Boundary layers and emitted excitations in nonlinear Schrodinger superflow past a disk

TL;DR

This paper investigates the stability and dynamics of nonlinear Schrödinger superflows past a disk, revealing how boundary layers and emitted excitations depend on parameters like Mach number and coherence length.

Contribution

It introduces a specialized pseudo-spectral numerical method and provides analytical and bifurcation analysis of stationary solutions in nonlinear Schrödinger superflows.

Findings

Critical Mach number depends on coherence length.

At large coherence length, rarefaction pulses replace vortices.

Bifurcation diagram of stationary solutions is mapped.

Abstract

The stability and dynamics of nonlinear Schrodinger superflows past a two-dimensional disk are investigated using a specially adapted pseudo-spectral method based on mapped Chebychev polynomials. This efficient numerical method allows the imposition of both Dirichlet and Neumann boundary conditions at the disk border. Small coherence length boundary-layer approximations to stationary solutions are obtained analytically. Newton branch-following is used to compute the complete bifurcation diagram of stationary solutions. The dependence of the critical Mach number on the coherence length is characterized. Above the critical Mach number, at coherence length larger than fifteen times the diameter of the disk, rarefaction pulses are dynamically nucleated, replacing the vortices that are nucleated at small coherence length.