Inertial Instability of Arbitrarily Meandering Currents Governed by the Eccentrically Cyclogeostrophic Equation

Using natural coordinates, we have derived a criterion for the inertial instability of arbitrarily meandering currents. Such currents, governed by the eccentrically cyclogeostrophic equation, are adopted as the basic current field for the parcel method. We assume that any virtual displacement which is given to a water parcel moving in the basic field has no influence on this field. From the conservation of mechanical energy for a virtual displacement we derive an inertial instability frequency ω _m = [(f + 2u/r)Z]^0.5 for the eccentrically cyclogeostrophic current, where f is the Coriolis parameter, u the velocity (always positive), r the radius of curvature of a streamline (negative for an anticyclonic meander), and Z the vertical component of absolute vorticity. If ω _m ² is negative, the eccentrically cyclogeostrophic current becomes unstable. Although the conventional, centrifugal instability criterion, derived from the conservation of angular momentum in a circularly symmetric current field, has a certain meaning for a monopolar vortex, it contains a radial shear vorticity that is difficult to use in arbitrarily meandering currents. The new criterion ω _m ² contains a lateral shear vorticity that is applicable to arbitrarily meandering currents. Examining instabilities of concentric rings with radii of 50–100 km, we consider reasons why the anticyclonic supersolid rotation has been very much less frequently observed than the cyclonic supersolid rotation, despite a prediction of some common stability and a rapid change in radial velocity gradient for the former. Classifying eccentric streamlines into the large and small curvature-gradient types, we point out that the large-gradient curvature in anticyclonic rings is apt to be unstable. This revised version was published online in July 2006 with corrections to the Cover Date.     

边界层高度和动量粗糙度的不确定性对台风“天鸽”(1713)模拟的影响

基于中国气象局区域台风数值预报系统(CMA-TYM),通过一系列敏感性试验,分析研究了台风“天鸽”(1713)生命过程中不同时间阶段的移动路径及强度的数值模拟对模式参数化方案中边界层高度(h)和动量粗糙度(z₀)的敏感性。试验结果表明,使用不同参数化方案计算的h在“天鸽”(1713)初期的热带风暴阶段对热带气旋的移动路径有较明显的影响,在台风成熟后对热带气旋的移动路径影响不显著 ;台风中心附近最大10 m风速对h的变化不敏感,而最低海平面气压对h的变化却非常敏感。同时发现在台风发展初期阶段,边界层过薄或过厚都不利于台风强度的发展加强。这表明边界层高度h在热带气旋数值模拟和预报中是非常重要的,尤其是在台风发展的初期阶段。动量粗糙度z0的变化对台风“天鸽”的影响主要体现在台风增强阶段,台风中心附近10 m风速最大值在台风增强阶段对z₀敏感,尤其是在台风发展的初期阶段     

Response of a two-layer ocean with a baroclinic current to a moving storm,part I

A storm moves with a constant speed parallel to a stationary geostrophic current which flows only in the upper layer of a two-layer, infinite ocean. It is assumed that the lower layer is motionless. The quasi-geostrophic approximation is valid for a moving speed less than 4 ms^–1 for a storm radius of 100 km. The primary change of the upper layer thickness is caused by the wind stress divergence and the time integral of the wind stress curl. A cyclonic storm generates upwelling in its wake. The effect of the stationary flow similar to a western boundary current is minor by an order of magnitude and noticeable only on the left edge of the flow. Scaling of equations of motion and continuity for a more general upper geostrophic flow leads to expansion with a parametera ²=gH _m(fL)^–2, whereg is reduced gravity,H _m is the maximum thickness of the upper layer,f is Coriolis' parameter andL is the storm radius. The zeroth order perturbations of transport and thickness do not include the stationary flow which appears only in the first order perturbations ina ². When there is a coast, the change of the interface near the coast is dependent on the time integral of the wind stress component parallel to the coast, thus leading to upwelling or downwelling according to the center being to the left or right of the coastline.     

