Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects

In hydraulic structures, free-surface aeration is commonly observed: i.e., the white waters. The air bubble entrainment may be localised (hydraulic jumps, plunging jets) or continuous along an interface (water jets, chutes). Despite recent advances, there are some basic concerns about the extrapolation of laboratory results to large size prototype structures. Herein the basic air bubble entrainment processes are reviewed and the relevant dynamic similarities are discussed. Traditionally, physical studies are conducted using a Froude similitude which implies drastically smaller laboratory Reynolds numbers than in the corresponding prototype flows. Basic dimensional analyses are developed for both singular and interfacial aeration processes. The results are discussed in the light of systematic investigations and they show that the notion of scale effects is closely linked with the selection of relevant characteristic air–water flow properties. Recent studies of local air–water flow properties highlight that turbulence levels, entrained bubble sizes and interfacial areas are improperly scaled based upon a Froude similitude even in large-size models operating with the so defined Reynolds numbers ρ _w × q _w/μ _w up to 5 E+5. In laboratory models, the dimensionless turbulence levels, air–water interfacial areas and mass transfer rates are drastically underestimated.     

Surface waves and roughness in self-aerated supercritical flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air–water flow properties are tested herein. The study simulates the air–water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.     

Turbulence structure and coherent vortices in open-channel flows with wind-induced water waves

When wind-induced water waves appear over the free-surface flows such as natural rivers and artificial channels, large amounts of oxygen gas and heat are transported toward the river bed through the interface between water and wind layers. In contrast, a bed region is a kind of turbulent boundary layer, in which turbulence generation and its transport is promoted by the production of bed shear stress. In particular, coherent hairpin vortices, together with strong ejection events toward the outer part of the layer, promote mass and momentum exchanges between the inner and outer layers. It is inferred that such a near-bed turbulence may be influenced significantly by these air–water interfacial fluctuations accompanied with free-surface velocity shear and wind-induced water waves. However, these wind effects on the wall-turbulence structure are less understood. To address these exciting and challenging topics, we conducted particle imagery velocimetry (PIV) measurements in open-channel flows combined with air flows, and furthermore the present measured data allows us to investigate the effects of air–water interactions on turbulence structure through the whole depth region.     

Experimental investigation of bubbly flow and turbulence in hydraulic jumps

Many environmental problems are linked to multiphase flows encompassing ecological issues, chemical processes and mixing or diffusion, with applications in different engineering fields. The transition from a supercritical flow to a subcritical motion constitutes a hydraulic jump. This flow regime is characterised by strong interactions between turbulence, free surface and air–water mixing. Although a hydraulic jump contributes to some dissipation of the flow kinetic energy, it is also associated with increases of turbulent shear stresses and the development of turbulent eddies with implications in terms of scour, erosion and sediment transport. Despite a number of experimental, theoretical and numerical studies, there is a lack of knowledge concerning the physical mechanisms involved in the diffusion and air–water mixing processes within hydraulic jumps, as well as on the interaction between the free-surface and turbulence. New experimental investigations were undertaken in hydraulic jumps with Froude numbers up to Fr = 8.3. Two-phase flow measurements were performed with phase-detection conductivity probes. Basic results related to the distributions of void fraction, bubble frequency and mean bubble chord length are presented. New developments are discussed for the interfacial bubble velocities and their fluctuations, characterizing the turbulence level and integral time scales of turbulence representing a “lifetime” of the longitudinal bubbly flow structures. The analyses show good agreement with previous studies in terms of the vertical profiles of void fraction, bubble frequency and mean bubble chord length. The dimensionless distributions of interfacial velocities compared favourably with wall-jet equations. Measurements showed high turbulence levels. Turbulence time scales were found to be dependent on the distance downstream of the toe as well as on the distance to the bottom showing the importance of the lower (channel bed) and upper (free surface) boundary conditions on the turbulence structure.     

