test cases presented here is set to 0.68 Hz with three different frequency bandwidth ratios (Δf/fc), in each case divided in 32 packets (Nf). The steepness of the wave is controlled by setting the gain to the input signal (Ga). For the current test case only non-breaking cases are presented. The time at which the wave-group reaches the focussing point is given by tf.

The description of the three test cases is given below:

Case Fc ΔF/Fc Flow Fhigh Tf Ga
  (Hz)   (Hz) (Hz) (sec)  
ccp_f068a20019a 0.68 0.50 0.51 0.85 64.00 0.0019
ccp_f068b20028a 0.68 0.75 0.42 0.94 48.00 0.0028
ccp_f068c20030a 0.68 1.00 0.34 1.02 38.00 0.0030

The .mat data file for each test case contains 5 variables:

Variable Description Units
wmt Paddle signal time array sec
wmd Paddle displacement array meter
wpl Wave-probe location from wave-maker meter
wpt Wave-probe signal time array sec
wpd Wave-elevation signal for each wave-probe meter

A detailed comparison of the focused wave generated for the above test cases using linear and second order wave-maker theory can be found in the article Sriram (2015). It also presents comparison of the above results with a Fully Non-linear Potential Theory (FNPT) based FEM code in 2D base don the work presented in Sriram (2006).

Relevant Case files:

Relevant References