The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Digital particle image velocimetry (DPIV) is a non-intrusive analysis technique that is very popular for mapping flows quantitatively. To get accurate results, in particular in complex flow fields, a number of challenges have to be faced and solved: The quality of the flow measurements is affected by computational details such as image pre-conditioning, sub-pixel peak estimators, data validation procedures, interpolation algorithms and smoothing methods. The accuracy of several algorithms was determined and the best performing methods were implemented in a user-friendly open-source tool for performing DPIV flow analysis in Matlab.

/pdf/pivlab-towards-user-friendly-affordable-and-accurate-digital-3pwqyjh6ub.pdf

PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB

Several physico-mechanical designs evolved in fish are currently inspiring robotic devices for propulsion and maneuvering purposes in underwater vehicles. Considering the potential benefits involved, this paper presents an overview of the swimming mechanisms employed by fish. The motivation is to provide a relevant and useful introduction to the existing literature for engineers with an interest in the emerging area of aquatic biomechanisms. The fish swimming types are presented, following the well-established classification scheme and nomenclature originally proposed by Breder. Fish swim either by body and/or caudal fin (BCF) movements or using median and/or paired fin (MPF) propulsion. The latter is generally employed at slow speeds, offering greater maneuverability and better propulsive efficiency, while BCF movements can achieve greater thrust and accelerations. For both BCF and MPF locomotion, specific swimming modes are identified, based on the propulsor and the type of movements (oscillatory or undulatory) employed for thrust generation. Along with general descriptions and kinematic data, the analytical approaches developed to study each swimming mode are also introduced. Particular reference is made to lunate tail propulsion, undulating fins, and labriform (oscillatory pectoral fin) swimming mechanisms, identified as having the greatest potential for exploitation in artificial systems.

/pdf/review-of-fish-swimming-modes-for-aquatic-locomotion-12dkkh88vr.pdf

Review of fish swimming modes for aquatic locomotion

Recent advances in integrative studies of locomotion have revealed several general principles. Energy storage and exchange mechanisms discovered in walking and running bipeds apply to multilegged locomotion and even to flying and swimming. Nonpropulsive lateral forces can be sizable, but they may benefit stability, maneuverability, or other criteria that become apparent in natural environments. Locomotor control systems combine rapid mechanical preflexes with multimodal sensory feedback and feedforward commands. Muscles have a surprising variety of functions in locomotion, serving as motors, brakes, springs, and struts. Integrative approaches reveal not only how each component within a locomotor system operates but how they function as a collective whole.

https://science.sciencemag.org/content/sci/288/5463/100.full.pdf

How Animals Move: An Integrative View

To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.

Theory of cross-correlation analysis of PIV images : Image analysis as measuring technique in flows

Kinetics of low-pressure methanol synthesis

The structure of the wake behind a continuously swimming mullet was analysed qualitatively and quantitatively by applying two-dimensional particle image velocimetry. A detailed analysis of the flow pattern and of the swimming movements of the fish allowed us to derive a kinematic explanation of the flow pattern as well as an estimate of the relative contributions of the body and the tail to thrust production. During active propulsion, the undulatory swimming fish shed a wake consisting in the medio-frontal plane of a rearward, zigzagging jet flow between alternating vortices. The fish shed one vortex per half tailbeat when the tail reached its most lateral position. Part of the circulation shed in the vortices had been generated previously on the body by the transverse body wave travelling down the body. This undulatory pump mechanism accounted for less than half of the energy shed in the wake. The remainder was generated by the tail. The vortex spacing matched the tailbeat amplitude and the stride length.

/pdf/fish-foot-prints-morphology-and-energetics-of-the-wake-13uqifruwh.pdf

Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet (Chelon labrosus Risso).

PIVlab - Time-Resolved Digital Particle Image Velocimetry Tool for MATLAB

Gliding birds continually change the shape and size of their wings, presumably to exploit the profound effect of wing morphology on aerodynamic performance. That birds should adjust wing sweep to suit glide speed has been predicted qualitatively by analytical glide models, which extrapolated the wing's performance envelope from aerodynamic theory. Here we describe the aerodynamic and structural performance of actual swift wings, as measured in a wind tunnel, and on this basis build a semi-empirical glide model. By measuring inside and outside swifts' behavioural envelope, we show that choosing the most suitable sweep can halve sink speed or triple turning rate. Extended wings are superior for slow glides and turns; swept wings are superior for fast glides and turns. This superiority is due to better aerodynamic performance-with the exception of fast turns. Swept wings are less effective at generating lift while turning at high speeds, but can bear the extreme loads. Finally, our glide model predicts that cost-effective gliding occurs at speeds of 8-10 m s(-1), whereas agility-related figures of merit peak at 15-25 m s(-1). In fact, swifts spend the night ('roost') in flight at 8-10 m s(-1) (ref. 11), thus our model can explain this choice for a resting behaviour. Morphing not only adjusts birds' wing performance to the task at hand, but could also control the flight of future aircraft.

Eize Stamhuis

Papers

PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB

Kinetics of low-pressure methanol synthesis

Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet (Chelon labrosus Risso).

PIVlab - Time-Resolved Digital Particle Image Velocimetry Tool for MATLAB

How swifts control their glide performance with morphing wings