scholarly journals Energy transfer in resonant and near-resonant internal wave triads for weakly non-uniform stratifications. Part 1. Unbounded domain

2020 ◽  
Vol 899 ◽  
Author(s):  
Saranraj Gururaj ◽  
Anirban Guha
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Unbounded Domain ◽  
Image Position

Abstract

scholarly journals Nonlinear interactions among standing surface and internal gravity waves

1974 ◽  
Vol 63 (4) ◽  
pp. 801-825 ◽  
Author(s):  
Terrence M. Joyce
Keyword(s):  
Energy Transfer ◽  
Steady State ◽  
Internal Wave ◽  
Surface Waves ◽  
Viscous Dissipation ◽  
Growth Rates ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Resonant Interaction ◽  
Initial Growth

A laboratory study has been undertaken to measure the energy transfer from two surface waves to one internal gravity wave in a nonlinear, resonant interaction. The interacting waves form triads for which \[ \sigma_{1s} - \sigma_{2s} \pm\sigma_1 = 0\quad {\rm and}\quad \kappa_{1s} - \kappa_2s} \pm \kappa_I = 0; \] σj and κj being the frequency and wavenumber of the jth wave. Unlike previously published results involving single triplets of interacting waves, all waves here considered are standing waves. For both a diffuse, two-layer density field and a linearly increasing density with depth, the growth to steady state of a resonant internal wave is observed while two deep water surface eigen-modes are simultaneously forced by a paddle. Internal-wave amplitudes, phases and initial growth rates are compared with theoretical results derived assuming an arbitrary Boussinesq stratification, viscous dissipation and slight detuning of the internal wave. Inclusion of viscous dissipation and slight detuning permit predictions of steady-state amplitudes and phases as well as initial growth rates. Satisfactory agreement is found between predicted and measured amplitudes and phases. Results also suggest that the internal wave in a resonant triad can act as a catalyst, permitting appreciable energy transfer among surface waves.

scholarly journals Estimates of wind power and radiative near-inertial internal wave flux

2020 ◽  
Vol 70 (11) ◽  
pp. 1357-1376
Author(s):  
Georg S. Voelker ◽  
Dirk Olbers ◽  
Maren Walter ◽  
Christian Mertens ◽  
Paul G. Myers
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Wind Power ◽  
Mixed Layer ◽  
North Atlantic ◽  
Mixed Layer Depth ◽  
Deep Ocean ◽  
Wave Radiation ◽  
Buoyancy Frequency ◽  
The North

Abstract Energy transfer mechanisms between the atmosphere and the deep ocean have been studied for many years. Their importance to the ocean’s energy balance and possible implications on mixing are widely accepted. The slab model by Pollard (Deep-Sea Res Oceanogr Abstr 17(4):795–812, 1970) is a well-established simulation of near-inertial motion and energy inferred through wind-ocean interaction. Such a model is set up with hourly wind forcing from the NCEP-CFSR reanalysis that allows computations up to high latitudes without loss of resonance. Augmenting the one-dimensional model with the horizontal divergence of the near-inertial current field leads to direct estimates of energy transfer spectra of internal wave radiation from the mixed layer base into the ocean interior. Calculations using this hybrid model are carried out for the North Atlantic during the years 1989 and 1996, which are associated with positive and negative North Atlantic Oscillation index, respectively. Results indicate a range of meridional regimes with distinct energy transfer ratios. These are interpreted in terms of the mixed layer depth, the buoyancy frequency at the mixed layer base, and the wind field structure. The average ratio of radiated energy fluxes from the mixed layer to near-inertial wind power for both years is approximately 12%. The dependence on the wind structure is supported by simulations of idealized wind stress fronts with variable width and translation speeds.

