On One Estimate of the Boundary of the Rossby Regime Zone in the Atmosphere

A two-zone model of the atmospheric circulation over the hemisphere is considered. The geographic latitude φ of the boundary between the Rossby circulation regime zone at middle and high latitudes and the Hadley circulation regime zone at low latitudes serves as a model variable. The closeness between the actual and reference (exponential) air-mass distribution over the hemisphere, with respect to Ertel’s modified potential vorticity (MPV), is accounted for. The informational entropy of the statistical MPV distribution in the hemispheric atmosphere and the informational entropy of the eddy regime in the basic storm-track zone are used to determine a statistically (climatically) equilibrium value of φ. The question of atmospheric blocking over the hemisphere is considered using the proposed statistical–dynamical model.     

Helicity in dynamic atmospheric processes

An overview on the helicity of the velocity field and the role played by this concept in modern research in the field of geophysical fluid dynamics and dynamic meteorology is given. Different (both previously known in the literature and first presented) formulations of the equation of helicity balance in atmospheric motions (including those with allowance for effects of air compressibility and Earth’s rotation) are brought together. Equations and relationships are given which are valid in different approximations accepted in dynamic meteorology: Boussinesq approximation, quasi-static approximation, and quasi-geostrophic approximation. Emphasis is placed on the analysis of helicity budget in large-scale quasi-geostrophic systems of motion; a formula for the helicity flux across the upper boundary of the nonlinear Ekman boundary layer is given, and this flux is shown to be exactly compensated for by the helicity destruction inside the Ekman boundary layer.     

Long-period topographic trapped waves in a two-layer ocean with basic flow

The characteristics of free topographic trapped waves are investigated numerically for a two-layer model with basic flow, which is uniform, geostrophically balanced motion flowing parallel to the coast. Six modes are identified for this model with depth variations. They are external and internal Kelvin modes, a topographic Rossby mode, and additional three modes. The two of the additional modes are interesting. The first one is a quasi-geostrophic surface-trapped mode, while the second one is a quasi-geostrophic bottom-trapped mode. It is suggested that baroclinic instability takes place when these two modes take a resonance coupling each other.     

Analysis of the differential-difference schemes of equations for the barotropic ocean

Difference schemes constructed for the problems using a barotropic approximation (Poincaré waves, Kelvin waves, Rossby waves, quasi-geostrophic normal modes, forced free oscillations) allow one to obtain exact solutions for a set of discrete equations. It is shown that the better approximation is achieved on thef-plane, using the grid different from gridsB andC. Translated by Vladimir A. Puchkin.     

Dynamic coupling of a liquid-tank system under transient excitations

It has been observed that the unrestrained free surface of a container can create relatively large liquid movements for even very small motions of the container. This excessive movement may endanger the stability as well as the maneuvering quality of the transporting vehicle. Therefore, the effects of the dynamic coupling of a liquid-tank system are of great concern. This dynamic coupling problem is studied analytically for a two-dimensional, rectangular rigid tank with no baffles. The governing equations of the liquid motion are derived with reference to a moving coordinate system which is fixed to the moving container. With the liquid forces generated by the fluid motion as the external exciting force for the tank, the motions of the liquid-tank system can be described according to Newton's Second Law of Motion. By using the Laplace transformation technique, the dynamic responses of the coupled system can be examined in detail. Numerical results for various types of external excitations and the resultant motions of the fluid-tank system are presented and compared with the equivalent non-shifting cargo system. The results of the comparison indicate that the discrepancy of responses in the two systems can obviously be observed when the ratio of the natural frequency of the fluid and the natural frequency of the tank is close to unity. Also, the amount of fluid inside the tank is a very important factor in determining the responses.     

Dynamic parameters in models of atmospheric vortex structures

Vortex simulation and the computation of fields of dynamic parameters of vortex structures (velocity, rotor velocity, and helicity) are carried out with the use of exact hydrodynamic equations in a cylindrical coordinate system. Components of centripetal and Coriolis accelerations are taken into account in the initial equations. Internal and external solutions are defined. Internal solutions ignore the disturbances of the pressure field, but they are considered in external solutions. The simulation is carried out so that the effect of accounting for spatial coordinates on the structure of the above fields is pronounced. It is shown that the initial kinetic energy of rotating motion transforms into the kinetic energy of radial and vertical velocity components in models with centripetal acceleration. In models with Coriolis acceleration, the Rossby effect is clearly pronounced. The method of an “inverse problem” is used for finding external solutions, i.e., reconstruction of the pressure field at specified velocity components. Computations have shown that tangential components mainly contribute to the velocity and helicity vortex moduli at the initial stage.     

