Not an obstacle, but a help: turbulence and birds

Technological progress has allowed us to do what many birds can do by nature – fly. Of course, a lot has changed since the days of the Wright brothers, and today’s aircraft are much more efficient, safer and more comfortable. However, unlike technology, which a person can change, weather conditions and atmospheric phenomena live by their own rules and have a very unpredictable nature. For many, even the quietest flights are already a test of character strength. And when the iron bird enters the turbulence zone, people with aerophobia check the strength of the armrests of their chairs. For aviation, turbulence, which can last from a few milliseconds to several minutes, is an obstacle that engineers and scientists are trying to overcome in every possible way by improving certain parts of aircraft. But how does turbulence affect birds? Scientists from Cornell University (USA) have found that for feathered pilots, turbulence is not a problem, but helps them to quickly overcome long distances. How exactly does turbulence affect the flight of a bird, how significant are these effects, and how can the obtained data be applied in aircraft construction? We will find answers to these questions in the report of scientists. Go.

Basis of research

The life of many birds is closely related to the sky. For them, this is not only a space to overcome the distance from point A to point B, but also a place for games, mating dances, hunting, and even recreation (the black swift spends about 10 months a year in the air, 2 months is the nesting period). Therefore, it is quite obvious that these creatures have learned not only to cope with the hardships and problems associated with an unpredictable sky, but also to use them to their advantage.

Turbulence in the sky is extremely unpredictable, it can appear out of nowhere and just stop instantly. The duration of the turbulence also depends on many factors. Therefore, if a bird cannot live without the sky, it needs to adapt to such variable conditions.

The problem is, as the authors of the work say, that we know very little about the relationship between turbulence and bird behavior. Various observations in vivo and experiments in a wind tunnel give very contradictory results. In some cases, turbulence leads to a decrease in flight costs, in others – to an increase. True, this applies to “shallow” turbulence.

Now, a different picture is observed with large-scale turbulence resulting from ascending flows due to topography, ascending heat flows, internal waves and fronts. All these factors contribute to the flight efficiency to one degree or another. In addition, the interaction of a bird (or even an apparatus) with such phenomena is much easier to carry out, because they are slower and more stable.

In the case of birds, the structure of the stream leaves its mark on the trajectory of their flight, the analysis of which suggests the presence of a positive effect of turbulence.

Scientists note that, despite the unpredictability of turbulence and its sensitivity to the slightest changes in environmental conditions, it exhibits unique features, including a certain distribution of energy between movements of different strengths, combined with a lack of precise scale invariance, called intermittency.

These unique features can be seen in the trajectories of particles carried by turbulent flows. A similar pattern is observed in the trajectories of birds.

Image No. 1

In order to understand this confusing situation, the scientists analyzed data from observations of an adult female golden eagle (Aquila chrysaetos; 1A). The weight of the bird was 5 kg, the wingspan was about 2 m.Scientists observed its flight from Alabama to New York along the Appalachian mountains from March 15 to March 31, 2016 (1B). An apparatus was attached to the body of the golden eagle, which recorded the position of the body and triaxial acceleration. The data was transmitted to scientists on the ground via a mobile network.

The golden eagle’s path ran through areas with different wind conditions. At the same time, the flight trajectory did not always follow the wind flow. This could be due to the strength of the flow, stops to make a decision (where to fly next), air resistance, thrust, etc.

The pattern of acceleration and position of the golden eagle indicates different behavior (eg takeoff, landing, flight). Scientists have identified those parts of the path (1B), where the golden eagle soared and where it was actively flapping its wings, which was defined as regular acceleration oscillations with a frequency of 2.8 Hz (image 2).

Image No. 2

Observation results

The soaring acceleration of the golden eagle was quite intermittent, as indicated by the long tails in the acceleration distribution (image # 3).

Image No. 3

The fact that the distributions are highly non-Gaussian is consistent with the pattern of particle acceleration under strong turbulence, despite the differences in scale and geometry between particles and birds. Turbulence indicator particles that closely follow turbulent flow exhibit extreme accelerations that are many orders of magnitude more probable than the Gaussian distribution predicts. An increase in the size and mass of particles leads to a narrowing tail * distribution that is measured Stokes number * (St) which is <1 for light and small particles.

