Related Experiment Video
Updated: Aug 2, 2026
13:02
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
Fractal aircraft trajectories and nonclassical turbulent exponents
S Lovejoy1, D Schertzer, A F Tuck
1Physics, McGill University, Montréal, Quebec, Canada.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
Summary
Aircraft flight paths exhibit fractal dimensions, revealing atmospheric structure. This study analyzed ER-2 aircraft data, finding fractal behavior between 3-300 km, crucial for interpreting airborne measurements.
Area of Science:
- Atmospheric science
- Aerospace engineering
- Geophysics
Background:
- Aircraft trajectories are essential for airborne data interpretation.
- Understanding trajectory dimensions aids in atmospheric studies.
Purpose of the Study:
- To estimate the dimension (D) of stratospheric aircraft trajectories.
- To investigate the fractal nature of these paths and its implications.
Main Methods:
- Analyzed 18 long-duration (1600 km) stratospheric flight trajectories from the ER-2 research aircraft.
- Utilized data from the "Mach cruise" autopilot mode, characterized by near-constant Mach number.
- Examined the relationship between vertical and horizontal coordinates (DeltaZ ~ Deltax (H(z))) to determine trajectory dimension.
Main Results:
- Identified a fractal dimension (D) of approximately 14/9 (1.56) for trajectories in the 3-300 km range, with H(z) ≈ 0.58 ± 0.02.
- Observed trajectory smoothing below 3 km due to aircraft inertia and D=1 above 300 km due to fuel consumption.
- Found horizontal velocity and temperature exponents near the nonclassical value of 1/2 within the fractal regime.
Conclusions:
- Stratospheric aircraft trajectories exhibit fractal characteristics within a specific scale range.
- The fractal dimension impacts the interpretation of airborne atmospheric measurements.
- Findings provide insights into atmospheric structure and dynamics relevant to flight data.
More Related Videos
Related Concept Videos
01:07Laminar and Turbulent Flow
Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the streamlines...
01:30Bernoulli's Equation for Flow Along a Streamline
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
01:16Bernoulli's Equation for Flow Normal to a Streamline
Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
01:15Dimensionless Groups in Fluid Mechanics
Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
01:24Turbulent Flow
Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent spots,...
01:18Boundary Layer Characteristics
When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...