周期性的或伴有贯穿流的西边界流跨隙流动的迟滞变异过程

使用1.5层准地转约化重力模式研究了周期性的或伴有贯穿流的西边界流跨隙流动的迟滞变异过程。当西边界流变化的周期比罗斯贝波在缺口处调整的时间尺度大得多时,在雷诺数增加和减少过程的霍夫分叉点都发生延迟,从而产生新的雷诺数迟滞区间;并且西边界流流态转变的临界值变化显著;且周期强迫越短,雷诺数迟滞区间越大。当西边界流变化的周期与罗斯贝波在缺口处调整的时间尺度相当时,西边界流在缺口的流态呈无迟滞的周期性变化,且西边界流入侵西海盆的程度随周期减少而变小。此外,当贯穿流的流量大于西边界流的一半时,会显著影响西边界流在缺口处的迟滞变异过程;西边界流向西入侵程度和流态转变发生的临界雷诺值均发生变化,且贯穿流流量越大变化越大。     

On the large-scale variability of the circulation and heat state of the ocean and atmosphere in the North Atlantic

A conclusion about two extreme regimes existing in the large-scale circulation in the North Atlantic has been drawn based on an analysis of the inter-annual variability of the analogue to the Rossby index, as well as that of the heat and dynamic characteristics in separate areas of the north subtropical circulation. The former is defined by a high level of circulation both in the atmosphere and in the subtropical water circulation. In the current century this regime was realized mainly in the years pertaining to the middle and end of a 22-year solar activity cycle (a 22-year cycle). The relatively low level of atmospheric circulation and the slackened water mass transport are typical of the second regime. It dominated mainly during the years relevant to the beginning and second half of a 22-year solar activity cycle.Translated by Mikhail M. Trufanov.     

浮基多体系统自激运动响应的时域分析方法

浮基多体系统上部机构作业时不仅存在多体系统内部各物体间的耦合作用 ,还存在浮基与流场间的耦合作用。本文将浮基在流场中引起的辐射势表示为浮基加速度与时域规范化速度势乘积的卷积形式 ,导出流体动压力及静水系泊恢复力与浮基运动的关系。使用多刚体力学的凯恩方法得到系统的动力学方程。最后给出了在时域中数值求解系统运动响应的具体步骤     

Wave mechanism of the seasonal variability of the largescale current field in the northern Tropical Atlantic

A spatial-temporal analysis of the density field in the large-scale hydrological observation areas in the Tropical Atlantic is carried out. The spectral maximum corresponding to the first baroclinic mode of the planetary Rossby wave is discriminated and studied. It is shown that the seasonal transformation of the large-scale circulation of the current field is connected with the propagation of this wave. A simple quasi-geostrophic model is suggested which describes the seasonal variability of the North Equatorial Countercurrent. The results obtained by this model are compared with the hydrological survey data.Translated by Mikhail M. Trufanov.     

Numerical model of currents generated by sources and sinks in a circular rotating channel

This paper presents the results of numerical calculations using shallow water equations for the currents in the laboratory experiments with a rotating circular channel. An axial symmetric function of mass source is introduced into the equations for the depth of the layer to model experimental sources and sinks of fluid, which induces opposing zonal flows together with the Coriolis force. Different configurations and amplitudes of mass sources lead to the appearance of vortex motions in the channel with different circular motions in the vortices and azimuthal displacements of their centers along the channel. Diagrams of regimes are presented in the parameters of relative angular velocities of the mean zonal flow and vortex transport around the axis of the system rotation. The differences of the theory and real experiments with currents of finite depth in a channel are discussed.     

