Non-stationary Boundary Layers
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Non-stationary Boundary Layers L. Mahrt1
· Elie Bou-Zeid2
Received: 30 December 2019 / Accepted: 19 May 2020 © Springer Nature B.V. 2020
Abstract The literature includes a wide variety of definitions or perceptions of non-stationarity. Nonstationarity can be expressed in terms of turbulence statistics or variability of the forcing of the turbulence such as time changes of the wind vector, the horizontal pressure gradient, or the surface heat flux. Our survey emphasizes the development of non-equilibrium turbulence caused by non-stationary forcing. The degree of non-equilibrium of the turbulence is most reliably evaluated following the local flow rather than using the more available fixed-point measurements. We survey methods to eliminate non-stationary records or partially filter out the non-stationarity. We also summarize issues with parametrization of the non-stationarity. Non-stationarity over the sea can be complex due to time-dependent wave state and surface roughness. The impact of non-stationarity is generally less understood in the stable boundary layer compared to the unstable boundary layer. Keywords Equilibrium turbulence · Non-stationarity · Spectral gap · Submeso · Turbulence adjustment
1 Introduction The term non-stationary is defined in different ways and on different scales. Non-stationarity may refer to the turbulence statistics or to the non-turbulent flow that forces the turbulence. For some investigations, examination of non-stationarity is motivated by possible violation of similarity theory (e.g., Smeets et al. 1998). Our review focuses on the impact of the non-stationary wind field on the turbulence and whether the turbulence can maintain quasiequilibrium with the changing flow. Boundary-layer stationarity is often approximately valid in certain situations such as the polar night (Yagüe and Cano 1994; Grachev et al. 2007; Petenko et al. 2019), although sometimes wave-like motions are important. Stationarity is also common in open-ocean conditions where the diurnal forcing is small. Stationarity additionally requires relatively steady horizontal pressure gradients.
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L. Mahrt [email protected]
1
NorthWest Research Associates, 2171 NW Kari Pl, Corvallis, OR 97330, USA
2
Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA
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L. Mahrt, E. Bou-Zeid
Frequently, the turbulence becomes non-stationary in response to time changes of the surface heat flux (thermal forcing). The diurnal trend with clear skies includes concentrated rapid changes of the thermal forcing during the late-afternoon transition to stable flow (Lothon et al. 2014; Angevine et al. 2020) and the morning transition to unstable flow (Hicks et al. 2018). To a lesser degree, the heat flux during the day is also non-stationary as it increases, reaches a maximum sometime after solar noon, and subsequently decreases with time, causing the turbulence intensity to decrease (Grimsdell and Angevine 2002; Nilsson et al. 2016). During both the evening and morning transitions, the relatio
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