Energy transfer in turbulent flows behind two side-by-side square cylinders

2020 ◽  
Vol 903 ◽  
Author(s):  
Yi Zhou ◽  
Koji Nagata ◽  
Yasuhiko Sakai ◽  
Tomoaki Watanabe ◽  
Yasumasa Ito ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Turbulent Flows ◽  
Square Cylinders ◽  
Image Position

Abstract

Liouville-type results for positive solutions of pseudo-relativistic Schrödinger system

2021 ◽  
pp. 1-33
Author(s):  
Yuxia Guo ◽  
Shaolong Peng
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Unbounded Domain ◽  
Direct Method ◽  
Strict Monotonicity ◽  
Liouville Type ◽  
Moving Plane ◽  
Liouville Type Results ◽  
Image Position ◽  
Schrödinger System

In this paper, we are concerned with the physically engaging pseudo-relativistic Schrödinger system: \[ \begin{cases} \left(-\Delta+m^{2}\right)^{s}u(x)=f(x,u,v,\nabla u) & \hbox{in } \Omega,\\ \left(-\Delta+m^{2}\right)^{t}v(x)=g(x,u,v,\nabla v) & \hbox{in } \Omega,\\ u>0,v>0 & \hbox{in } \Omega, \\ u=v\equiv 0 & \hbox{in } \mathbb{R}^{N}\setminus\Omega, \end{cases} \] where $s,t\in (0,1)$ and the mass $m>0.$ By using the direct method of moving plane, we prove the strict monotonicity, symmetry and uniqueness for positive solutions to the above system in a bounded domain, unbounded domain, $\mathbb {R}^{N}$ , $\mathbb {R}^{N}_{+}$ and a coercive epigraph domain $\Omega$ in $\mathbb {R}^{N}$ , respectively.

Least energy solutions for elliptic equations in unbounded domains

1996 ◽  
Vol 126 (1) ◽  
pp. 195-208 ◽  
Author(s):  
Manuel A. del Pino ◽  
Patricio L. Felmer
Keyword(s):  
Critical Point ◽  
Unbounded Domain ◽  
Elliptic Equations ◽  
Unbounded Domains ◽  
Asymptotic Results ◽  
Semilinear Elliptic ◽  
Superlinear Growth ◽  
Image Position ◽  
Least Energy Solutions ◽  
Least Energy

In this paper we study the existence of least energy solutions to subcritical semilinear elliptic equations of the formwhere Ω is an unbounded domain in RN and f is a C1 function, with appropriate superlinear growth. We state general conditions on the domain Ω so that the associated functional has a nontrivial critical point, thus yielding a solution to the equation. Asymptotic results for domains stretched in one direction are also provided.

scholarly journals Eikonal Calculations for Energy Transfer in the Deep-Ocean Internal Wave Field near Mixing Hotspots

2017 ◽  
Vol 47 (1) ◽  
pp. 199-210 ◽  
Author(s):  
Takashi Ijichi ◽  
Toshiyuki Hibiya
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Wave Field ◽  
Vertical Velocity ◽  
Deep Ocean ◽  
Wave Spectra ◽  
Scale Separation ◽  
Transfer Rates ◽  
Calculated Energy ◽  
Internal Wave Field

AbstractIn the proximity of mixing hotspots in the deep ocean, the observed internal wave spectra are usually distorted from the Garrett–Munk (GM) spectrum and are characterized by the high energy level E as well as a shear–strain ratio Rω quite different from that of the GM spectrum. On the basis of the eikonal theoretical model, Ijichi and Hibiya (IH) recently proposed the revised finescale parameterization of turbulent dissipation rates in the distorted internal wave field, although the vertical velocity associated with background internal waves and the strict WKB scale separation, for example, were not taken into account. To see the effects of such simplifying assumptions on the revised parameterization, this study carries out a series of eikonal calculations for energy transfer through various internal wave spectra distorted from the GM. Although the background vertical velocity and the strict WKB scale separation somewhat affect the calculated energy transfer rates, their parameter dependence is confirmed as expected; the calculated energy transfer rates ε follow the basic scaling ε ∝ E2N2f with the local buoyancy frequency N and the local inertial frequency f and exhibit strong Rω dependence quite similar to that predicted by IH.

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