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points of the projectile is more difficult to assess. A technique for estimating the magnitude of the statistical variations of ballistic trajectories due to atmospheric turbulence along the path of the projectile is provided in this paper. These estimates can be used to bound the scatter due to atmospheric processes, and they allow more meaningful interpretations of measured scatter during ballistics testing. These estimates together with suitable measurements can also be used to identify low
points of the projectile is more difficult to assess. A technique for estimating the magnitude of the statistical variations of ballistic trajectories due to atmospheric turbulence along the path of the projectile is provided in this paper. These estimates can be used to bound the scatter due to atmospheric processes, and they allow more meaningful interpretations of measured scatter during ballistics testing. These estimates together with suitable measurements can also be used to identify low
). While interleaving signals are often of large amplitude and therefore demand a nonlinear theoretical treatment (e.g., Walsh and Ruddick 1998 ; Mueller et al. 2007 ), linear perturbation theory provides an essential starting point for defining spatial and temporal scales and for identifying the central mechanisms (e.g., Stern 1967 ; May and Kelley 1997 ; Walsh and Ruddick 2000 ; Smyth 2007 ). Here, we use linear analysis to explore the role of ambient turbulence in interleaving driven by salt
). While interleaving signals are often of large amplitude and therefore demand a nonlinear theoretical treatment (e.g., Walsh and Ruddick 1998 ; Mueller et al. 2007 ), linear perturbation theory provides an essential starting point for defining spatial and temporal scales and for identifying the central mechanisms (e.g., Stern 1967 ; May and Kelley 1997 ; Walsh and Ruddick 2000 ; Smyth 2007 ). Here, we use linear analysis to explore the role of ambient turbulence in interleaving driven by salt
1. Introduction Pointwise velocimeters allow us to determine benthic and water column shear stresses via the direct calculation of Reynolds stresses from fluctuating velocities. However, because variance associated with waves is often much larger than that associated with turbulence, some form of wave–turbulence decomposition must be used ( Jiang and Street 1991 ; Thais and Magnaudet 1995 ; Trowbridge 1998 ). In a flow with both waves and currents, the instantaneous horizontal velocity u
1. Introduction Pointwise velocimeters allow us to determine benthic and water column shear stresses via the direct calculation of Reynolds stresses from fluctuating velocities. However, because variance associated with waves is often much larger than that associated with turbulence, some form of wave–turbulence decomposition must be used ( Jiang and Street 1991 ; Thais and Magnaudet 1995 ; Trowbridge 1998 ). In a flow with both waves and currents, the instantaneous horizontal velocity u
1. Introduction Turbulence at aircraft scale (10–1000 m) or that directly affects aircraft is commonly referred to as aviation turbulence ( Lester 1994 ). Aviation turbulence in the free atmosphere is a serious concern in the general aviation industry because it frequently causes occupant injuries, flight delays, fuel losses, and structural damage. It is more dangerous when it occurs unexpectedly at cruising levels, where most of the passengers and crew are unbuckled. According to the 2009
1. Introduction Turbulence at aircraft scale (10–1000 m) or that directly affects aircraft is commonly referred to as aviation turbulence ( Lester 1994 ). Aviation turbulence in the free atmosphere is a serious concern in the general aviation industry because it frequently causes occupant injuries, flight delays, fuel losses, and structural damage. It is more dangerous when it occurs unexpectedly at cruising levels, where most of the passengers and crew are unbuckled. According to the 2009
). The most notorious difficulty is how turbulence affects the collisional growth. This problem has a long history and was recently reviewed by Shaw (2003) , Devenish et al. (2012) , Grabowski and Wang (2013) , and Pumir and Wilkinson (2016) . The pioneering work by Saffman and Turner (1956) proposed a theoretical model for the collision rate (Saffman–Turner model) of cloud droplets. The key idea of the Saffman–Turner model is that the collision rate is dominated by small scales of turbulence
). The most notorious difficulty is how turbulence affects the collisional growth. This problem has a long history and was recently reviewed by Shaw (2003) , Devenish et al. (2012) , Grabowski and Wang (2013) , and Pumir and Wilkinson (2016) . The pioneering work by Saffman and Turner (1956) proposed a theoretical model for the collision rate (Saffman–Turner model) of cloud droplets. The key idea of the Saffman–Turner model is that the collision rate is dominated by small scales of turbulence