Mean circulation induced over bottom topography by mesoscale variabilities in the Kuroshio Extension

Circulation could be generated over bottom topography by vertical shrinking or stretching of a water parcel, in which potential vorticity is conserved. The water parcel moves up or down over the bottom topography yielding shrinking or stretching. In addition to a prevailing current which advects the water parcel in one direction, an oscillatory motion can also induce shrinking and stretching, and circulation is consequently generated over the bottom topography, once it is averaged in time. A two-layer quasi-geostrophic model has been used to reproduce mesoscale variabilities both in and under the Kuroshio Extension around the Shatsky Rise. A combination of TOPEX and ERS altimeters provided information on an eddy field near the sea surface, while a data assimilation method was used to reconstruct the flow field below the main thermocline. Among various mesoscale processes associated with the Kuroshio, it is remarkable that topographic Rossby waves trapped over the Shatsky Rise are generated by the upper-layer mesoscale variability. A persistent anticyclonic circulation is produced on the Shatsky Rise through a water parcel moving up and down over the bottom slope, and is consistent with the observed density anomaly in the WOA94.     

Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank

A time-independent finite-difference method and a fifth-order Runge–Kutta–Felhberg scheme were used to analyze the dynamic responses of sea-wave-induced fully non-linear sloshing fluid in a floating tank. The interaction effect between the fully non-linear sloshing fluid and the floating tank associated with coupled surge, heave and pitch motions of the tank are analyzed for the first time in the present pilot study. For the analysis of fluid motion in the tank, the coordinate system is moving (translating and rotating) with tank motion. The time-dependent water surface of the sloshing fluid is transformed to a horizontal plane and the flow field is mapped on to a rectangular region. The Euler equations as well as the fully non-linear kinematic free surface condition were used in the analysis of the sloshing fluid. The strip theory for linearized harmonic sea-wave loading was adopted to evaluate the regular encounter wave force. In addition, the dynamic coefficients used in the dynamic equations of tank motion were also derived based on strip theory and a harmonic motion of the tank. The characteristics of free and forced tank motions with and without the sloshing effect are studied. By the damping effect, the response of free oscillation will damp out and that of forced oscillation will approach a steady state. Without sea-wave action, the contribution of the sloshing load would enlarge the angular response of tank motion as well as the rise of free surface and the sloshing effect will delay the damping effect on angular displacement. On the contrary, under sea-wave action, the sloshing effect will decrease the dynamic response of tank motion and rise of free surface. The interaction, sloshing and coupling effects are found to be significant and should be considered in the analysis and design of floating tanks.     

On nonlinear planetary waves: A class of solutions missed by the traditional quasi-geostrophic approximation

Weakly nonlinear quasi-geostrophic planetary waves on a beta-plane and topographic waves over a linearly inclined bottom are examined by use of shallow water equations for a small beta parameter. Long solitary wave solutions missed by the use of the traditional quasi-geostrophic approximation are found in a channel ocean with neither a sheared current nor a curved (non-linearly inclined) bottom topography. The solutions are missed in the traditional approach because the irrotational motion associated with the geostrophic divergence is neglected by the quasi-geostrophic approximation. Another example which calls attention to the limitation of the traditional quasi-geostrophic approximation is the nonlinear evolution of divergent planetary eddies whose scale is much larger than the Rossby's radius of deformation. Some aspects of a new evolution equation are briefly discussed.     

Sloshing waves and resonance modes of fluid in a 3D tank by a time-independent finite difference method

A 3D time-independent finite difference method is developed to solve for wave sloshing in a three-dimensional tank excited by coupled surge and sway motions. The 3D equations of fluid motion are derived in a moving coordinate system. The three-dimensional tank, with an arbitrary depth and a square base, is subjected to a range of excitation frequencies with motions that exhibit multiple degrees of freedom. For demonstration purposes the numerical scheme is validated by a benchmark study. Five types of sloshing waves were observed when the tank is excited by various excitation frequencies. A spectral analysis identified the resonant frequencies of each type of wave and the results show a strong correlation between resonant modes and the occurrence of the sloshing wave types. The method can be used to simulate fluid sloshing in a 3D tank with six-degrees of freedom.     

