We present a formulation of the incompressible viscous Navier-Stokes equation based on a generalization of the inviscid Weber formula, in terms of a diffusive “back-to-labels” map and a virtual velocity. We derive a generalization of the inviscid Cauchy formula and obtain certain bounds for the objects introduced.

Parallel shear flows problem is a classical hydrodynamic instability problem and continues to attract attention of researchers [1,2,3,5]. Kuo [8] considered slightly general case of a homogeneous, inviscid, parallel shear flow problem in the β -plane. He obtained the linearized perturbation equation for this problem and derived an extension of the celebrated Rayleigh’s [9] inflexion point crite...

We study the Rayleigh-Taylor instabolity for two incompressible, immiscible, inviscid magnetohydrodynamic (MHD) fluids with zero resistivity, evolving with a free interface in the presence of a uniform gravitational field. We first construct the Rayleigh-Taylor steady-state solution with a denser fluid lying above the light one. Then, we turn to an analysis of the equations obtained from linear...

Steady hydromagnetic Couette flow of class-II of a viscous, incompressible and electrically conducting fluid through a porous medium in a rotating system taking Hall current into account is investigated. Heat transfer characteristics of the fluid flow are considered taking viscous and Joule dissipations into account. It is noticed that there exists flow separation at the moving plate in the sec...

The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched programme to address global existence problem for Navier Stokes equations based concept universality. Inspired this proposal, in article we prove that stationary exhibit several universality features. More precisely, show any non-autonomous compact can be...

In this paper, we present rational approximations based on Fourier series representation. For periodic piecewise analytic functions, the well-known Gibbs phenomenon hampers the convergence of the standard Fourier method. Here, for a given set of the Fourier coefficients from a periodic piecewise analytic function, we define Fourier–Padé–Galerkin and Fourier–Padé collocation methods by expressin...

An approximation method of Moore for Kelvin-Helmholtz instability is formulated as a general method for two-dimensional, incompressible, inviscid flows generated by a vortex sheet. In this method the nonlocal equations describing evolution of the sheet are approximated by a system of (local) differential equations. These equations are useful for predicting singularity formation on the sheet and...