Design diagrams for wavelength discrepancy in tank testing with inconsistently scaled intermediate water depth

The title or this paper is a bit of a mouthful, but actually it covers a relatively simple subject: the errors that may arise if the water depth is not scaled consistently with other parameters when tank testing devices, particularly those designed to harness power from waves.

Water waves are affected by the depth of water in which they propagate. This is described by the well-known dispersion relation, which links the wavelength, period and water depth. To accurately reproduce waves in a test tank, the water depth must therefore be correctly scaled. This is not always the case for various reasons, particularly when testing marine renewable energy devices.

Having consistently scaled water depth is also important for wave-energy devices, as the wave steepness and the power in waves will be incorrectly scaled if the water depth is wrong. This may affect testing of device motion and power capture, which are key reasons for tank-testing. The discrepancy introduced from scaling the water depth inconsistently may be up to ±30% for wavelength/steepness, and up to ±20% for power, although this reduces with the discrepancy in the scaled water depth.

The paper presents for the first time a method to quantify potential errors, with diagrams to visualise these errors graphically. This design tool will facilitate experimental planning, quantification of uncertainties, and correlation of model test results with field data.

Contours of relative error in wavelength or steepness or celerity for a range of scaled depth discrepancies and non-dimensional tank scale periods. Secondary axes show example scale factor and site depth for other parameters fixed. Dashed and dash-dot lines shows deep water limits for site and tank respectively

This work was published in the International Journal of Marine Energy in June 2017, and is freely available with open access funded by the EPSRC.

Noble, D R, Draycott, S, Davey, T A D, & Bruce, T (2017) Design diagrams for wavelength discrepancy in tank testing with inconsistently scaled intermediate water depth. International Journal of Marine Energy. doi:10.1016/j.ijome.2017.04.001