Trophic relationships on a fucoid shore in south-western Iceland as revealed by stable isotope analyses, laboratory experiments, field observations and gut analyses

Rocky shores in the North Atlantic are known for their zonation patterns of both algae and animals, which can be expected to greatly affect food availability to consumers at different height levels on the shore. We tested the hypothesis that consumers would feed on the most abundant suitable food source in their surroundings. In total 36 species/taxa of common primary producers and consumers were sampled for stable isotope analyses from a sheltered fucoid shore at Hvassahraun in south-western Iceland. A selection of these species was also collected seasonally and from different height levels. Feeding experiments, field observations and gut analyses were also conducted. Our results were in good overall agreement with pre-existing knowledge of trophic relationships in the rocky intertidal. Consumers often appeared to be assimilating carbon and nitrogen from the most common diet in their immediate surroundings. The predator Nucella lapillus was thus feeding on different prey at different height levels in accordance with different densities of prey species. When tested in the laboratory, individuals taken from low on the shore would ignore the gastropod Littorina obtusata, uncommon at that height level, even when starved, while individuals from mid-shore readily ate the gastropod. This indicated that some kind of learned behaviour was involved. There were, however, important exceptions, most noteworthy the relatively small contribution to herbivores, both slow moving (the gastropod L. obtusata) and fast moving (the isopod Idotea granulosa and the amphipod Gammarus obtusatus) of the dominant alga at this site, Ascophyllum nodosum. The recent colonizer Fucus serratus seemed to be favoured. Selective feeding was indicated both by isotope signatures as well as by results of feeding experiments. Seasonal migrations of both slow and fast moving species could partly explain patterns observed.     

Unsteady ship waves in shallow water of varying depth based on Green–Naghdi equation

Based on Green–Naghdi equation this work studies unsteady ship waves in shallow water of varying depth. A moving ship is regarded as a moving pressure disturbance on free surface. The moving pressure is incorporated into the Green–Naghdi equation to formulate forcing of ship waves in shallow water. The frequency dispersion term of the Green–Naghdi equation accounts for the effects of finite water depth on ship waves. A wave equation model and the finite element method (WE/FEM) are adopted to solve the Green–Naghdi equation. The numerical examples of a Series 60 (C_B=0.6) ship moving in shallow water are presented. Three-dimensional ship wave profiles and wave resistance are given when the ship moves in shallow water with a bed bump (or a trench). The numerical results indicate that the wave resistance increases first, then decreases, and finally returns to normal value as the ship passes a bed bump. A comparison between the numerical results predicted by the Green–Naghdi equation and the shallow water equations is made. It is found that the wave resistance predicted by the Green–Naghdi equation is larger than that predicted by the shallow water equations in subcritical flow , and the Green–Naghdi equation and the shallow water equations predict almost the same wave resistance when , the frequency dispersion can be neglected in supercritical flows.     

中国对虾幼体对运动物体的感觉能力及其与环境照度的关系

甲壳动物具有明显的视觉运动反应。这种对视野内移动目标的反应有两种形式,一种是眼柄的颤动反应(Optokinetic response),另一种为全身性的视觉运动反应(Optomotor response)。对于前一种反应形式国外已有许多研究,尤其对爬行亚目某些种类眼柄颤动反应特点和机制进行了大量实验。后一种反应形式的研究工作较少。有关游泳亚目视觉     

Wave resistance of a hovercraft moving in water with nonrigid bottom

Surface waves generated by a moving ship in water of finite depth are affected by the rheological properties of the movable bottom. The aim of this work is to evaluate the wave resistance exerted on a hovercraft modeled as a two-dimensional pressure distribution moving on the free surface of water with nonrigid bottom. Analysis of three-dimensional flows in two-fluid layers of finite depths is performed by assuming an inviscid upper layer (water) and a viscous lower layer (nonrigid bottom). Numerical calculations show that the maximum wave resistance occurs in the vicinity of the critical Froude number F=1. This maximum value decreases as the muddy bottom becomes less rigid.     

The typhoon swell Doppler effect

The swell of a moving typhoon has the same Doppler effect as a moving sound source. Both originate from the variations in an energy flux. In a sound source this is called a frequency shift. In a typhoon it is a swell wave height change. A distant typhoon may generate very high waves through the Doppler effect as the typhoon approaches. A modification λ is proposed for engineering practice.     