Variations of temperature and hydrologic regimes of the region of Ladoga Lake catchment basin in the 20th and 21st centuries according to data of modern climate models

In the region of the Ladoga Lake catchment basin, we perform data analysis on a set of different modern climate models with different Intergovernmental Panel on Climate Change (IPCC) scenarios in the 20th and 21st centuries; this set includes global models such as ECHAM4/OPYC3 (Max Planck Institute for Meteorology, Germany), HadCM3 (Hadley Centre Coupled Model, England), and RCAO (Rossby Centre Regional Atmosphere-Ocean) models. Two variants of the boundary conditions for these climate models (Rossby Center of Swedish Meteorological and Hydrological Institute, SMHI) are used. We present the results of a diagnosis of the model-predicted near-surface temperature (T), precipitation (P), evaporation (E), and water budget (P-E) in the Ladoga Lake catchment based on their comparison with empirical data in twentieth century. We obtain scenario estimates of the variations of temperature and hydrologic regimes of Ladoga Lake catchment when IPCC IS92a, A2, and B2 scenarios are fulfilled, describing the prognostic growth of anthropogenic emissions of greenhouse gases and aerosol to the atmosphere, and discuss the recommendations for their use.     

Adjustment time of the first baroclinic Rossby wave in the global oceans

1Introduction Planetary waves involve the main processes bywhich perturbation signal in one part of the ocean istransferred to another part.In the1970s,mostof theprevious theoretical studies focus on the local Ekmanpumping and the nondispersive long baroc…     

Time domain simulation of side-by-side floating bodies using a 3D numerical wave tank approach

The coupled system of two side-by-side fixed and/or floating bodies interacting with a large amplitude nonlinear wave is studied using a direct time domain solution method. The numerical model is based on a three-dimensional mixed Eulerian–Lagrangian (MEL) method under certain simplifying approximations permitting Rankine panel scheme to be implemented over a time-invariant boundary surface to solve the boundary value problem for the unknown velocity potentials. A 4th order Adams–Bashforth–Moulton scheme is used for time marching of rigid-body motion histories of the individual bodies and evolution of the free-surface including the gap region in which large resonant fluid motions occur. A systematic study has been carried out to evaluate the performance of the developed time domain method in simulating the forces and motions as well as the fluid motion in the gap region for the two body system under various arrangements and in different wave-headings. At first, the computed numerical results have been validated and verified with computational and experimental results available in literature for standard geometries such as vertical truncated cylinders and rectangular boxes. Secondly, effectiveness of the damping lid model which is introduced to suppress wave resonance in the gap region is investigated including its influence on maximum sway forces on fixed and floating rectangular barges in side-by-side configurations. Thirdly, comparative studies on absolute and relative motion response for two cases (two rectangular barges, and a FLNG-FPSO + shuttle tanker) in side-by-side arrangement are detailed to bring out the importance of nonlinearities arising due to steep nonlinear incident waves. Finally, coupled motions of the two-body system of an FPSO and a shuttle tanker floating in side-by-side configuration in a steep nonlinear wave field are studied in which the two bodies are connected through hawsers, and also the FPSO is moored to the ground. Additionally there is a fender between the two bodies.     

The eigenvalue equations of equatorial waves on a sphere

Zonally propagating wave solutions of the linearized shallow water equations (LSWE) in a zonal channel on the rotating spherical earth are constructed from numerical solutions of eigenvalue equations that yield the meridional variation of the waves' amplitudes and the phase speeds of these waves. An approximate Schrödinger equation, whose potential depends on one parameter only, is derived, and this equation yields analytic expressions for the dispersion relations and for the meridional structure of the waves' amplitudes in two asymptotic cases. These analytic solutions validate the accuracy of the numerical solutions of the exact eigenvalue equation. Our results show the existence of Kelvin, Poincaré and Rossby waves that are harmonic for large radius of deformation. For small radius of deformation, the latter two waves vary as Hermite functions. In addition, our results show that the mixed mode of the planar theory (a meridional wavenumber zero mode that behaves as a Rossby wave for large zonal wavenumbers and as a Poincaré wave for small ones) does not exist on a sphere; instead, the first Rossby mode and the first westward propagating Poincaré mode are separated by the anti-Kelvin mode for all values of the zonal wavenumber.