Self-aeration in the rapidly- and gradually-varying flow regions of steep smooth and stepped spillways

In high-velocity chute flows, free-surface aeration is often observed. The phenomenon is called self-aeration or white waters. When the turbulent shear stresses next to the free-surface are large enough, air bubbles are entrained throughout the entire air–water column. A rapidly-varied flow region is observed immediately downstream of the inception point of free-surface aeration. An analytical solution of the air diffusion equation is proposed and the results compare well with new experimental data. Both experiments and theory indicate that the flow bulking spans over approximately 3–4 step cavities downstream of the inception point of free-surface aeration on a stepped chute. Further downstream the void fraction distributions follow closely earlier solutions of the air diffusion equation. The application of the diffusion equation solution to prototype and laboratory data shows air bubble diffusivities typically larger than the momentum transfer coefficient. The result highlights however a marked decrease in the ratio of air bubble diffusivity to eddy viscosity with increasing Reynolds number. The finding might indicate some limitation of laboratory investigations of air bubble diffusion process in self-aerated flows and of their extrapolation to full-scale prototype applications.     

Advanced post-processing and correlation analyses in high-velocity air–water flows

The interest in air–water flows has not diminished in recent years, but it is accompanied by frequent citations of early, sometimes outdated articles. A basic issue is the inadequate, incomplete interpretation of air–water flow instrumentation by hydraulic engineers and researchers. This article comments on high-velocity air–water flow measurements by means of intrusive phase detection probes. This article focus on the bubbly flow structure of high-velocity air–water flow based upon measurements by means of intrusive phase detection probes. It is shown that some advanced post-processing techniques may yield expanded information on the air–water turbulent flow properties and bubbly flow structures. The outcomes demonstrate simple techniques in high-velocity air–water flow analysis.     

Flow aeration, cavity processes and energy dissipation on flat and pooled stepped spillways for embankments

The design floods of several reservoirs were recently re-evaluated and the revised spillway outflow could result in dam overtopping with catastrophic consequences for some embankment structures. Herein a physical study was performed on flat and pooled stepped spillways with a slope typical of embankments $(\uptheta = 26.6^{\circ })$ and four stepped configurations were tested: a stepped spillway with flat horizontal steps, a pooled stepped spillway, and two stepped spillways with in-line and staggered configurations of flat and pooled steps. The focus of the study was on the flow aeration, air–water flow properties, cavity flow processes, and energy dissipation performances. The results demonstrated the strong aeration of the flow for all configurations. On the in-line and staggered configurations of flat and pooled steps, the flow was highly three-dimensional. The residual head and energy dissipation rates at the stepped chute downstream end were calculated based upon the detailed air–water flow properties. The results showed that the residual energy was the lowest for the flat stepped weir. The data for the stepped spillway configuration with in-line and staggered configurations of flat and pooled steps showed large differences in terms of residual head in the transverse direction. Altogether the present results showed that, on a $26.6^{\circ }$ slope stepped chute, the designs with in-line and staggered configurations of flat and pooled steps did not provide any advantageous performances in terms of energy dissipation and flow aeration, but they were affected by three-dimensional patterns leading to some flow concentration.     

Characteristics of clustered particles in skimming flows on a stepped spillway

Air–water flows at hydraulic structures are commonly observed and called white waters. The free-surface aeration is characterised by some intense exchanges of air and water leading to complex air–water structures including some clustering. The number and properties of clusters may provide some measure of the level of particle-turbulence and particle–particle interactions in the high-velocity air–water flows. Herein a re-analysis of air–water clusters was applied to a highly aerated free-surface flow data set (Chanson and Carosi, Exp Fluids 42:385–401, 2007). A two-dimensional cluster analysis was introduced combining a longitudinal clustering criterion based on near-wake effect and a side-by-side particle detection method. The results highlighted a significant number of clustered particles in the high-velocity free-surface flows. The number of bubble/droplet clusters per second and the percentage of clustered particles were significantly larger using the two-dimensional cluster analysis than those derived from earlier longitudinal detection techniques only. A number of large cluster structures were further detected. The results illustrated the complex interactions between entrained air and turbulent structures in skimming flow on a stepped spillway, and the cluster detection method may apply to other highly aerated free-surface flows.     

Emergence of an oocytic circumnuclear ring in response to increasing day length in Atlantic herring (<Emphasis Type="Italic">Clupea harengus</Emphasis>)

Understanding physiological and environmental variables that initiate sexual maturity would provide fundamental information on life history dynamics. The aim of this study was to test the usefulness of the common circumnuclear ring (CNR), an oocytic structure similar to the Balbiani body, which appears just prior to oocyte development as a predictor of first maturation in Atlantic herring (Clupea harengus). The relative roles of physiology (e.g. fat) and photoperiod as triggers of maturation were also investigated. Samples were collected in May 2008 (72°26′–73°84′N/11°26′–18°40′E) and February 2009 (56°12′–59°45′N/00°25′–03°06′W). These data suggested that thresholds in body size may influence the decision to mature. We also found that short days (winter solstice) may be the photoperiod trigger for a first-decision window for both Norwegian spring-spawning (NSS) and North Sea autumn-spawning (NSAS) herring. The second-decision window for NSAS herring maturation appears to be triggered by longer days (spring equinox), while a decreasing rate of day lengthening may trigger NSS herring maturation. So, photoperiodic cycle is a key determinate of the timing of maturation in Atlantic herring.     

