The mechanics of locomotion in the squid Loligo Pealei: Locomotory function and unsteady hydrodynamics of the jet and intramantle pressure

Abstract

High-speed, high-resolution digital video recordings of swimming squid (Loligo pealei) were acquired. These recordings were used to determine very accurate swimming kinematics, body deformations and mantle cavity volume. The time-varying squid profile was digitized automatically from the acquired swimming sequences. Mantle cavity volume flow rates were determined under the assumption of axisymmetry and the condition of incompressibility. The data were then used to calculate jet velocity, jet thrust and intramantle pressure, including unsteady effects. Because of the accurate measurements of volume flow rate, the standard use of estimated discharge coefficients was avoided. Equations for jet and whole-cycle propulsive efficiency were developed, including a general equation incorporating unsteady effects. Squid were observed to eject up to 94 % of their intramantle working fluid at relatively high swimming speeds. As a result, the standard use of the so-called large-reservoir approximation in the determination of intramantle pressure by the Bernoulli equation leads to significant errors in calculating intramantle pressure from jet velocity and vice versa. The failure of this approximation in squid locomotion also implies that pressure variation throughout the mantle cannot be ignored. In addition, the unsteady terms of the Bernoulli equation and the momentum equation proved to be significant to the determination of intramantle pressure and jet thrust. Equations of propulsive efficiency derived for squid did not resemble Froude efficiency. Instead, they resembled the equation of rocket motor propulsive efficiency. The Froude equation was found to underestimate the propulsive efficiency of the jet period of the squid locomotory cycle and to overestimate whole-cycle propulsive efficiency when compared with efficiencies calculated from equations derived with the squid locomotory apparatus in mind. The equations for squid propulsive efficiency reveal that the refill period of squid plays a greater role, and the jet period a lesser role, in the low whole-cycle efficiencies predicted in squid and similar jet-propelled organisms. These findings offer new perspectives on locomotory hydrodynamics, intramantle pressure measurements and functional morphology with regard to squid and other jet-propelled organisms.

Cool your jets: biological jet propulsion in marine invertebrates

“…Incorporates effects of passive refill by jet-propelled swimmers. Developed by Anderson and Demont (2000). Zooid A single-animal, functional unit that is part of a multi-unit colony.…”

“…Squid do have the highest propulsive efficiency during the jetting phase (equivalent to rocket motor efficiency) of all currently measured jetting taxa with values that can exceed 90% (Anderson and Grosenbaugh, 2005;Bartol et al, 2009a), whereas the propulsive efficiency of salps is lower, with mean values ranging from 65 to 78% (Sutherland and Madin, 2010a). The Froude equation (see Glossary) has often been used as a measure of mechanical swimming efficiency; however, it is known to underestimate propulsive efficiencies of squid jet periods while simultaneously overestimating whole-cycle propulsive efficiency (Anderson and DeMont, 2000). The Re of jet-propelled locomotion can vary by many orders of magnitude: early developmental stages of medusae (1 mm diameter Sarsia tubulosa) and squid [1.0 and 1.8 mm mantle length (ML) for Ommastrephid hatchlings and D. pealeii, respectively] jet effectively at an Re of 15 and 25, respectively (Bartol et al, 2009b;Katija and Jiang, 2013;Staaf et al, 2014), whereas adult squid can have Re of 160,000 (30 cm ML D. pealeii) (Anderson and Grosenbaugh, 2005) to roughly 800,000 (40 cm ML Loligo vulgaris) (Packard, 1972).…”

Valve-mediated flow control in salp-like locomotion

“…By measuring the speed of the jet, the thrust generation and propulsive efficiency were also estimated. However, the efficiency was calculated by using a simplified model based on quasi-steady assumption 12 , whose accuracy in the highly unsteady pulsed-jet scenario is questionable 13 . Based on theoretical analysis, Sutherland and Weihs pointed out that in the aggregate form salps achieved better locomotion performance since the asynchronous jetting of individuals led to less oscillations in the forward speed 14 .…”

Body size and fin length as determinants in the geographic distribution of Loliginid squids

“…Loliginid squids have elongated apping ns which produce large-amplitude waves for economical, gentle swimming and hovering as well as for controlling stability and aiding jet escape (Clarke 1988). By combining nning and jetting, cephalopods can generate different swimming gaits (Anderson and DeMont 2000;Stewart et al 2010). The general loliginid evolutionary trend corresponds to the direction of morpho-physiological adaptation, pioneering new trails (Nesis 1980).…”