Turbulent aspects of Berenstein-Maldacena-Nastase membrane dynamics

We investigate the large-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>N</a:mi></a:mrow></a:math> limit of the Berenstein-Maldacena-Nastase (BMN) matrix model with classical bosonic membranes which have spherical topologies and spin inside the 11-dimensional maximally supersymmetric plane-wave background. First we classify all possible M2-brane configurations based on the distribution of their components inside the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>S</c:mi><c:mi>O</c:mi><c:mo stretchy="false">(</c:mo><c:mn>3</c:mn><c:mo stretchy="false">)</c:mo><c:mo>×</c:mo><c:mi>S</c:mi><c:mi>O</c:mi><c:mo stretchy="false">(</c:mo><c:mn>6</c:mn><c:mo stretchy="false">)</c:mo></c:math> symmetric plane-wave spacetime. We then formulate a number of simple but very representative of dielectric tops that rotate in this space. We examine the leading-order radial and angular/multipole stability for a wide range of these configurations. By analyzing perturbations at the next-to-leading order, we find that they exhibit the phenomenon of turbulent cascading of instabilities. Thereby, long-wavelength perturbations generate higher-order multipole instabilities through their nonlinear couplings.