Log-Skew-Normality of Turbulent Kinetic Energy Dissipation Rate in a Buoyant Coastal Plume

Our current understanding of turbulence relies on statistical representations of the underlying chaotic motion. One such representation is the Probability Density Function (PDF) of Turbulent Kinetic Energy (TKE) dissipation rate. Measuring TKE dissipation rates is challenging, and these measurements in the ocean remain relatively sparse. Building an energy-consistent representation of the turbulent cascade of energy therefore relies on the inferences that can be made from the statistics of these measurements. The traditional representation of the PDF of TKE dissipation rate is a log-normal distribution, which is derived theoretically for a single, statistically-steady source of turbulence. However, turbulence is very rarely isolated from other sources in oceanic environments and as such, observations often deviate from the log-normal description. Cael and Mashayek (2021, Phys. Rev. Lett.) argue that a more appropriate approximation of the PDF of TKE dissipation rate is a log-skew-normal distribution because it accurately describes the sum of log-normal random variables, representing the separate contributions of different sources to the total turbulent intensity. We present high resolution (5 cm, 0.25 s) ADCP velocity measurements along the axis of a submarine spring plume that we posit provide direct evidence to support this conclusion. We show that the PDF of TKE dissipation rate estimates exhibits three distinct peaks that we argue two of which represent distinct contributions to total dissipation rate from the high turbulent intensity buoyant plume and low dissipation rate ambient. We suggest that the intermediate dissipation rate peak results from the combination and interaction of the separate sources of turbulence. We demonstrate that while the two peaks representing the independent sources of turbulence are well-represented by log-normal distributions, the peak corresponding to their combination is better characterized by a log-skew-normal distribution.