# Estimating Eddy Dissipation Rate with QAR Flight Big Data
## 1 Introduction  
Air turbulence (AT) is a typical risk that seriously threatens civil aviation safety. It could typically cause sudden airplane shakes, from side to side or up and down, or trembles by itself during the flight [1]. It generally brings about anxieties for airline passengers [2], yet severe turbulences might result in aircrafts thrown up and down sharply and frequently, which makes it difficult for pilots to manipulate the aircraft effectively, and even results in structural damages or casualty accidents in extreme cases. On 11 th August, 2015, strong ATs caused injuries to several passengers and crew members. To avoid serious losses, it is rather important to explore the occurrence mechanism, influencing factors, detection, or prediction models for ATs. AT can be categorized into different types, including convective turbulence, clear air turbulence, low-level thermals, and wake turbulence. It is mainly caused or affected by meteorological factors [3]. Some of them could be observed or anticipated via weather radar onboard, but some cannot be detected intuitively, like clear air turbulence (CAT). A number of studies on AT have been conducted, and several indices have been developed to measure clear AT, like [PERSON]'s index [4], an objective index by [PERSON] [5], and a real-time estimation technique of AT severity [6]. For the civil aviation of China, the vertical acceleration (VA), however is generally used for measuring AT [7], empirically identifying them with regarding VA less than 0.3 g (gravity unit) or greater than 1.8 g as an unsafe event due to AT. However, the severity of AT affecting an aircraft could be related to nature of the turbulence, airspeed, mass of the aircraft, and altitude [8]. AT reports simply relying on the VA is, thus, of limited application and aircraft specificity. In essence, turbulence refers to a fluid motion, which is characterized by nonlinearity, vorticity, diffusivity, and energy dissipation [9]. It could be too complicated to define it precisely [10] but can be broadly regarded as a dissipative flow state with nonlinear fluctuating three-dimensional vorticity [11]. Since the early time of aviation industry, studies on turbulence have been involved in designing geometry parameter of an aircraft via computer simulation techniques [12; 13]. Eddy is another useful concept for discussing the mechanism of turbulence [10; 14; 15], and eddy viscosity is an important property for describing turbulence [16]. In particular, eddy dissipation rate (EDR) could be an ideal measurement for evaluating aircraft vortices due to the ambient atmospheric turbulence [17; 18; 19]. The World Meteorological Organization (WMO) started to add turbulence monitoring information in the aircraft meteorological data relay (AMDAR) since 2002, where both EDR and derived equivalent vertical gust velocity (DEVG) are reported as measurement indices [8]. Note that VA or DEVG reflects more of turbulent appearances when aircraft going through an atmospheric turbulence zone. Different types of aircrafts, however, may respond distinctively to accelerations due to different configurations, even when they go through areas of the same atmospheric condition. Thus, measuring AT via VA or DEVG could be sensitive to different aircrafts. This characteristic leads to a potentially weak point in studying AT risk with them, particularly in the spatially and temporally perspectives. On the contrary, EDR measures the physical impacts of air flows on AT intensity. It tends to be an ideal measurement for studying AT risks, but experiences difficulty when calculating due to the complicated information required. In particular, EDR is a parameter to determine the amount of energy lost by the viscous forces in the turbulent flow [20]. It is the rate at which the turbulence energy is absorbed by breaking the eddy down into smaller and smaller eddies until it is ultimately converted into heat by viscous forces.