arXiv subjects

Oliver S. Kerr

Publications and source records attributed to Oliver S. Kerr.

3 recordsLinked to original sources

arXiv2024

Periodic Steady Vortices in a Stagnation Point Flow II

Steady-state perturbations to a stagnation point flow of the form ${\bf U}=(0,A'y,-A'z)$ are known which consist of a periodic array of counter-rotating vortices whose axes are parallel to the $y$-axis and which lie in the plane $z=0$. A new understanding of how these vortices depend on the supply of incoming vorticity from afar has lead to the discovery of new families of steady-state periodic vortices that can exist in a stagnation point flow. These new flows have a greater variety of structures than those previously known. An understanding of the linkage between the vortices and the weak inflow of vorticity can have important implications for situations where such vortices are observed.

physics.flu-dyn↗

arXiv2016

Critical Rayleigh number of for error function temperature profile with a quasi-static assumption

When a semi-infinite body is heated from below by a sudden increase in temperature (or cooled from above) an error function temperature profile grows as the heat diffuses into the fluid. The stability of such a profile is investigated using a large-wavelength asymptotic expansion under the quasi-static, or frozen-time, approximation. The critical Rayleigh number for this layer is found to be $Ra=π^{1/2}$ based on the length-scale $(κt)^{1/2}$ where $κ$ is the thermal diffusivity and $t$ the time since the onset of heating.

physics.flu-dyn↗

arXiv2014

On "Nonlinear eigenvalue problems"

The asymptotic behaviour of solutions to $y'(x)=\cos[πx y(x)]$ was investigated by Bender, Fring and Komijani \cite{BenderEtAl:2014}. They found, for example, a relation between the initial value $y(0)=a$ and the number of maxima that the solution exhibited. We present an alternative derivation of the asymptotic results that looks at the solutions in the regions $x y$, and confirms the behaviour found previously for larger values of $a$. This method uses the small amplitude and high frequency of the oscillatory behaviour in the region $x<y$.

math-ph↗