Evolution of complex singularities in Kida–Pelz and Taylor–Green inviscid flows

The analyticity strip method is used to trace complex singularities in direct numerical simulations of the Kida–Pelz and Taylor–Green flows, performed with up to 2048³ collocation points. Oscillations found in the Kida–Pelz energy spectrum are attributed to interferences of complex singularities. A generalized least-square fit that separates out the oscillations from the measure of the width of the analyticity strip δ is introduced. Using the available resolution, δ is found to decay exponentially in time up to t = 1.25. It is argued that resolutions in the range 16384³–32768³ (within reach of the Earth Simulator) are needed to really probe the Pelz singularity at t∼2.