Potential temperature-related third-order structure function in the logarithmic region of the atmosphere boundary layer

This study investigates the potential-temperature-related third-order structure function in the atmospheric surface layer (ASL), which reflects the properties of potential-energy transfer in the flow, using theory and data from the Qingtu Lake Observation Array (QLOA). We formulated a K\'arm\'an--Howarth--Monin equation for potential energy and, using Townsend's attached eddy hypothesis, derived that the structure function exhibits a horizontal logarithmic region and proposed a universal expression. The image reveals a distinct logarithmic region and demonstrates the validity of our expression for QLOA data.