Proof of quasilinear equations in the strongly nonlinear regime of the weak warm beam instability

2003 ◽  
Vol 10 (5) ◽  
pp. 1588-1594 ◽  
Author(s):  
D. F. Escande ◽  
Y. Elskens
Keyword(s):  
Nonlinear Regime ◽  
Beam Instability ◽  
Quasilinear Equations ◽  
Strongly Nonlinear

Dynamics in a confined mass–spring chain with 1∕r repulsive potential: Strongly nonlinear regime

2020 ◽  
Vol 553 ◽  
pp. 124651
Author(s):  
Edgar Avalos ◽  
Amitava Datta ◽  
Anthony D. Rosato ◽  
Denis Blackmore ◽  
Surajit Sen
Keyword(s):  
Nonlinear Regime ◽  
Repulsive Potential ◽  
Strongly Nonlinear ◽  
Mass Spring

scholarly journals Numerical Simulations of Lateral Dispersion by the Relaxation of Diapycnal Mixing Events

2005 ◽  
Vol 35 (12) ◽  
pp. 2368-2386 ◽  
Author(s):  
Miles A. Sundermeyer ◽  
M-Pascale Lelong
Keyword(s):  
New England ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Scale Factor ◽  
Nonlinear Regime ◽  
Small Scale ◽  
Diapycnal Mixing ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Advection Diffusion Equation

Abstract In this second of two companion papers, numerical simulations of lateral dispersion by small-scale geostrophic motions, or vortical modes, generated by the adjustment of mixed patches following diapycnal mixing events are examined. A three-dimensional model was used to solve the Navier–Stokes equations and an advection/diffusion equation for a passive tracer. Model results were compared with theoretical predictions for vortical mode stirring with results from dye release experiments conducted over the New England continental shelf. For “weakly nonlinear” cases in which adjustment events were isolated in space and time, lateral dispersion in the model was consistent to within a constant scale factor with the parameter dependencepredicted by Sundermeyer et al., where h and L are the vertical and horizontal scales of the mixed patches, ΔN 2 is the change in stratification associated with the mixed patches, f is the Coriolis parameter, ϕ is the frequency of diapycnal mixing events, and νB is the background viscosity. The associated scale factor, assumed to be of order 1, had an actual value of about 7, although this value will depend, in an unknown way, on the assumed horizontal scale of the mixed patches, which was here held constant at close to the deformation radius. A second more energetic parameter regime was also identified in which vortical mode stirring became strongly nonlinear and the effective lateral dispersion was larger. Estimates of the relevant parameters over the New England shelf suggest that this strongly nonlinear regime is more relevant to the real ocean than the weakly nonlinear regime, at least under late summer conditions. This suggests that stirring by small-scale geostrophic motion may, under certain conditions, contribute significantly to lateral dispersion on scales of 1–10 km in the ocean.

scholarly journals Scale-Invariant Correlation Functions of Cosmological Density Fluctuations in the Strong Clustering Regime and the Stability

1999 ◽  
Vol 183 ◽  
pp. 274-274
Author(s):  
Taihei Yano ◽  
Naoteru Gouda
Keyword(s):  
Correlation Function ◽  
Spatial Correlation ◽  
Correlation Functions ◽  
Power Index ◽  
Nonlinear Regime ◽  
Peculiar Velocity ◽  
Strongly Nonlinear ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Mean

We have investigated the scale-invariant solutions of the BBGKY equations for spatial correlation functions of cosmological density fluctuations and the mean relative peculiar velocity in the strongly nonlinear regime. It is found that the solutions for the mean relative physical velocity depend on the three-point spatial correlation function and the skewness of the velocity fields. We find that the stable condition in which the mean relative physical velocity vanishes on the virialized regions is satisfied only under the assumptions which Davis & Peebles took in there paper. It is found, however, that their assumptions may not be general in real. The power index of the two-point correlation function in the strongly nonlinear regime depends on the mean relative peculiar velocity, the three-point correlation function and the skewness. If self-similar solutions exist, then the power index in the strongly nonlinear regime is related to the power index of the initial power spectrum and its relation depends on the three-point correlation function and the skewness through the mean relative peculiar velocity. We also investigate stability of the solutions of the BBGKY equations for two-point spatial correlation functions. In the case that the background skewness is equal to 0, we found that there is no local instability in the strongly non-linear regime.

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