Conservation Laws of Space-Time Fractional mZK Equation for Rossby Solitary Waves with Complete Coriolis Force

2019 ◽  
Vol 20 (1) ◽  
pp. 17-32 ◽  
Author(s):  
Hong Wei Yang ◽  
Min Guo ◽  
Hailun He
Keyword(s):  
Coriolis Force ◽  
Solitary Waves ◽  
Inverse Method ◽  
Space Time ◽  
Atmospheric Physics ◽  
Similarity Reduction ◽  
Integer Order ◽  
Rossby Solitary Waves ◽  
New Research ◽  
Complete Coriolis Force

AbstractThe study of Rossby solitary waves are of great significance in physical oceanography, atmospheric physics, water conservancy project, military and communications engineering, etc. All the time, in the study of Rossby solitary waves, people have been focusing on integer order models. Recently, fractional calculus has become a new research hotspot, and it has opened a new door to research atmospheric and ocean. Thus, the fractional order model has the potential value in the study of Rossby solitary waves. In the present paper, according to the quasi-geostrophic potential vorticity equation with the complete Coriolis force, we get a new integer order mZK equation. Using the semi-inverse method and the fractional variational principle, the space-time fractional mZK(STFmZK) equation is obtained. To better understand the property of Rossby solitary waves, we study Lie symmetry analysis, nonlinear self-adjointness, similarity reduction by applying the STFmZK equation. In the end, the conservation and Caputo fractional derivative are discussed, respectively.

Structure of equatorial envelope Rossby solitary waves with complete Coriolis force and the external source

2018 ◽  
Vol 111 ◽  
pp. 68-74 ◽  
Author(s):  
Xiao-Jun Yin ◽  
Lian-Gui Yang ◽  
Quan-Sheng Liu ◽  
Jin-Mei Su ◽  
Guo-rong Wu
Keyword(s):  
Coriolis Force ◽  
Solitary Waves ◽  
External Source ◽  
Rossby Solitary Waves ◽  
Complete Coriolis Force

Rossby solitary waves excited by the unstable topography in weak shear flow

2017 ◽  
Vol 90 (2) ◽  
pp. 889-897 ◽  
Author(s):  
Bao-Jun Zhao ◽  
Ru-Yun Wang ◽  
Qing Fang ◽  
Wen-Jin Sun ◽  
Tian-Ming Zhan
Keyword(s):  
Shear Flow ◽  
Solitary Waves ◽  
Rossby Solitary Waves

Wellposedness and regularity of a variable-order space-time fractional diffusion equation

2020 ◽  
Vol 18 (04) ◽  
pp. 615-638 ◽  
Author(s):  
Xiangcheng Zheng ◽  
Hong Wang
Keyword(s):  
Diffusion Equation ◽  
Linear Space ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Variable Order ◽  
Order Linear ◽  
Integer Order ◽  
Time Fractional Diffusion Equation ◽  
Full Regularity

We prove wellposedness of a variable-order linear space-time fractional diffusion equation in multiple space dimensions. In addition we prove that the regularity of its solutions depends on the behavior of the variable order (and its derivatives) at time [Formula: see text], in addition to the usual smoothness assumptions. More precisely, we prove that its solutions have full regularity like its integer-order analogue if the variable order has an integer limit at [Formula: see text] or have certain singularity at [Formula: see text] like its constant-order fractional analogue if the variable order has a non-integer value at time [Formula: see text].

scholarly journals (2 + 1)-Dimensional Coupled Model for Envelope Rossby Solitary Waves and Its Solutions as well as Chirp Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Xin Chen ◽  
Hongwei Yang ◽  
Min Guo ◽  
Baoshu Yin
Keyword(s):  
Solitary Waves ◽  
Rossby Waves ◽  
Modulation Instability ◽  
Multiple Scales ◽  
Coupled Model ◽  
Nls Equation ◽  
Coupled Models ◽  
Trial Function Method ◽  
Rossby Solitary Waves ◽  
Stable Feature

Using the method of multiple scales and perturbation method, a set of coupled models describing the envelope Rossby solitary waves in (2+1)-dimensional condition are obtained, also can be called coupled NLS (CNLS) equations. Following this, based on trial function method, the solutions of the NLS equation are deduced. Moreover, the modulation instability of coupled envelope Rossby waves is studied. We can find that the stable feature of coupled envelope Rossby waves is decided by the value of S. Finally, learning from the concept of chirp in the optical soliton communication field, we study the chirp effect caused by nonlinearity and dispersion in the propagation of Rossby waves.

Multilayer shallow water equations with complete Coriolis force. Part 3. Hyperbolicity and stability under shear

2013 ◽  
Vol 723 ◽  
pp. 289-317 ◽  
Author(s):  
Andrew L. Stewart ◽  
Paul J. Dellar
Keyword(s):  
Shallow Water ◽  
Coriolis Force ◽  
Shallow Water Equations ◽  
Three Dimensional ◽  
Direct Calculation ◽  
Shear Instability ◽  
Vertical Shear ◽  
Vortex Sheets ◽  
Multilayer Shallow Water Equations ◽  
Complete Coriolis Force

AbstractWe analyse the hyperbolicity of our multilayer shallow water equations that include the complete Coriolis force due to the Earth’s rotation. Shallow water theory represents flows in which the vertical shear is concentrated into vortex sheets between layers of uniform velocity. Such configurations are subject to Kelvin–Helmholtz instabilities, with arbitrarily large growth rates for sufficiently short-wavelength disturbances. These instabilities manifest themselves through a loss of hyperbolicity in the shallow water equations, rendering them ill-posed for the solution of initial value problems. We show that, in the limit of vanishingly small density difference between the two layers, our two-layer shallow water equations remain hyperbolic when the velocity difference remains below the same threshold that also ensures the hyperbolicity of the standard shallow water equations. Direct calculation of the domain of hyperbolicity becomes much less tractable for three or more layers, so we demonstrate numerically that the threshold for the velocity differences, below which the three-layer equations remain hyperbolic, is also unchanged by the inclusion of the complete Coriolis force. In all cases, the shape of the domain of hyperbolicity, which extends outside the threshold, changes considerably. The standard shallow water equations only lose hyperbolicity due to shear parallel to the direction of wave propagation, but the complete Coriolis force introduces another mechanism for loss of hyperbolicity due to shear in the perpendicular direction. We demonstrate that this additional mechanism corresponds to the onset of a transverse shear instability driven by the non-traditional components of the Coriolis force in a three-dimensional continuously stratified fluid.

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