In this paper, we study Whittaker modules over the loop Virasoro algebra relative to some total order. We give a description of all Whittaker vectors for the universal Whittaker modules. We also show that any universal Whittaker module admits a unique simple quotient modules except for a special case.

A new family of finite-dimensional simple modular Lie superalgebra ℳ is constructed based on results of Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321: 3601–3619]. The simplicity and generators of ℳ are discussed and the derivation superalgebra of ℳ is characterized. Furthermore, the invariance of the nonnatural filtration of ℳ is determined by the method of minimal dimension of image spaces.