arXiv subjects

Anandhan Jayaraman

Publications and source records attributed to Anandhan Jayaraman.

5 recordsLinked to original sources

arXiv2002

Monotone Solutions of a Nonautonomous Differential Equation for a Sedimenting Sphere

We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem.

math-ph↗

arXiv2002

Oscillations of a solid sphere falling through a wormlike micellar fluid

We present an experimental study of the motion of a solid sphere falling through a wormlike micellar fluid. While smaller or lighter spheres quickly reach a terminal velocity, larger or heavier spheres are found to oscillate in the direction of their falling motion. The onset of this instability correlates with a critical value of the velocity gradient scale $Γ_{c}\sim 1$ s$^{-1}$. We relate this condition to the known complex rheology of wormlike micellar fluids, and suggest that the unsteady motion of the sphere is caused by the formation and breaking of flow-induced structures.

physics.flu-dyn↗

arXiv1998

First Principles Justification of a ``Single Wave Model'' for Electrostatic Instabilities

The nonlinear evolution of a unstable electrostatic wave is considered for a multi-species Vlasov plasma. From the singularity structure of the associated amplitude expansions, the asymptotic features of the electric field and distribution functions are determined in the limit of weak instability, i.e. $γ\to 0^+$ where $γ$ is the linear growth rate. The asymptotic electric field is monochromatic at the wavelength of the linear mode with a nonlinear time dependence. The structure of the distibutions outside the resonant region is given by the linear eigenfunction but in the resonant region the distribution is nonlinear. The details depend on whether the ions are fixed or mobile; in either case the physical picture corresponds to the single wave model originally proposed by O"Neil, Winfrey, and Malmberg for the interaction of a cold weak beam with a plasma of fixed ions.

physics.plasm-ph↗

arXiv1997

Amplitude Equations for Electrostatic Waves: multiple species

The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude $A(t)$. In the limit of weak instability, i.e. $γ\to 0^+$ where $γ$ is the linear growth rate, the nonlinear coefficients are singular and their singularities predict the dependence of $A(t)$ on $γ$. Generically the scaling $|A(t)|=γ^{5/2}r(γt)$ as $γ\to 0^+$ is required to cancel the coefficient singularities to all orders. This result predicts the electric field scaling $|E_k|\simγ^{5/2}$ will hold universally for these instabilities (including beam-plasma and two-stream configurations) throughout the dynamical evolution and in the time-asymptotic state. In exceptional cases, such as infinitely massive ions, the coefficients are less singular and the more familiar trapping scaling $|E_k|\simγ^2$ is recovered.

patt-sol↗

arXiv1996

Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $ρ(t)$ is studied using an expansion in $ρ$; in particular, in the limit $γ\rightarrow0^+$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $γ$. Generically $|E_k|\sim γ^{5/2}$, as $γ\rightarrow0^+$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim γ^{2}$ is predicted.

patt-sol↗