Movement patterns of an endemic South African sparid,the black musselcracker Cymatoceps nasutus,determined using mark-recapture methods

This study made use of data from three long-term fish tagging projects along the South African coastline to investigate the movement behaviour of the endemic black musselcracker Cymatoceps nasutus (Sparidae). From 1984 to 2016, a total of 3 430 C. nasutus (178–980 mm fork length) were tagged (with small plastic dart tags) throughout the species’ distributional range, with an overall reported recapture rate of 7.2%. Recaptured individuals displayed high levels of residency, moving an average of 14.8 km, with time-at-liberty ranging from 0 to 6 809 days. The majority of recaptures (84.6%) were made within 1 km of the tagging sites; however, some large-scale movements, of up to 528 km, were recorded. Although C. nasutus individuals moving greater distances were characterised by greater mean sizes (mm fork length) at time of recapture, the distances moved by juveniles were not significantly different from those of adults (p > 0.05). Low levels of connectivity among coastal regions were therefore expected due to the high degree of residency displayed by this species. Combining traditional management approaches together with a well-designed network of no-take marine protected areas is likely to be the most effective way to protect this vulnerable species. A lack of data on the movements of adults remains a challenge, but this could be overcome by tracking large individuals tagged with long-life acoustic transmitters.     

Assessment of South African Umbrina robinsoni based on per-recruit models

Slender baardman Umbrina robinsoni are an important component of recreational shore-angler and spearfisher catches along the eastern seaboard of South Africa. Stocks of U. robinsoni at three sites—False Bay, Stil Bay and the KwaZulu-Natal (KZN) coast—were modelled using a per-recruit approach. Total (Z) and fishing (F) mortality rates were estimated by catch-curve analyses using measures of individual size (length or weight) recorded by researchers, divers (log books) or during spearfishing competitions. Based on estimates of F during the period 2001–2003, spawner biomass per-recruit ratios were estimated to be either at or below the 25% threshold (False Bay SB/R = 21% SB/R_{F = 0}, Stil Bay SB/R = 25% SB/R_{F = 0}, and KZN SB/R = 21% SB/R_{F = 0}), suggesting that rates of F were too high. Reductions in F necessary to achieve target fishing mortality levels (F _{F = 0}) at the current minimum size limit (l 40 cm total length) were 51% for Stil Bay and the KZN coast and 57% for False Bay. Based on the bag frequencies from 927 diver outings in KZN (1989–2003), a reduction in bag limit from the current five to two fish is predicted to reduce F in this region by approximately 25%. Increasing the l to 50 cm is predicted to increase SB/R ratios to 36% SB/R_{F = 0} in False Bay, 43% SB/R_{F = 0} in KZN and 52% SB/R_{F = 0} in Stil Bay, at current levels of F. Owing to the philopatric nature of U. robinsoni and the consequent existence of temporary refugia, catch curves are likely to underestimate fishing mortality. The reductions in F estimated to attain the target reference points are therefore probably conservative.     

Dynamics of a mesoscale eddy off Cape Ann, Massachusetts in May 2005

Observations and numerical modeling indicate that a mesoscale anti-cyclonic eddy formed south of Cape Ann at the northern entrance of Massachusetts Bay (MB) during May 2005, when large river discharges in the western Gulf of Maine and two strong Nor'easters passing through the regions led to an unprecedented toxic Alexandrium fundyense bloom (red tide). Both model results and field measurements suggest that the western Maine Coastal Current separated from Cape Ann around May 7–8, and the eddy formed on around May 10. The eddy was trapped at the formation location for about a week before detaching from the coastline and moving slowly southward on May 17. Both model results and theoretical analysis suggest that the separation of the coastal current from the coast and subsequent eddy formation were initiated at the subsurface by an adverse pressure gradient between Cape Ann and MB due to the higher sea level set up by onshore Ekman transport and higher density in downstream MB. After the formation, the eddy was maintained by the input of vorticity transported by the coastal current from the north, and local vorticity generation around the cape by the horizontal gradients of wind-driven currents, bottom stress, and water density induced by the Merrimack River plume. Observations and model results indicate that the anti-cyclonic eddy significantly changed the pathway of nutrient and biota transport into the coastal areas and enhanced phytoplankton including Alexandrium abundances around the perimeter of the eddy and in the western coast of MB.     

Barotropic disturbances caused by a point storm in aβ-plane ocean

Barotropic equation for vorticity balance in the-plane is solved for a volume transport stream function with a northward moving wind stress torque concentrated at a point (tweak). Asymptotic techniques are applied to the solution expressed by Fourier type integrals. In the front zone (northern half from the tweak) the stream function behaves asO(¦X¦^–5) whereX is a scaled eastward coordinate. In the wake, the stream function behaves asO(¦X¦^–1/2) within a wedge bounded by the westward axis and a line directed SSE approximately, but behaves asO(¦X¦^–5) in the rest of the half plane. On these boundaries it behaves asO(¦X¦^–5/2) andO(¦X¦^–1/3), respectively. East-west asymmetry is a result of asymmetry in zonal propagation of the planetary waves, which also cause the wavy pattern of the streamline in the western half of the wake. Friction is most effective in decreasing the stream function in the south to SSW sector and least effective to the west. Effect of divergence changes the wave pattern in the western half of the wake but does not change magnitude of the stream function. It is speculated that abnormal changes in daily mean sea levels observed in 1965 to 1971 along the south coast of Japan may be caused by the wake effect of moving typhoons east off Japan.     