Aerobic metabolic rates of swimming juvenile mako sharks, <Emphasis Type="Italic">Isurus oxyrinchus</Emphasis>

The shortfin mako shark, Isurus oxyrinchus, is a highly streamlined epipelagic predator that has several anatomical and physiological specializations hypothesized to increase aerobic swimming performance. A large swim-tunnel respirometer was used to measure oxygen consumption (MO₂) in juvenile mako sharks (swimming under controlled temperature and flow conditions) to test the hypothesis that the mako shark has an elevated maintenance metabolism when compared to other sharks of similar size swimming at the same water temperature. Specimen collections were conducted off the coast of southern California, USA (32.94°N and 117.37°W) in 2001-2002 at sea-surface temperatures of 16.0–21.0°C. Swimming MO₂ and tail beat frequency (TBF) were measured for nine mako sharks [77–107 cm in total length (TL) and 4.4 to 9.5 kg body mass] at speeds from 28 to 54 cm s⁻¹ (0.27–0.65 TL s⁻¹) and water temperatures of 16.5–19.5°C. Standard metabolic rate (SMR) was estimated from the extrapolation to 0-velocity of the linear regression through the LogMO₂ and swimming speed data. The estimated LogSMR (±SE) for the pooled data was 2.0937 ± 0.058 or 124 mg O₂ kg⁻¹ h⁻¹. The routine metabolic rate (RMR) calculated from seventeen MO₂ measurements from all specimens, at all test speeds was (mean ± SE) 344 ± 22 mg O₂ kg⁻¹h⁻¹ at 0.44 ± 0.03 TL s⁻¹. The maximum metabolic rate (MMR) measured for any one shark in this study was 541 mg O₂ kg⁻¹h⁻¹ at 54 cm s⁻¹ (0.65 TL s⁻¹). The mean (±SE) TBF for 39 observations of steady swimming at all test speeds was 1.00 ± 0.01 Hz, which agrees with field observations of 1.03 ± 0.03 Hz in four undisturbed free-swimming mako sharks observed during the same time period. These findings suggest that the estimate of SMR for juvenile makos is comparable to that recorded for other similar-sized, ram-ventilating shark species (when corrected for differences in experimental temperature). However, the mako RMR and MMR are apparently among the highest measured for any shark species.     

Depth and muscle temperature of Pacific bluefin tuna examined with acoustic and pop-up satellite archival tags

Six Pacific bluefin tuna were tracked with ultrasonic telemetry and two with pop-up satellite archival tags (PSATs) in the eastern Pacific Ocean in 1997, 1998, and 1999. Both pressure and temperature ultrasonic transmitters were used to examine the behavior of the 2- to 4-year-old bluefin tuna. The bluefin spent over 80% of their time in the top 40 m of the water column and made occasional dives into deeper, cooler water. The mean slow-oxidative muscle temperatures of three fish instrumented with pressure and temperature transmitters were 22.0–26.1 °C in water temperatures that averaged 15.7–17.5 °C. The thermal excesses in slow-oxidative muscle averaged 6.2–8.6 °C. Variation in the temperature of the slow-oxidative muscle in the bluefin was not correlated with water temperature or swimming speeds. For comparison with the acoustic tracking data we examined the depth and ambient temperature of two Pacific bluefin tagged with pop-up satellite archival tags for 24 and 52 days. The PSAT data sets show depth and temperature distributions of the bluefin tuna similar to the acoustic data set. Swimming speeds calculated from horizontal distances with the acoustic data indicate the fish mean speeds were 1.1–1.4 fork lengths/s (FL s⁻¹). These Pacific bluefin spent the majority of their time in the top parts of the water column in the eastern Pacific Ocean in a pattern similar to that observed for yellowfin tuna. Received: 4 April 2000 / Accepted: 25 October 2000     

Temperature, salinity and prey availability shape the marine migration of Arctic char, Salvelinus alpinus, in a macrotidal estuary

