The influence of solitary external centers of action with disturbances of the velocity field in the form of a vortex or dipole is simulated in experiments in a rotating channel with an inclined bottom. If the disturbance intensity thresholds are exceeded, it is possible to change the number of cyclones and anticyclones throughout the channel and the angular velocity of their movement.
Numerical and laboratory experiments have been carried out to study the intrusion of anomalies into the axisymmetric distribution of the velocity field generated by sink sources and the MHD method in a rotating circular channel with a sloping bottom. A sectoral decrease in the intensity of the external force in a certain range of values has a decelerating effect on the velocity of propagation of anticyclones through the channel, while it has almost no influence on the dynamics of cyclones. At the same time, a significant part of moving anticyclones can disappear or almost stop, or new quasi-stationary anticyclones appear, despite there being no notable changes in the visible pattern of eddy propagation in the channel in the sector in which external intervention had been performed. However, changes are notable over the entire channel or in its individual parts in the mean characteristics of the eddy field. These anomalies can be interpreted as a decrease in the intensity of the subtropical Hadley cell, which is accompanied by a weakening of the trade winds in a sector of the equatorial atmospheric circulation and a decrease in the westerly transport at midlatitudes. The state of the mixture of standing and moving eddies is considered on the basis of a simple analytical model of the resonant interaction of transient (with an intermediate velocity maximum) modes in a shear flow. In this case, the amplitude of the stationary background state has the same dependence on the β effect as in the well-known Sverdrup relation for the stream function of the surface current in the ocean basin in the studies of the western boundary current intensification.
The possible existence of distinct regimes of barotropic circulation in closed annular channels at the same external parameters governing the flow dynamics is investigated both experimentally and numerically. Transitions between the regimes are realized by means of varying the value of the main parameter determining the velocity field energy (for example, the current controlling the Ampere force in the case of MHD generation of a velocity field) with subsequent reconstruction of the former parameter value. Depending on the channel rotation period or the configurations of magnet locations in the case of MHD generation or sources and sinks in numerical experiments the following results are possible. (1) The initial and final regimes differ quantitavely in the number of cyclonic or anticyclonic vortices generatted. (2) The number of vortex formations does not change but their localization in space, for example, the angular coordinates of their centers, varies. (3) After the change and reconstruction of the original value of the governing parameter the flow returns to the regime almost undistinguishable from the original regime. The flow patterns and the corresponding diagrams for laboratory experiments and numerical simulations based on shallow water equations are presented.
The results of the laboratory and numerical experiments in circular rotating trays with thin layers of a conductive fluid under the MHD generation of small-scale velocity fields are presented. The configurations of constant magnets for MHD generation were determined based on the numerical calculations with shallow water equations. Both the laboratory and numerical experiments with rotating trays demonstrate the emergence of nonaxisymmetric structures and large-scale near-circular vortices caused by the energy transfer from the system of the externally generated small-scale vortices to the large-scale velocity fields under the action of the Coriolis force. The near-circular vortex has areas with differential rotation when the angular velocity of rotation decreases with the radius. The single large-scale vortices and wide jet flows arise in the regimes of subrotation and superrotation relative to the external rotation depending on its angular velocity. The emergence of the flow structures with the azimuthal wave number m = 2 is demonstrated, and their probable relation to the anomalies of the geomagnetic field observed on the Earth’s surface is considered.
This paper presents the results of experiments in a circular stationary and rotating channels with thin layers of conductive fluid for configurations consisting of a large number of permanent magnets and providing the MHD generation of small-scale velocity fields. The alternating radial configurations of magnets were chosen in such a way as to ensure the conservation of a discrete symmetry of their mutual arrangement relative to rotations of the circular channel around a central axis and were formed on the basis of numerical calculations with the shallow-water equations. Both in numerical and laboratory experiments, large-scale nearly circular vortices were obtained as a result of the energy transfer from the system of externally generated small-scale vortices to large-scale velocity fields (inverse cascade) under the influence of the Coriolis force in the rotating case. Single large-scale vortices and wide jet streams appear in subrotation and superrotation modes relative to external rotation, depending on its angular velocity. Rotation in a nearly circular vortex has a differential character with a decrease in the angular velocity of rotation with the radius in most area of the channel.
