Inthispaper,wediscussthetopologicalstructuresofthevortexfilamentsandvortextubeswithanexactsolutionofastraightspiralvortextube.Wefindthattherearesomeconfusionsaboutthecalculationofthehelicitiesofaknottedvortexfilamentandsomelinkedvortexfilamentsbyusingdifferentmethods.Weexplainhowtounifythesemethodsandgivetherightresults.