Resonant and Near-Resonant Internal Wave Interactions

Based on an experiment and simulations, we report that an energy cascade in surface capillary waves can be bi-directional, that is, can simultaneously flow towards large and small wavelength scales from the pumping scales. The bi-directional energy cascade provides an effective global coupling mechanism between the scales. We show that formation of the bi-directional cascade leads to creation of large-scale, large-amplitude waves on the fluid surface.

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“…The total resonance width is estimated in Eq. (9) as a sum of individual broadenings of the resonances [37,42]. In Eq.…”

Section: Numerical Simulations a Numerical Modelmentioning

confidence: 99%

Bidirectional energy cascade in surface capillary waves

et al. 2015

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“…In numerical computations, it has been shown that near-resonant three-wave interactions are responsible for generation of the slow wave modes corresponding to zonal flows on the β-plane, and cyclonic vortical columns in purely rotating flow (Smith & Lee 2005;Lee & Smith 2007). Near-resonant three-wave interactions have also been included in the WT theory of oceanic spectra (Lvov, Polzin & Yokoyama 2012). Reductions based on exact and near resonances have physical-space representation as integro-differential equations, for which numerical solution techniques have received less attention by fluid dynamicists compared to the widely used pseudo-spectral methods for partial differential equations (PDEs) (Boyd 2001;Canuto et al 2006).…”

Section: Introductionmentioning

confidence: 99%

Investigation of Boussinesq dynamics using intermediate models based on wave–vortical interactions

2014

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Nonlinear coupling among wave modes and vortical modes is investigated with the following question in mind: can we distinguish the wave-vortical interactions largely responsible for formation versus evolution of coherent, balanced structures? The two main case studies use initial conditions that project only onto the vortical-mode flow component of the rotating Boussinesq equations: (i) an initially balanced dipole and (ii) random initial data in the vortical modes. Both case studies compare quasi-geostrophic (QG) dynamics (involving only nonlinear interactions between vortical modes) to the dynamics of intermediate models allowing for two-way feedback between wave modes and vortical modes. For an initially balanced dipole with symmetry across thex-axis, the QG dipole will propagate along thex-axis while the trajectory of the Boussinesq dipole exhibits a cyclonic drift. Compared to a forced linear (FL) model with one-way forcing of wave modes by the vortical modes, the simplest intermediate model with two-way feedback involving vortical-vortical-wave interactions is able to capture the speed and trajectory of the dipole for roughly ten times longer at Rossby Ro and Froude Fr numbers Ro = Fr ≈ 0.1. Despite its success at tracking the dipole, the latter intermediate model does not accurately capture the details of the flow structure within the adjusted dipole. For decay from random initial conditions in the vortical modes, the full Boussinesq equations generate vortices that are smaller than QG vortices, indicating that wave-vortical interactions are fundamental for creating the correct balanced state. The intermediate model with QG and vortical-vortical-wave interactions actually prevents the formation of vortices. Taken together these case studies suggest that: vortical-vortical-wave interactions create waves and thereby influence the evolution of balanced structures; vortical-wave-wave interactions take energy out of the wave modes and contribute in an essential way to the formation of coherent balanced structures.

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“…Therefore, a better understanding of nonlinear wave-wave interactions would be an important step toward full knowledge of the wave field itself, from the generation processes to the physicalbiogeochemical impacts of wave dissipation. Nonlinear wave-wave interaction has been demonstrated a few times in the field (Carter and Gregg 2006;MacKinnon et al 2013;Pinkel 2012, 2013) and numerous times in models (e.g., Hazewinkel and Winters 2011;Korobov and Lamb 2008;Legg and Huijts 2006;Nikurashin and Legg 2011), and it has been shown to enhance turbulence dissipation in the open ocean environment (Lvov et al 2012;Nikurashin and Legg 2011;Polzin 2004a,b;Winters and D'Asaro 1997).…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Nonlinearity and Spectral Structure of Internal Tides at an Idealized Mid-Atlantic Bight Shelf Break

Zhang

Duda

2013

Journal of Physical Oceanography

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To quantify dynamical aspects of internal-tide generation at the Mid-Atlantic Bight shelf break, this study employs an idealized ocean model initialized by climatological summertime stratification and forced by monochromatic barotropic tidal currents at the offshore boundary. The Froude number of the scenario is subunity, and the bathymetric slope offshore of the shelf break is supercritical. A barotropic-to-baroclinic energy conversion rate of 335 W m 21 is found, with 14% of the energy locally dissipated through turbulence and bottom friction and 18% radiated onto the shelf. Consistent with prior studies, nonlinear effects result in additional super-and subharmonic internal waves at the shelf break. The subharmonic waves are subinertial, evanescent, and mostly trapped within a narrow beam of internal waves at the forcing frequency. They likely result from nonresonant triad interaction associated with strong nonlinearity. Strong vertical shear associated with the subharmonic waves tends to enhance local energy dissipation and turbulent momentum exchange (TME). A simulation with reduced tidal forcing shows an expected diminished level of harmonic energy. A quasi-linear simulation verifies the role of momentum advection in controlling the relative phases of internal tides and the efficiency of barotropic-to-baroclinic energy conversion. The local TME is tightly coupled with the internal-wave dynamics: for the chosen configuration, neglecting TME causes the internal-wave energy to be overestimated by 12%, and increasing it to high levels damps the waves on the continental shelf. This work implies a necessity to carefully consider nonlinearity and turbulent processes in the calculation of internal tidal waves generated at the shelf break.

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Resonant and Near-Resonant Internal Wave Interactions

Cited by 47 publications

References 40 publications

Bidirectional energy cascade in surface capillary waves

Bidirectional energy cascade in surface capillary waves

Investigation of Boussinesq dynamics using intermediate models based on wave–vortical interactions

Intrinsic Nonlinearity and Spectral Structure of Internal Tides at an Idealized Mid-Atlantic Bight Shelf Break

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