Hello Paul

No matter what the cause for periodicity you might model that by cos and sin. However I like to bring to your attention that this is a better form

Exp[d((x-a)^2+(x-b)^2)]*Cos[e(x-a)]*Cos[e(x-b)]

the more variable you add, the more the terms in the norm in the exp and more Cos terms.

The above gives flexible modelling with more control.