Novel approaches to estimating the turbulent kinetic energy dissipation rate from low- and moderate-resolution velocity fluctuation time series

Abstract

Abstract. In this paper we propose two approaches to estimating the turbulent kinetic energy (TKE) dissipation rate, based on the zero-crossing method by Sreenivasan et al. (1983). The original formulation requires a fine resolution of the measured signal, down to the smallest dissipative scales. However, due to finite sampling frequency, as well as measurement errors, velocity time series obtained from airborne experiments are characterized by the presence of effective spectral cutoffs. In contrast to the original formulation the new approaches are suitable for use with signals originating from airborne experiments. The suitability of the new approaches is tested using measurement data obtained during the Physics of Stratocumulus Top (POST) airborne research campaign as well as synthetic turbulence data. They appear useful and complementary to existing methods. We show the number-of-crossings-based approaches respond differently to errors due to finite sampling and finite averaging than the classical power spectral method. Hence, their application for the case of short signals and small sampling frequencies is particularly interesting, as it can increase the robustness of turbulent kinetic energy dissipation rate retrieval.

Estimating Turbulence Kinetic Energy Dissipation Rates in the Numerically Simulated Stratocumulus Cloud-Top Mixing Layer: Evaluation of Different Methods

“…In case a signal is low-pass filtered the number of zero crossings per unit length depends on cutoff wavenumber. Hence, Wacławczyk et al (2017) proposed a possible modification for zero-crossing method to retrieve « from the restricted range of k values. The motivation was to increase robustness of « retrieval using different statistics.…”

“…The motivation was to increase robustness of « retrieval using different statistics. Two procedures formulated in Wacławczyk et al (2017) are discussed in more detail in section 2b, below.…”

“…The socalled Liepmann scale, defined as L 5 1/(pN L ), is assumed to be equal to the transverse Taylor's microscale l n , which is used to calculate «. Since N L in signals with spectral cutoff are much smaller than in fully resolved signals, Wacławczyk et al (2017) proposed two possible modifications to the zero-crossing method in order to estimate « from moderate-resolution measurement data.…”

“…In the second approach, an analytical model for the unresolved section of the spectrum is used to calculate a correcting factor to N L , so the actual relation between « and N L can be used. Wacławczyk et al (2017) validated these approaches on the data obtained during the Physics of Stratocumulus Top (POST) research campaign designed to investigate the marine stratocumulus clouds as well as the details of the vertical structure of the stratocumulus-topped boundary layer (Gerber et al 2013;Malinowski et al 2013).…”

“…Due to the abovementioned difficulties, the present work focuses on the second method proposed in Wacławczyk et al (2017), based on an analytical model to resolving the missing part of the spectrum. We propose its alternative form, replacing the Liepmann scale with the Taylor microscale.…”