The influence of salinity, temperature and prey availability on the marine migration of anadromous fishes was determined by describing the movements, habitat use and feeding behaviours of Arctic char (Salvelinus alpinus). The objectives were to determine whether char are restricted to the upper water column of the inter-/subtidal zones due to warmer temperatures. Twenty-seven char were tracked with acoustic temperature/pressure (depth) transmitters from June to September, 2008/2009, in inner Frobisher Bay, Canada. Most detections were in surface waters (0–3 m). Inter-/subtidal movements and consecutive repetitive dives (maximum 52.8 m) resulted in extreme body temperature shifts (−0.2–18.1 °C). Approximately half of intertidal and subtidal detections were between 9–13 °C and 1–3 °C, respectively. Stomach contents and deep diving suggested feeding in both inter-/subtidal zones. We suggest that char tolerate cold water at depth to capture prey in the subtidal zone, then seek warmer water to enhance feeding/digestion physiology.     

Beat frequency of cilia in the branchial basket of the ascidian Ciona intestinalis in relation to temperature and algal cell concentration

To elucidate the effects of temperature and algal cell concentration on pumping of water in the ascidian Ciona intestinalis a number of different experiments were performed. Beat frequency of the lateral cilia in the openings of the branchial sac was measured in intact specimens using a microprojection objective and a monochrome CCD video camera. At constant low algal cell concentration, beat frequencies increased linearly with temperature from 4.0 Hz (±0.5) at 7.4 °C to 13.6 Hz (±1.6) at 20.1 °C. At a constant temperature of 15 °C, beat frequency decreased with increasing algal cell concentration from approximately 3000 to >10 000 Rhodomonas sp. cells ml⁻¹. The decrease was observed both in experiments where the ascidians had been acclimated to a fixed algal cell concentration and in experiments with changing concentrations. Effect of algal cell concentration on squirting/siphon closure and flow velocity in the exhalent siphon was measured using a thermistor. At low algal cell concentrations, flow velocity in the exhalent siphon was stable, apart from a few short squirts. At very high algal cell concentrations, the flow velocity was reduced and much less stable, with prolonged squirting. The effect of gut content on filtration was studied in experiments with specimens acclimated to high algal cell concentrations. Results showed a close relation between gut clearance and filtration rate. From the experimental results and a qualitative analysis of the Ciona-pump it was concluded that the ciliary beat frequency is proportional to the water flow through the sea squirt and that changes in pumping caused by temperature or algal cell concentration are under nervous control or governed by enzyme kinetics, rather than being a result of physico-mechanical properties, i.e. pump efficiency versus flow resistance, of the ascidian pump. Received: 6 October 1997 / Accepted: 8 October 1998     

Boundary between the north and south Atlantic populations of the swordfish (<Emphasis Type="Italic">Xiphias gladius</Emphasis>) inferred by a single nucleotide polymorphism at calmodulin gene intron

Genetic differentiation of the Atlantic swordfish (Xiphias gladius) was investigated by a single nucleotide polymorphism (SNP) at the calmodulin gene (CAM) intron locus. Clearly distinct allele and genotype frequencies were observed between the north (20–41°N) and mid-south (10°N–33°S) Atlantic samples. Much lower frequency of A allele (37.5–57.1%) was observed in the north samples (n = 160 in total) than in the mid-south samples (83.3–92.6%; n=354), and homozygote BB was common in the north samples (23.4–31.3%) but very rare or absent (0–3.9%) in the mid-south samples. Very strong population subdivision was observed between the two groups (F _ST = 0.34, P < 0.001), while the allele and genotype frequencies within each ocean basin persisted over time (1990–2002 in the north, and 1994–2002 in the mid-south). Of two samples from the presumed boundary zone, one (n = 18) (14°N, 48°W) presented intermediate frequencies of the A allele (66.7%) and BB homozygote (11.1%), while the other (n = 23) (10–17°N, 28–37°W) shared similar frequencies of the A allele (89.1%) and BB homozygote (4.3%) with those of the mid-south Atlantic samples. These results indicate that the gene flow and individual migration between the north and mid-south Atlantic populations are considerably restricted and that the current management boundary between the north and south Atlantic swordfish stocks of 5°N should be reconsidered.     

