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While it has long been recognized that Lagrangian drift at the ocean surface plays a critical role in the kinematics and dynamics of upper ocean processes, only recently has the contribution of wave breaking to this drift begun to be investigated through direct numerical simulations (Deike et al. , J. Fluid Mech. , vol. 829, 2017, pp. 364–391; Pizzo et al. , J. Phys. Oceanogr. , vol. 49(4), 2019, pp. 983–992). In this work, laboratory measurements of the surface Lagrangian transport due to focusing deep-water non-breaking and breaking waves are presented. It is found that wave breaking greatly enhances mass transport, compared to non-breaking focusing wave packets. These results are in agreement with the direct numerical simulations of Deike et al. ( J. Fluid Mech. , vol. 829, 2017, pp. 364–391), and the increased transport due to breaking agrees with their scaling argument. In particular, the transport at the surface scales with $$S$$ , the linear prediction of the maximum slope at focusing, while the surface transport due to non-breaking waves scales with $$S^{2}$$ , in agreement with the classical Stokes prediction.
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Nonlinear travelling internal waves with piecewise-linear shear profiles
In this work, we study the nonlinear travelling waves in density stratified fluids with piecewise-linear shear currents. Beginning with the formulation of the water-wave problem due to Ablowitz et al. ( J. Fluid Mech. , vol. 562, 2006, pp. 313–343), we extend the work of Ashton & Fokas ( J. Fluid Mech. , vol. 689, 2011, pp. 129–148) and Haut & Ablowitz ( J. Fluid Mech. , vol. 631, 2009, pp. 375–396) to examine the interface between two fluids of differing densities and varying linear shear. We derive a systems of equations depending only on variables at the interface, and numerically solve for periodic travelling wave solutions using numerical continuation. Here, we consider only branches which bifurcate from solutions where there is no slip in the tangential velocity at the interface for the trivial flow. The spectral stability of these solutions is then determined using a numerical Fourier–Floquet technique. We find that the strength of the linear shear in each fluid impacts the stability of the corresponding travelling wave solutions. Specifically, opposing shears may amplify or suppress instabilities.
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- Award ID(s):
- 1715039
- PAR ID:
- 10220371
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 856
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 984 to 1013
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2018.679
