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

Jacek M. Kopeć,Szymon P. Malinowski,Yong-Feng Ma,Marta Wacławczyk

doi:10.5194/amt-10-4573-2017

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.

Highlights

Despite the fact that turbulence is one of the key physical mechanisms responsible for many atmospheric phenomena, information on the turbulent kinetic energy (TKE) dissipation rate based on in situ airborne measurements is scarce
Due to various problems related to, for example, inhomogeneity of turbulence along the aircraft track and/or artifacts related to inevitable aerodynamic problems (Khelif et al, 1999; Kalgorios and Wang, 2002; Mallaun et al, 2015), estimates of at such low resolutions using power spectral density (PSD) or structure functions are complex and far from being standardized
Let us consider a homogeneous velocity field converted to time series u(t) with the use of Taylor’s hypothesis

Summary

Introduction

Despite the fact that turbulence is one of the key physical mechanisms responsible for many atmospheric phenomena, information on the turbulent kinetic energy (TKE) dissipation rate based on in situ airborne measurements is scarce. One of them is the zero- or threshold-crossing method (Sreenivasan et al, 1983) which, instead of calculating the energy spectrum or velocity structure functions, requires counting of the signal zero- or threshold-crossing events (see Fig. 1a) Their mean number per unit length is related to the turbulent kinetic energy dissipation rate. The zero-crossing method is based on a direct relation between and the root mean square of the velocity derivative (Pope, 2000); the measured signal should be resolved down to the smallest scales. This is not achievable in the case of flight measurements with moderate time resolutions.

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