skip to main content

Explore Research Products in the NSF-PAR

Title: Excitation of interfacial waves via surface–interfacial wave interactions
We consider interactions between surface and interfacial waves in a two-layer system. Our approach is based on the Hamiltonian structure of the equations of motion, and includes the general procedure for diagonalization of the quadratic part of the Hamiltonian. Such diagonalization allows us to derive the interaction cross-section between surface and interfacial waves and to derive the coupled kinetic equations describing spectral energy transfers in this system. Our kinetic equation allows resonant and near-resonant interactions. We find that the energy transfers are dominated by the class III resonances of Alam ( J. Fluid Mech. , vol. 691, 2012, pp. 267–278). We apply our formalism to calculate the rate of growth for interfacial waves for different values of wind velocity. Using our kinetic equation, we also consider the energy transfer from wind-generated surface waves to interfacial waves for the case when the spectrum of the surface waves is given by the JONSWAP spectrum and interfacial waves are initially absent. We find that such energy transfer can occur along a time scale of hours; there is a range of wind speeds for the most effective energy transfer at approximately the wind speed corresponding to white capping of the sea. Furthermore, interfacial waves oblique to the direction of the wind are also generated.  more » « less
Award ID(s):
1635866
NSF-PAR ID:
10168300
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Fluid Mechanics
Volume:
887
ISSN:
0022-1120
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ( , Journal of Fluid Mechanics)

    We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed energy conservation of the triadic resonant interactions. In a first application to isotropic systems, we re-derive the previously used formula for the energy flux as a particular case for adjacent sets. We then exploit the new formalism to quantify the level of locality of the energy transfers in the example of surface capillary waves. A second application to anisotropic wave systems expands the currently available set of tools to investigate magnitude and direction of the energy fluxes in these systems. We illustrate the use of the formalism by characterizing the energy pathways in the oceanic internal wavefield. Our proposed approach, unlike traditional approaches, is not limited to stationarity, scale invariance and strict locality. In addition, we define a number$w$that quantifies the scale separation necessary for two sets of modes to having negligible mutual energy exchange, with potential consequences in the interpretation of wave turbulence experiments. The methodology presented here provides a general, simple and systematic approach to energy fluxes in wave turbulence.

     
    more » « less
  2. ( , Journal of Plasma Physics)
    This paper presents quasilinear theory (QLT) for a classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic and gravitational effects are subsumed. A Fokker–Planck equation for the dressed ‘oscillation-centre’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, interaction with the background fields and ponderomotive effects simultaneously. The local diffusion coefficient is manifestly positive-semidefinite. Waves are allowed to be off-shell (i.e. not constrained by a dispersion relation), and a collision integral of the Balescu–Lenard type emerges in a form that is not restricted to any particular Hamiltonian. This operator conserves particles, momentum and energy, and it also satisfies the $\smash {H}$ -theorem, as usual. As a spin-off, a general expression for the spectrum of microscopic fluctuations is derived. For on-shell waves, which satisfy a quasilinear wave-kinetic equation, the theory conserves the momentum and energy of the wave–plasma system. The action of non-resonant waves is also conserved, unlike in the standard version of QLT. Dewar's oscillation-centre QLT of electrostatic turbulence ( Phys. Fluids , vol. 16, 1973, p. 1102) is proven formally as a particular case and given a concise formulation. Also discussed as examples are relativistic electromagnetic and gravitational interactions, and QLT for gravitational waves is proposed. 
    more » « less
  3. ; ( , Quarterly Journal of the Royal Meteorological Society)

    Although monsoon depressions are a principal synoptic‐scale element of the South Asian monsoon, producing extreme rainfall over India and surrounding regions, there exists no widely accepted mechanism explaining their occurrence. This study presents a hierarchy of numerical experiments aimed at finding such an explanation. Using a perturbation‐basic state decomposition, we derive an anelastic system of equations that can represent disturbances growing in the complex, three‐dimensional monsoon basic state. We find that modal solutions to these equations linearized about this basic state can explain many features of observed monsoon depressions, including their warm‐over‐cold core structure, westward propagation, and lower‐tropospheric wind maximum. For the zonally symmetric case, these modes are barotropically unstable, drawing energy from the meridional shear of the monsoon trough. For the zonally varying basic state, modal solutions still derive energy from barotropic conversion, but fail to achieve positive net growth rates when dissipative processes are included. For the nonlinear equation set, these modes can be excited by a heating impulse, and their energy then remains roughly constant over several days as barotropic energy transfers oppose dissipative losses. Our results support the idea that the general concept of barotropic instability can explain the structure, propagation, and geographic distribution of monsoon depressions, but not their rapid growth rates. We speculate that condensational heating coupled to these waves is needed to obtain a positive growth rate.

     
    more » « less
  4. ; ; ( , Journal of Fluid Mechanics)
    The momentum and energy exchanges at the ocean surface are central factors determining the sea state, weather patterns and climate. To investigate the effects of surface waves on the air–sea energy exchanges, we analyse high-resolution laboratory measurements of the airflow velocity acquired above wind-generated surface waves using the particle image velocimetry technique. The velocity fields were further decomposed into the mean, wave-coherent and turbulent components, and the corresponding energy budgets were explored in detail. We specifically focused on the terms of the budget equations that represent turbulence production, wave production and wave–turbulence interactions. Over wind waves, the turbulent kinetic energy (TKE) production is positive at all heights with a sharp peak near the interface, indicating the transfer of energy from the mean shear to the turbulence. Away from the surface, however, the TKE production approaches zero. Similarly, the wave kinetic energy (WKE) production is positive in the lower portion of the wave boundary layer (WBL), representing the transfer of energy from the mean flow to the wave-coherent field. In the upper part of the WBL, WKE production becomes slightly negative, wherein the energy is transferred from the wave perturbation to the mean flow. The viscous and Stokes sublayer heights emerge as natural vertical scales for the TKE and WKE production terms, respectively. The interactions between the wave and turbulence perturbations show an energy transfer from the wave to the turbulence in the bulk of the WBL and from the turbulence to the wave in a thin layer near the interface. 
    more » « less
  5. ; ( , Journal of Fluid Mechanics)

    We study the spectral energy transfer due to wave–triad interactions in the Garrett–Munk spectrum of internal gravity waves based on a numerical evaluation of the collision integral in the wave kinetic equation. Our numerical evaluation builds on the reduction of the collision integral on the resonant manifold for a horizontally isotropic spectrum. We evaluate directly the downscale energy flux available for ocean mixing, whose value is in close agreement with the finescale parameterization. We further decompose the energy transfer into contributions from different mechanisms, including local interactions and three types of non-local interactions, namely parametric subharmonic instability, elastic scattering (ES) and induced diffusion (ID). Through analysis on the role of each mechanism, we resolve two long-standing paradoxes regarding the mechanism for forward cascade in frequency and zero ID flux for the GM76 spectrum. In addition, our analysis estimates the contribution of each mechanism to the energy transfer in each spectral direction, and reveals new understanding of the importance of local interactions and ES in the energy transfer.

     
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email