Kernels with low arithmetic intensity with memory footprint exceeding cache sizes are typically categorised as memory bandwidth bound. Kernels of this class are typically limited by hardware memory bandwidth. In this work we contribute a simple memory access pattern, derived from a widely-used upwinded stencil-style benchmark, which presents significant challenges for cache-based architectures. The problem appears to grow worse as CPU core counts increase, and the pattern in its initial form shows no benefit from the new high-bandwidth memory now appearing on the Intel Xeon Phi (Knights Landing) family of processors. We describe the memory access scenarios which appear to be causing lower than expected cache performance, before presenting optimisations to mitigate the problem. These optimisations result in useful effective memory bandwidth and runtime improvements by up to 4X on cache based architectures. Results are presented on the Intel Xeon (Broadwell) and Xeon Phi (Knights Landing) processors.