Collection Tags: Theory and Computation - Princeton Data Commons Discovery Search Results

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21. Formation of solitary zonal structures via the modulational instability of drift waves

Author(s):: Zhou, Yao; Zhu, Hongxuan; Dodin, I. Y.
Abstract:: {\rtf1\ansi\ansicpg1252\cocoartf1561\cocoasubrtf600 {\fonttbl\f0\fswiss\fcharset0 Helvetica;} {\colortbl;\red255\green255\blue255;\red0\green0\blue0;} {\*\expandedcolortbl;;\cssrgb\c0\c0\c0;} \margl1440\margr1440\vieww10800\viewh8400\viewkind0 \pard\tx887\tx1775\tx2662\tx3550\tx4438\tx5325\tx6213\tx7101\tx7988\tx8876\tx9764\tx10651\tx11539\tx12427\tx13314\tx14202\tx15090\tx15977\tx16865\tx17753\tx18640\tx19528\tx20416\tx21303\tx22191\tx23079\tx23966\tx24854\tx25742\tx26629\tx27517\tx28405\tx29292\tx30180\tx31067\tx31955\tx32843\tx33730\tx34618\tx35506\tx36393\tx37281\tx38169\tx39056\tx39944\tx40832\tx41719\tx42607\tx43495\tx44382\tx45270\tx46158\tx47045\tx47933\tx48821\tx49708\tx50596\tx51484\tx52371\tx53259\tx54147\tx55034\tx55922\tx56810\tx57697\tx58585\tx59472\tx60360\tx61248\tx62135\tx63023\tx63911\tx64798\tx65686\tx66574\tx67461\tx68349\tx69237\tx70124\tx71012\tx71900\tx72787\tx73675\tx74563\tx75450\tx76338\tx77226\tx78113\tx79001\tx79889\tx80776\tx81664\tx82552\tx83439\tx84327\tx85215\tx86102\tx86990\tx87877\tx88765\slleading20\pardirnatural\partightenfactor0 \f0\fs38 \cf2 The dynamics of the radial envelope of a weak coherent drift wave is approximately governed by a nonlinear Schr\'f6dinger equation, which emerges as a limit of the modified Hasegawa\'97Mima equation. The nonlinear Schr\'f6dinger equation has well-known soliton solutions, and its modulational instability can naturally generate solitary structures. In this paper, we demonstrate that this simple model can adequately describe the formation of solitary zonal structures in the modified Hasegawa\'97Mima equation, but only when the amplitude of the coherent drift wave is relatively small. At larger amplitudes, the modulational instability produces stationary zonal structures instead. Furthermore, we find that incoherent drift waves with beam-like spectra can also be modulationally unstable to the formation of solitary or stationary zonal structures, depending on the beam intensity. Notably, we show that these drift waves can be modeled as quantumlike particles (\'93driftons\'94) within a recently developed phase-space (Wigner\'97Moyal) formulation, which intuitively depicts the solitary zonal structures as quasi-monochromatic drifton condensates. Quantumlike effects, such as diffraction, are essential to these condensates; hence, the latter cannot be described by wave-kinetic models that are based on the ray approximation.\ }
Type:: Dataset
Issue Date:: June 2019

22. Nonlinear saturation and oscillations of collisionless zonal flows

Author(s):: Zhu, Hongxuan; Zhou, Yao; Dodin, I. Y.
Abstract:: In homogeneous drift-wave (DW) turbulence, zonal flows (ZFs) can be generated via a modulational instability (MI) that either saturates monotonically or leads to oscillations of the ZF energy at the nonlinear stage. This dynamics is often attributed as the predator-prey oscillations induced by ZF collisional damping; however, similar dynamics is also observed in collisionless ZFs, in which case a different mechanism must be involved. Here, we propose a semi-analytic theory that explains the transition between the oscillations and saturation of collisionless ZFs within the quasilinear Hasegawa-Mima model. By analyzing phase-space trajectories of DW quanta (driftons) within the geometrical-optics (GO) approximation, we argue that the parameter that controls this transition is N ~ \gamma_MI/\omega_DW, where \gamma_MI is the MI growth rate and \omega_DW is the linear DW frequency. We argue that at N << 1, ZFs oscillate due to the presence of so-called passing drifton trajectories, and we derive an approximate formula for the ZF amplitude as a function of time in this regime. We also show that at N >~ 1, the passing trajectories vanish and ZFs saturate monotonically, which can be attributed to phase mixing of higher-order sidebands. A modification of N that accounts for effects beyond the GO limit is also proposed. These analytic results are tested against both quasilinear and fully-nonlinear simulations. They also explain the earlier numerical results by Connaughton et al. [J. Fluid Mech. 654, 207 (2010)] and Gallagher et al. [Phys. Plasmas 19, 122115 (2012)] and offer a revised perspective on what the control parameter is that determines the transition from the oscillations to saturation of collisionless ZFs.
Type:: Dataset
Issue Date:: May 2019

23. Electron inertial effects on linearly polarized electromagnetic ion cyclotron waves at Earth's magnetosphere

Author(s):: Kim, Eun-Hwa; Johnson, Jay; Lee, Dong-Hun
Abstract:: We discuss a role of the electron inertial effect on linearly polarized electromagnetic ion cyclotron (EMIC) waves at Earth. The linearly polarized EMIC waves have been previously suggested to be generated via mode conversion from the fast compressional wave at the ion-ion hybrid (IIH) resonance. When the electron inertial effects are neglected, the wave normal angle of the mode-converted IIH waves is 90 degrees because the wavevector perpendicular to the magnetic field becomes infinite at the IIH resonance. When the electron inertial effect is considered, the mode-converted IIH waves can propagate across the magnetic field lines and the wavelength perpendicular to the magnetic field approaches the electron inertial length scale near the Buchsbaum resonance. These waves are referred to as electron inertial waves. Due to the electron inertial effect, the perpendicular wavenumber to the ambient magnetic field near the IIH resonance remains finite and the wave normal angle is less than 90 degrees. The wave normal angle where the maximum absorption occurs in a dipole magnetic field is 30-80 degrees, which is consistent with the observed values near the magnetic equator. Therefore, the numerical results suggest that the linearly polarized EMIC wave generated via mode conversion near the IIH resonance can be detected in between the Buchsbaum and the IIH resonance frequencies, and these waves can have normal angle less than 90 degrees.
Type:: Dataset
Issue Date:: April 2019