Conserved Vectors for a Model of Nonlinear Atmospheric Flows Around The Rotating Spherical Surface

Abstract

Abstract. We derive the conserved vectors for the nonlinear two-dimensional Euler equations describing nonviscous incompressible fluid flows on a three-dimensional rotating spherical surface superimposed by a particular stationary latitude dependent flow. Under the assumption of no friction and a distribution of temperature dependent only upon latitude, the equations in question can be used to model zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. As a particualr example, the conserved densities are analyzed by visualizing the exact invariant solutions associated with the given model for the particular form of finite disturbances for which the invariant solutions are also exact solutions of Navier-Stokes equations.

Conservation laws for time-fractional subdiffusion and diffusion-wave equations

“…Using the Noether operators (13) and (15), the symmetries (23)- (25), and the formal Lagrangian (5) with the function v(t, x) given by (28), only one new conserved vector has been found for Eq. (1) with the Riemann-Liouville time-fractional derivative of order α ∈ (0, 1).…”

“…The components of conserved vectors are obtained in this algorithm by acting the so-called Noether operators to a Lagrangian function. Using this approach, the conservation laws for different integer-order differential equations and its systems having only formal Lagrangians have been constructed by their symmetries [23][24][25][28][29][30][31][32][33].…”

Symmetries and Conservation Laws of a Spectral Nonlinear Model for Atmospheric Baroclinic Jets

“…In this paper, we shall we shall obtain the symmetries associated with the nonlinear modeling describing spontaneous relaxation of eastward jets into a meandering state and use these symmetries for constructing the conservation laws by the method of nonlinear self-adjointness [13]. Similar analysis for the derivation of the conservation laws for the model of nonlinear atmospheric flows around the rotating spherical surface can be found in [14].…”