Oceanographic preferences of Atlantic bluefin tuna, <Emphasis Type="Italic">Thunnus thynnus</Emphasis>, on their Gulf of Mexico breeding grounds

Electronic tagging and remotely sensed oceanographic data were used to determine the oceanographic habitat use and preferences of Atlantic bluefin tuna (Thunnus thynnus L.) exhibiting behaviors associated with breeding in the Gulf of Mexico (GOM). Oceanographic habitats used by 28 Atlantic bluefin tuna exhibiting breeding behavior (259 days) were compared with available habitats in the GOM, using Monte Carlo tests and discrete choice models. Habitat utilization and preference patterns for ten environmental parameters were quantified: bathymetry, bathymetric gradient, SST, SST gradient, surface chlorophyll concentration, surface chlorophyll gradient, sea surface height anomaly, eddy kinetic energy, surface wind speed, and surface current speed. Atlantic bluefin tuna exhibited breeding behavior in the western GOM and the frontal zone of the Loop Current. Breeding areas used by the bluefin tuna were significantly associated with bathymetry, SST, eddy kinetic energy, surface chlorophyll concentration, and surface wind speed, with SST being the most important parameter. The bluefin tuna exhibited significant preference for areas with continental slope waters (2,800–3,400 m), moderate SSTs (24–25 and 26–27°C), moderate eddy kinetic energy (251–355 cm² s⁻²), low surface chlorophyll concentrations (0.10–0.16 mg m⁻³), and moderate wind speeds (6–7 and 9–9.5 m s⁻¹). A resource selection function of the bluefin tuna in the GOM was estimated using a discrete choice model and was found to be highly sensitive to SST. These habitat utilization and preference patterns exhibited by breeding bluefin tuna can be used to develop habitat models and estimate the probable breeding areas of bluefin tuna in a dynamic environment.     

Predator biomass,prey density,and species composition effects on group size in recruit coral reef fishes

Group incidence and size are described for recruit parrotfishes, wrasses, and damselfishes on Hawaiian reefs over 3 years (2006–2008) at sites spanning the archipelago (20–28°N, 155–177°W). Coral-poor and coral-rich areas were surveyed at sites with both low (Hawaii Island) and high (Midway Atoll) predator densities, facilitating examination of relations among predator and recruit densities, habitat, and group metrics. Predator and recruit densities varied spatially and temporally, with a sixfold range in total recruit densities among years. Group (≥2 recruits) metrics varied with time and tracked predator and recruit densities and the proportion of schooling species. Groups often included heterospecifics whose proportion increased with group size. A non-saturating relationship between group size and recruit density suggests that the anti-predator benefits of aggregation exceeded competitive costs. Grouping behavior may have overarching importance for recruit survival–even at high recruit densities–and merits further study on Hawaiian reefs and elsewhere.     

Intraspecific physiological variability of the gastropod Littorina saxatilis related to the vertical shore gradient in the White and North Seas

 Physiological responses to desiccation and temperature stress as well as behavioural responses to fast and abrupt environmental changes were investigated in high- and low-shore Littorina saxatilis (Olivi) from several populations from the White and North Seas. Variations in evaporation rates, resistance to air exposure and to acute and chronic temperature stress between animals from different shore levels were similar in White and North Sea periwinkles, consistent with the adaptive nature of these variations. High-shore snails were found to be able to conserve body water reserves better, to resist higher temperatures and to survive longer under conditions of combined temperature and desiccation stress than their low-shore counterparts. In a temperature range of 25 to 35 °C, the rate of evaporative water loss was positively correlated with temperature in low-shore snails while being largely temperature-independent in high-shore snails. Median lethal time during air exposure in L. saxatilis was negatively but not linearly related to the temperature of exposure. In a temperature range of 30 to 38 °C, the resistance to heat exposure in air was only slightly dependent on the temperature, with Q ₁₀ = 1.4 for the median lethal time; the heat resistance dropped drastically at temperatures above 38 °C, with Q ₁₀ = 593.8. This suggests different mechanisms of temperature resistance in different parts of the studied temperature range. In contrast, behavioural response to extreme salinity fluctuations was not uniform in the high- and low-shore periwinkles from the White and North Seas, which may reflect specific environmental conditions at different shore levels in the two areas studied. Observed physiological and behavioural variations are discussed from the viewpoint of different adaptive strategies employed by eulittoral and eulittoral-fringe animals within populations of a single species. Received: 13 December 1999 / Accepted: 11 April 2000     

