This study examines influences of transverse annulation on characteristics of flow over an orthocone. This work is inspired by Spyroceras, a fossilized genus of the nautiloid family during the Paleozoic era, whose method of locomotion is understudied. As a baseline case, a flow over a smooth, orthoconic model with a blunt apertural end was investigated numerically at Reynolds numbers from 50 to 1500. We find that a critical transition from steady to unsteady flow state occurs between Reof 50 and 500. Two different shedding mechanisms are captured as Reincreases. We notice that an introduction of annulation over the cone surface changes the critical Reynolds number for the transition of different shedding mechanisms. The time-averaged drag coefficient increases due to the annulation along the cone surface. We have also observed that the dominant shedding frequency increases as Re increases. Moreover, Proper Orthogonal Decomposition (POD) analysis is performed to optimally capture most energetic modes in the wake for both smooth and annulated cone flows. POD analysis shows that the coherent structures become twisted and more complex, and it requires more POD modes to contain 80% total energy for the flows at higher Reynolds number. The leading modes for the annulated cone cases indicates that the annulation reduces the twisting effect in the wake.