1
R E S E A R C H A RT I C L E
Wind speed inference from environmental flow-structure
interactions
Jennifer L. Cardona
1
, Katherine L. Bouman
2
and John O. Dabiri
3*
1
Department of Mechanical Engineering, Stanford University, Stanford, California, 94305, USA
2
Computing and Mathematical Sciences & Electrical Engineering & Astronomy, California Institute of Technology, Pasadena,
California, 91125, USA
3
Graduate Aerospace Laboratories & Mechanical Engineering, California Institute of Technology, Pasadena, California, 91125,
USA
*Corresponding author. E-mail: jodabiri@caltech.edu
Keywords:
Flow imaging and velocimetry, optical based flow diagnostics, fluid-structure interactions
Abstract
This study aims to leverage the relationship between fluid dynamic loading and resulting structural deformation
to infer the incident flow speed from measurements of time-dependent structure kinematics. Wind tunnel studies
are performed on cantilevered cylinders and trees. Tip deflections of the wind-loaded structures are captured in
time series data, and a physical model of the relationship between force and deflection is applied to calculate
the instantaneous wind speed normalized with respect to a known reference wind speed. Wind speeds inferred
from visual measurements showed consistent agreement with ground truth anemometer measurements for different
cylinder and tree configurations. These results suggest an approach for non-intrusive, quantitative flow velocimetry
that eliminates the need to directly visualize or instrument the flow itself.
Impact Statement
We present a velocimetry method that infers time-dependent flow speeds using visual observations of flow-
structure interactions such as the swaying of trees. This can alleviate the need to directly instrument or visualize
the flow to quantify its speed, instead relying on preexisting objects in an environment that are deflecting due
to the incident flow. The method has the potential to turn ubiquitous objects like trees into abundant, natural,
environmental flow sensors for applications such as weather forecasting, wind energy resource quantification,
and studies of wildfire propagation.
1. Introduction
Fluid-structure interactions such as the bending and swaying of trees in the wind provide visual cues
that contain information about the surrounding flow. If visual measurements of deflections can be used
to infer quantitative estimates of local wind speeds, then common objects like trees could be used
as abundant natural anemometers, requiring only non-intrusive visual access to record wind speed
measurements. This would potentially be useful in applications such as data assimilation for weather
forecasting, wind energy resource quantification, and understanding wildfire behavior. Recent work has
examined this visual anemometry task through a data-driven approach, where a neural network based
model was trained to output wind speeds based on input videos of flags and trees in naturally occurring
arXiv:2011.09609v2 [physics.flu-dyn] 18 Mar 2021
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wind (Cardona et al., 2019). However, achieving a data-driven model that would generalize to a wide
variety of objects (e.g. trees of different sizes and species) could potentially require an extensive data
collection campaign. Physical models for fluid-structure interactions may be advantageous in provid-
ing a framework that could be used for visual anemometry across a broader range of structures. Here,
we focus on objects that can be modelled as cantilever beams under wind loading.
Flow-sensing cantilevers are found in nature. For instance, the lateral line system allows fish to
sense the surrounding flow via the deflection of hair-like structures (Bleckmann and Zelick, 2009).
Artificial lateral line sensors have been developed to mimic this flow sensing function as discussed
by Shizhe (2014). Cantilever beam deflections have also been used to measure wind speeds specifi-
cally. Tritton (1959) used optical measurements of cantilevered quartz fiber deflections, and Kraitse and
Fralick (1977) used strain gauge measurements of millimeter-scale silicone beams. These drag-based
anemometers relied on knowledge of the material properties of the beam. These physical properties
could then be used in conjunction with beam bending theory to calculate the drag force on the beam and
quantify the wind speed. In these cases, the beam materials were specifically chosen for sensing pur-
poses. Another example of cantilever deflection-based anemometry can be seen in Barth et al. (2005),
where the deflection of a millimeter-scale cantilever affects the position of a reflected laser, which is
calibrated to measure flow speeds.
While these prior studies have shown success in measuring flow speeds by instrumenting the flow
with cantilevers specifically designed and intended for sensing, the present work aims to extend the
concept of flow-sensing cantilevers so that it can ultimately be used with a variety of pre-existing
structures in an environment without further instrumenting the flow. Natural structures such as trees
have material properties that are unknown
a priori
, and they are more geometrically complex than
single beams. Hence, in this work we exploit simplified models of the flow-structure interactions to
avoid the need for direct consideration of these details, while still capturing the physical influence of
the wind on structure deformation. By this approach, we can leverage the prevalence of trees and other
vegetation in both rural and built environments for use in visual anemometry.
Approximate wind speed scales have been developed based on field observations of fluid-structure
interactions in the past. The Fujita scale, for example, is used to infer tornado wind speed based on
the damage to structures in its path (Doswell et al., 2009). This has been particularly useful since more
conventional wind speed measurements are rare and difficult to obtain for tornadoes. The Beaufort scale
is another well-known wind speed scale that relies on visual cues. The version of the scale adapted for
use on land employs qualitative descriptions of tree behavior (e.g. branch motion or breaking of twigs)
to estimate an instantaneous wind speed range, and it has also been applied to region-specific vegetation
(Jemison, 1934). Visual observations of trees and other vegetation have also been used to estimate
mean annual wind speeds. The Griggs-Putnam Index uses qualitative descriptions of tree deformation
to categorize mean annual wind speeds into seven binned increments of 1-2
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