In the absence of any name on any map, I have labelled this Ruswarp Beck. Along with Fitts Beck it forms more-or-less a boundary between Whitby proper and Ruswarp. It has two long tributories that join below Ashes Farm.
Ruswarp Beck's northern tributory flows from springs near the Guisborough Road A171/Slieghts New Road A169 roundabout (NZ 8717 0983). It then flows north-easterly towards Cross Butts before tiwning south-easterly and flowing towards Ashes Farm on Ruswarp Bank. Here it joins the southern tributory (NZ 8860 0954) and flows south towards Turnerdale Hall. The geology causes a right-angle turn and it flows eastwards, passing the allotments and flowing under Ruswarp High Street and alongside (and sometime on top of) Water Lane. It flows under the level crossing halfway along Water Lane and runs into the Esk just above Fitts Beck.
Ruswarp Beck's southern tributory flows from springs at the side of Sleights New Road/A169 about 200m downhill of the northern springs (NZ 8713 0957). Contours and field boundaries suggest that headwaters may flow underground from Hawthornedale Farm just further west. It flows almost directly eastwards until it meets the northern tributory near Ashes Farm.