Evaluation of a class of possible simple interim management procedures for the Namibian hake fishery

During 1997, considerable scientific differences arose about the status of the Namibian hake (Merluccius capensis and M. paradoxus) resource, and as to whether the hake Total Allowable Catch (TAC) should be substantially decreased or increased. These differences revolved primarily around whether or not abundance estimates from the swept-area trawl surveys by the Norwegian research vessel Dr Fridtjof Nansen should be considered as reliable measures of biomass in absolute (as distinct from relative) terms. The paper relates the computations underlying the Interim Management Procedure (IMP) approach that was put forward at that time as a basis to resolve this impasse. The anticipated performance, in terms of catch and risk of resource depletion, of a number of simple candidate IMPs for the Namibian hake resource is evaluated. The IMPs depend on two parameters, whose values are to be chosen by decision-makers, and adjust the TAC up or down from one year to the next according to whether trends in recent commercial catch rate and survey indices of abundance are positive or negative. Performances are evaluated across the then current wide range argued for resource abundance and status. Trade-offs in performance across the candidates considered are discussed. One of the candidates was subsequently selected by a joint meeting of scientists, industry and Ministry officials in February 1998 and served as the basis for scientific recommendations for the TAC for the hake resource for the following three years.     

Tidal Currents in the Tsushima Straits Estimated from ADCP Data by Ferryboat

Tidal currents in the Tsushima Straits have been analyzed using measurements obtained since February 1997 by an acoustic Doppler current profiler (ADCP) mounted on the ferryboat Camellia. Tidal current constituents (M ₂, S ₂, K ₁, O ₁) are dominant among the ten tidal current constituents (Q ₁, O ₁, P ₁, K ₁, N ₂, M ₂, S ₂, K ₂, MSf, Mf), and generally 1.4–2.1 times stronger at the western channel of the straits than those at the eastern channel. The ratio between amplitude of M ₂, S ₂, K ₁ and O ₁ averaged along the ferryboat track is 1:0.45:0.59:0.51. The major axis directions of tidal current ellipses are generally SW to NE, exceptionally in the vicinity of the Tsushima Islands. Approaching the Tsushima Islands from the Korean Peninsula side, the major axis gradually rotates clockwise. At the western channel, the M ₂ and K ₁ constituents change the rotation direction of current vectors from clockwise to counterclockwise at about 90–130 m depth. The contributions of the tidal currents to the mean kinetic energy and the mean eddy kinetic energy along the ferryboat track are, on average, 0.56 and 0.71, respectively. This suggests that tidal current activities are generally more dominant than the mean current activities and much more dominant than eddy activities. The only region where the eddy activities are comparable to the tidal current activities is located on the east side of the Tsushima Islands. This revised version was published online in July 2006 with corrections to the Cover Date.     

Aggregational behavior of the blue mussels Mytilus edulis and Mytilus trossulus: a potential pre‐zygotic reproductive isolation mechanism

The blue mussels Mytilus edulis and Mytilus trossulus occur sympatrically and are able to hybridize in populations on the eastern coast of Newfoundland, Canada, presenting an opportunity to study their aggregational behavior. Aggregation behavior may therefore provide insight into post‐settlement interactions and pre‐zygotic reproductive isolation between the species. Three treatments were designed using M. edulis and M. trossulus to investigate their intraspecific and interspecific spatial distribution patterns. With Ripley’s K‐function and Monte Carlo simulation analysis, we found that in the single‐species treatment, M. edulis aggregated significantly but not M. trossulus. Based on results of two‐way ANOVAs, both the number of aggregations and the moving distance were significantly affected by the treatments (single‐species or mixed‐species treatment) and times (24, 48, 72 and 96 h). In further pairwise comparisons using Tukey’s test, M. edulis aggregated differently with or without M. trossulus occupying the same tank, suggesting that the aggregational behavior of M. edulis could be driven by species‐specific chemical cues. The result that M. edulis aggregates intraspecifically may increase the probability of intraspecific fertilization of the spawned gametes and thus function as a pre‐zygotic reproductive isolation mechanism maintaining the blue mussel hybrid zone.     

