  Stochastic modelling necessitates an interpretation of noise. In this paper,
we describe the loss of deterministically stable behaviour in a fundamental
fluid mechanics problem, conditional to whether noise is introduced in the
sense of It\^o, Stratonovich or a limit of Wong-Zakai type. We examine this
comparison in the wider context of discretising stochastic differential
equations with and without the L\'evy area. From the numerical viewpoint, we
demonstrate performing higher order discretisations with the use of a L\'evy
area can lead to the loss of conserved area and angle quantities. Such
behaviour is not physically expected in the Stratonovich model. Conversely, we
study Stochastic Advection by Lie Transport and its derivation from
homogenisation theory, which introduces drift corrections of the same class
naturally. From the viewpoint of homogenisation, the qualitative properties of
the Wong-Zakai anomaly are physically motivated as arising due to correlations
from a fast and mean scale fluid decomposition.