Facultative lecithotrophy during larval development of the burrowing shrimp Callianassa tyrrhena (Decapoda: Callianassidae)

Survival, developmental and consumption rate (Artemia nauplii ingested per day) as well as predation efficiency (ingested per available Artemia nauplii) were studied during the larval development of the shallow-water burrowing thalassinid Callianassa tyrrhena (Petagna, 1792), which exhibits an abbreviated type of development with only two zoeal stages and a megalopa. The larvae, hatched from berried females from S. Euboikos Bay (Aegean Sea, Greece), were reared at 10 temperature–food density combinations (19 and 24 °C; 0, 2, 4, 8 and 16 Artemia nauplii d⁻¹). Enhanced starvation resistance was evident: 92 and 58% of starved zoeas I molted to zoea II, while metamorphosis to megalopa was achieved by 76 and 42% of the hatched zoeas at 19 and 24 °C, respectively. The duration of both zoeal stages was affected by temperature, food density and their interaction. Nevertheless, starvation showed different effects at the two temperatures: compared to the fed shrimp, the starved zoeae exhibited accelerated development at 19 °C (8.4 d) but delayed metamorphosis at 24 °C (5.9 d). On the other hand, both zoeal stages were able to consume food at an increased rate as food density and temperature increased. Predation efficiency also increased with temperature, but never exceeded 0.6. Facultative lecithotrophy, more pronounced during the first zoeal stage of C.tyrrhena, can be regarded as an adaptation of a species whose larvae can respond physiologically to the different temperature–food density combinations encountered in the wide geographical range of their natural habitat. Received: 28 February 1998 / Accepted: 21 October 1998     

Distribution and trophic links of gelatinous zooplankton on Dogger Bank,North Sea

The ecology of small, gelatinous zooplankton is not integrated into management of Dogger Bank (54° 00′ N, 3° 25′ E to 55° 35′ N, 2° 20′ E). In pursuit of this goal, gelatinous zooplankton and their potential prey were sampled along a transect across the bank on June 10–16, 2007. Eleven species of small medusae and ctenophores were collected, with six abundant taxa occurring in greater numbers below the thermocline and in the shallower, southeastern portion of the bank. There were no statistically significant diel changes in distribution. In contrast, potential prey were distributed more evenly across the bank and throughout the water column. Isotopic analyses revealed that gelatinous zooplankton fed on both smaller (100–300 μm) and larger (>300 μm) mesozooplankton, but also potentially on each other. These ecological insights suggest that small medusae and ctenophores should be integrated into sustainable management of Dogger Bank.     

Strontium/Calcium ratios in statoliths of the neon flying squid, Ommastrephes bartrami (Cephalopoda), in the North Pacific Ocean

Strontium to calcium ratios were observed along longitudinal sections of statoliths of nine neon flying squid, Ommastrephes bartrami (LeSueur, 1821), including three mature females (422 to 454 mm mantle length, ML; 207 to 306 d old) obtained from the North Pacific (27–35°N; 144–150°E) during winter and six immature males and females (187 to 226 mm ML; 126 to 164 d old) collected from 39°N; 145°E and 39°N; 169°W during summer. The distances between the nucleus (core) and the edge of the dorsal dome were approximately 660 to 690 μm in mature females and 450 to 510 μm in the immature squid. Sr/Ca ratios were determined at intervals of 30 μm between the nucleus and edge of the dorsal dome. Sr/Ca ratios were higher in areas near the nuclei and peripheral portions of the dorsal dome than in the middle portions of the statoliths (270 to 420 μm from the nuclei, corresponding to ages of 60 to 90 d) in mature females; thus a U-shaped pattern was evident. Sr/Ca ratios in the six immature squid decreased from nucleus to the dorsal dome; in three squid the ratios slightly increased toward the dorsal dome edge. The observed Sr/Ca ratios in immature squid were considered to represent younger portions of the U-shaped pattern. In the present study we discuss this pattern in relation to environmental and biological conditions of O. bartrami, which undertakes seasonal migrations between spawning grounds in the Subtropical Domain and feeding grounds in the Subarctic Domain and Transitional Zone in the North Pacific Ocean. Although Sr/Ca ratios are potentially affected by ambient water temperature and ontogenetic conditions, including somatic growth and statolith growth, it was impossible to evaluate each environmental and biological effect separately, as variations in these factors are complicated and effects could be interdependent. Received: 11 April 1997 / Accepted: 27 December 1997