Movable bed roughness and current profiles in the presence of irregular waves with an arbitrary angle to currents

The bed roughness k_s and current velocity profiles in the presence of waves with an arbitrary angle θ to currents are studied. It is found that the movable bed roughness is affected by both the wave and the current and only slightly by the angle θ between the wave propagation and the current, and that existing formulae derived in purely oscillatory flows generally fail to predict k_s. In the present study, a new formula which takes account the effect of the wave and the current on the bed roughness is suggested to calculate k_s in combined wave-current flows. With the present formula, the current profiles calculated by the model of You agree satisfactorily with the laboratory data of van Kampen and Nap and Havinga, and the field measurements of Grant and Williams and Drake et al.     

Diffusion in the ocean with diffusion coefficient depending on the scale and concentration of impurities

We solve a nonlinear problem of diffusion from a concentrated source in a moving medium with diffusion coefficient depending on the scale of the phenomenon, time, and the concentration of impurities. We obtain a family of exact solutions of this problem, which can be regarded as a generalization of the class of linear problems of diffusion considered earlier for the conditions of the ocean and atmosphere by Roberts, Ozmidov, Obukhov,et al. Translated by Peter V. Malyshev and Dmitry V. Malyshev.     

Does the Ulleung eddy owe its existence to β and nonlinearities?

A nonlinear theory for the generation of the Ulleung Warm Eddy (UWE) is proposed. Using the nonlinear reduced gravity (shallow water) equations, it is shown analytically that the eddy is established in order to balance the northward momentum flux (i.e., the flow force) exerted by the separating western boundary current (WBC). In this scenario, the presence of β produces a southward (eddy) force balancing the northward momentum flux imparted by the separating East Korean Warm Current (EKWC).It is found that, for a high Rossby number EKWC (i.e., highly nonlinear current), the eddy radius is roughly 2R_d/ε^1/6 (here ε≡βR_d/f₀, where R_d is the Rossby radius), implying that the UWE has a scale larger than that of most eddies (R_d). This solution suggests that, in contrast to the familiar idea attributing the formation of eddies to instabilities (i.e., the breakdown of a known steady solution), the UWE is an integral part of the steady stable solution. The solution also suggests that a weak WBC does not produce an eddy (due to the absence of nonlinearity).A reduced gravity numerical model is used to further analyze the relationship between β, nonlinearity and the eddy formation. First, we show that a high Rossby number WBC which is forced to separate from the wall on an f plane does not produce an eddy near the separation. To balance the northward momentum force imparted by the nonlinear boundary current, the f plane system moves constantly offshore, producing a southward Coriolis force. We then show that, as β is introduced to the problem, an anticyclonic eddy is formed. The numerical balance of forces shows that, as suggested by the analytical reasoning, the southward force produced by the eddy balances the northward flow force imparted by the boundary current. We also found that the observed eddy scale in the Japan/East Sea agrees with the analytical estimate for a nonlinear current.     

Baroclinic Buoyancy-Inertia Joint Stability Parameter

At present, the barotropic buoyant stability parameter has been derived from a vertical virtual displacement of a water parcel. The barotropic inertial stability parameter in the eccentrically cyclogeostrophic, basic current field was derived in 2003 from a horizontal cross-stream virtual displacement of a parcel. By expressing acceleration of a parcel due to a virtual displacement, which is arbitrarily sloping within a vertical section across the basic current, in terms of natural coordinates, we derived the vertical component of baroclinic buoyant stability parameter B ₂ ², the horizontal component of baroclinic inertial stability parameter I ₂ ², the baroclinic joint stability parameter J ², its buoyant component B ² and its inertial component I ². B ² is far greater than I ₂ ², and when neglecting relative vorticity except for vertical shear, a downward convex curve of J ² plotted against the slope of a virtual displacement follows a trend of B ² curve. If a parcel displaces along a horizontal surface or an isopycnal surface, however, B ² vanishes, and J ² becomes equal to I ². Actual parcel is apt to displace not only along the bottom slope, but also along the sea surface and an isopycnal interfacial surface, which is approximately equivalent to an isentropic surface, preferred by lateral mixing and exchange of momentum. Such actual displacement makes B ² vanishing, and grants I ² an important role. The present analysis of I ² examining effects due to curvature and horizontal and vertical shear vorticities are useful in deepening our understanding of baroclinic instability in actual oceanic streams.