Tail* – the elongated part of the distribution, which, when graphically presented, looks like a part of the curve.

Stokes number * – similarity criterion, which determines the relationship between the kinetic energy of suspended particles and the energy of their interaction with the liquid. If it is <1, then the particles will bend around obstacles in their path, if ﹥ 1 - they will crash into them.

The distribution of the golden eagle’s acceleration is between the distribution of the acceleration of tracer particles (without inertia) and the distribution of the acceleration of weakly inertial particles (St = 0.09 ± 0.03). Turbulence distributions often resemble stretched exponential functions, and these functions describe the tail of the golden eagle’s acceleration distribution as an extension of about 1.8, which corresponds to values ​​for small-scale quantities. The standard deviations of the components of the accelerations x, y and z are 0.90, 0.88, and 1.62 m / s² respectively.

The most obvious and frequent characteristic of the acceleration spectra during migration and stay in one place for the golden eagle was power law *prevailing between frequencies of about 0.2 and 2 Hz.

Power law * – functional dependence between two quantities, when a change in one leads to a change in the second, regardless of their initial values.

The area that obeys the power law is limited at high frequencies with oscillation that occurs at a frequency of about 2.8 Hz. It is not known exactly what limits the zoom range at low frequencies.

The acceleration spectra of the golden eagle have a logarithmic slope close to -5/3 – a slope that does not change significantly when the spectra vary depending on wind speed or migration route.

Image No. 4

The acceleration spectra of the golden eagle were described using Newton’s second law, taking into account the fact that the changes in aerodynamic forces acting on the bird were linear with respect to the changes in the relative velocity between the golden eagle and the air. That is, fluctuations in the bird’s speed relative to the average wind speed cause changes in aerodynamic forces that are linear with respect to the fluctuations in speed. This explanation can be observed in several cases: the lift generated by the wing is linear in vertical perturbations with respect to the wind vector until the moment of stall; the thrust created by the propeller is linear with respect to changes in its airspeed, which is small compared to the wind generated by it; nonlinear resistance, which manifests itself at high Reynolds numbers, is linear with small changes in airspeed.

The resulting calculations showed that the fluctuations in the acceleration of the golden eagle have the same spectrum as the fluctuations in the wind speed that the golden eagle encounters in flight. The data show (image # 4) that higher wind speeds are associated with larger accelerations of the golden eagle in the range from 0.2 to 2 Hz. Curiously, the acceleration spectrum does not disappear at zero wind speed. This may be due to turbulence generated by thermals *even in the absence of noticeable wind.

Thermik * – the mass of rising air, arises from the uneven heating of the Earth’s surface by solar radiation.

The increase in acceleration with stronger winds can be attributed to an increase in turbulence force. The key point is that the wind speed spectrum is proportional to 2/3 of the turbulence dissipation rate, which is proportional to the cube of the turbulence intensity. At a given altitude in the boundary layer of the atmosphere, where the golden eagle flies, the intensity of turbulence changes in proportion to the wind speed. Given the linear relationship between bird acceleration and wind speed, it can be assumed that the preliminary acceleration spectrum coefficient increases quadratically with wind speed.

For a more detailed acquaintance with the nuances of the study, I recommend that you look at scientists report…

Epilogue

In the course of this study, scientists analyzed data obtained from observations of a golden eagle flying from Alabama to New York. According to these data, the flight of the bird was uneven, which was associated with zones of turbulence. The picture that scientists observed during the analysis resembled the one that describes the behavior of particles in turbulent air currents. So, in the period from 0.5 to 10 seconds, the acceleration of the bird and atmospheric turbulence were completely synchronized. In other words, the golden eagle used turbulent currents to simplify its task of flying from point A to point B. For birds migrating long distances, it is not surprising to minimize the energy costs associated with flight.

It’s funny that aeronautical engineers and scientists do their best to reduce the impact of turbulence on aircraft, while birds use it to their advantage. This study not only shows the existence of such a possibility, but also provides more empirical data for such a study of a mysterious and unpredictable phenomenon such as turbulence.