1. Introduction Turbulence in the free atmosphere remains a major concern for aircraft operations, causing flight delays and occupant injuries and fatalities, which, when combined, lead to economic losses typically worth millions of dollars annually. Further, turbulence is a major dissipative mechanism in the atmospheric energy budget and must be understood to develop realistic parameterizations for numerical weather prediction (NWP) and general circulation models (GCMs). Yet the mechanisms
1. Introduction Turbulence in the free atmosphere remains a major concern for aircraft operations, causing flight delays and occupant injuries and fatalities, which, when combined, lead to economic losses typically worth millions of dollars annually. Further, turbulence is a major dissipative mechanism in the atmospheric energy budget and must be understood to develop realistic parameterizations for numerical weather prediction (NWP) and general circulation models (GCMs). Yet the mechanisms
dissipation. We describe a similar deployment of ARIES II in a weakly stratified region of the Irish Sea at times when boils are observed, when nearby there are vertical profiles of turbulent dissipation rates made using Fast Light Yo-yo (FLY) profiler casts, and when horizontal sections of turbulent dissipation are made by sensors mounted on the Autonomous Underwater Vehicle (AUV) Autosub ( Thorpe et al. 2003 ). Our purpose is to describe the new findings about boils and the related turbulence. Although
dissipation. We describe a similar deployment of ARIES II in a weakly stratified region of the Irish Sea at times when boils are observed, when nearby there are vertical profiles of turbulent dissipation rates made using Fast Light Yo-yo (FLY) profiler casts, and when horizontal sections of turbulent dissipation are made by sensors mounted on the Autonomous Underwater Vehicle (AUV) Autosub ( Thorpe et al. 2003 ). Our purpose is to describe the new findings about boils and the related turbulence. Although
1. Introduction Spontaneous zonal jet formation is a well-known significant feature in two-dimensional β -plane turbulence ( Rhines 1975 ; Vallis and Maltrud 1993 ). The formation itself is considered due to the upward cascade of energy that favors a zonal structure because of the β term. Vallis and Maltrud (1993) found asymmetry between eastward and westward jet profiles that emerged from turbulent states in the forced-dissipative numerical experiments. That is, eastward jets are
1. Introduction Spontaneous zonal jet formation is a well-known significant feature in two-dimensional β -plane turbulence ( Rhines 1975 ; Vallis and Maltrud 1993 ). The formation itself is considered due to the upward cascade of energy that favors a zonal structure because of the β term. Vallis and Maltrud (1993) found asymmetry between eastward and westward jet profiles that emerged from turbulent states in the forced-dissipative numerical experiments. That is, eastward jets are
1. Introduction This is the continuation of a two-part paper that describes a method for developing automated (strategic) forecasts and (tactical) nowcasts of energy dissipation rate to the one-third power (EDR) for aviation turbulence applications. Part I provided a description of the forecast method along with statistical-performance results from comparisons with observations ( Sharman and Pearson 2017 ). The turbulence-forecasting technique is an extension of the Graphical Turbulence
1. Introduction This is the continuation of a two-part paper that describes a method for developing automated (strategic) forecasts and (tactical) nowcasts of energy dissipation rate to the one-third power (EDR) for aviation turbulence applications. Part I provided a description of the forecast method along with statistical-performance results from comparisons with observations ( Sharman and Pearson 2017 ). The turbulence-forecasting technique is an extension of the Graphical Turbulence
produced from the wind turbine is directly proportional to the cube of the wind speed, at least below turbine-rated wind speeds. Atmospheric turbulence is one of the main inputs in assessing loads on the wind turbines. Thus, accurate estimation of wind speed and turbulence at several heights is crucial for the successful development of a wind farm. In wind energy, the current standard is the use of meteorological masts equipped with cup and/or sonic anemometers. However, tall meteorological masts are
produced from the wind turbine is directly proportional to the cube of the wind speed, at least below turbine-rated wind speeds. Atmospheric turbulence is one of the main inputs in assessing loads on the wind turbines. Thus, accurate estimation of wind speed and turbulence at several heights is crucial for the successful development of a wind farm. In wind energy, the current standard is the use of meteorological masts equipped with cup and/or sonic anemometers. However, tall meteorological masts are
