EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents

Ton van den Bremer1, James Steer2, Dimitris Stagonas3, Eugeny Buldakov4, and Alistair Borthwick5
Ton van den Bremer et al.
  • 1University of Oxford, Oxford, United Kingdom (
  • 2University College Dublin, Dublin, Ireland (
  • 3Cranfield University, Cranfield, United Kingdom(
  • 4University College London, London, United Kingdom (
  • 5University of Edinburgh, Edinburgh, United Kingdom (

We examine experimentally the dispersion and stability of weakly nonlinear waves on opposing linearly vertically sheared current profiles (with constant vorticity). Measurements are compared against predictions from the unidirectional  1D+1 constant vorticity nonlinear Schrödinger equation (the vor-NLSE) derived by Thomas et al. (Phys. Fluids, vol. 24, no. 12, 2012, 127102). The shear rate is negative in opposing currents when the magnitude of the current in the laboratory reference frame is negative (i.e. opposing the direction of wave propagation) and reduces with depth, as is most commonly encountered in nature. Compared to a uniform current with the same surface velocity, negative shear has the effect of increasing wavelength and enhancing stability. In experiments with a regular low-steepness wave, the dispersion relationship between wavelength and frequency is examined on five opposing current profiles with shear rates from 0 to -0,87 s-1 For all current profiles, the linear constant vorticity dispersion relation predicts the wavenumber to within the 95% confidence bounds associated with estimates of shear rate and surface current velocity. The effect of shear on modulational instability was determined by the spectral evolution of a carrier wave seeded with spectral sidebands on opposing current profiles with shear rates between 0 and -0.48 s-1. Numerical solutions of the vor-NLSE are consistently found to predict sideband growth to within two standard deviations across repeated experiments, performing considerably better than its uniform-current NLSE counterpart. Similarly, the amplification of experimental wave envelopes is predicted well by numerical solutions of the vor-NLSE, and significantly over-predicted by the uniform-current NLSE.

How to cite: van den Bremer, T., Steer, J., Stagonas, D., Buldakov, E., and Borthwick, A.: Experimental study of dispersion and modulational instability of surface gravity waves on constant vorticity currents, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-2322,, 2020


Display file