Methods for solving shallow-water equations that describe flows in rotating annular channels are considered and the results of numerical calculations are analyzed for the possible generation of global large-scale flows, narrow jets, and numerous small-scale vortices in laboratory experiments. External effects in fluids are induced using a mass source–sink and the MHD-method of interaction of radial electric current with the magnetic field generated by the field of permanent magnets. A central–upwind scheme modified to suit the specific aspects of geophysical hydrodynamics. Initially, this method was used to solve shallow-water equations only in hydraulic problems, such as for flows in dam breaks, channels, rivers, and lakes. Geophysical hydrodynamics (in addition to free surface and topography) requires a rotation of the system as a whole, which is accompanied by the appearance of a complex system of vortices, jets, and turbulence (these should be taken into account in the formulation of the problem). Accordingly, the basic features of the central–upwind method should be changed. The modifications should ensure that the scheme is well-balanced and choose interpolation methods for desired variables. The main result of this modification is the control over numerical viscosity affecting the fluid motion variety. The active dynamics of a large number of vortices transformed into jets or generating large-scale streams is the general result of modifications suitable for geophysical hydrodynamics. Because there are technical difficulties in the creation of an appropriate laboratory setup for modeling of geophysical flows with the help of numerous source–sinks, it will be appropriate to use numerical experiments for studying the motions generated by this method. Unlike this method, the MHD-method can be rather easily used in laboratory conditions to generate a large variety of flows and vortex currents in the channel by a relatively small number of permanent magnets. Specifically, this method made it possible to obtain large-scale circular flows over the entire channel area, jets, and systems of interacting vortices. For the purpose of experiments, the distributions of source–sinks and systems of permanent magnets over the bottom of annular channels are determined.
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.
Results of experiments are considered for flows generated by different sources-sinks of mass in the rotating annular channel with beta-effect simulation using the inclined bottom. Diagrams of regimes are presented in parameters of the dimensionless angular velocity of the zonal flow averaged over the channel width and the dimensionless angular velocity of transport of vortex perturbations of cyclonic and anticyclonic types. In experiments and the simplest linear theories, most attention is paid to diagram regions with a slow motion of vortices relative to the rotating coordinate system near the parameters for stationary Rossby waves.
Experiments on the excitation of counterpropagating zonal flows by the magnetohydrodynamic (MHD) method in a rotating cylindrical vessel with a conic bottom have been performed. Flows appear in a conducting fluid layer in the field of ring magnets under the action of a radial electric field. The velocity fields have been reconstructed by the particle image velocimetry (PIV) method. In the fast rotation regimes with a thin fluid layer, where the Rossby-Obukhov scale does not exceed the characteristic sizes of the vessel, the system of perturbations appears with almost immobile blocked anticyclones in the outer part of the flow and rapidly moving cyclones in the main stream. The diagram of regimes is plotted in the variables of the relative angular velocities of the averaged zonal flow and transfer of vortices about the system rotation axis. Attention is focused on the results for the regions of the diagram with slow motion of vortices with respect to the rotating coordinate system near the parameters for stationary Rossby waves (blocking of circulation). The results are compared to the results previously obtained in similar experiments using the source-sink method.
BACKGROUND : Wharton’s jelly of the human umbilical cord is one of the sources of multipotent mesenchymal stromal cells. The cell population obtained from the postpartum biomaterial is characterized by high proliferative and regenerative properties. Isolation of a culture of multipotent mesenchymal stromal cells from the umbilical cord does not pose a threat to the health and life of the donor. AIM : Optimization of the technique for isolating a reproducible population of multipotent mesenchymal stromal cells from Wharton’s jelly is an urgent task in biomedicine, which can accelerate the process of obtaining donor cells for cell therapy and tissue engineering. MATERIALS AND METHODS : In the study, the main techniques and methods for isolating the culture of umbilical cord stroma cells were tested, the cultivation process was optimized to increase its efficiency and reduce the time of growth of cell biomass. The effect of the components of the nutrient medium on the cells obtained from Wharton’s jelly of the human umbilical cord was studied. Currently, there is no universal composition of the growth medium; in various studies, nutrient media from different manufacturers are used, which differ in composition. The most discussed issue is the selection of serum, which is part of the nutrient medium. RESULTS : In the work, a comparative evaluation of five different sera was carried out. It has been shown that the most stable physiological parameters are observed in cell suspension samples with the addition of FBS (SKPK, Russia) and FBS (Capricorn, USA) sera. A study of the effect of hypoxia on cell culture in combination with the most effective sera showed that hypoxic stress acts as an activator of primary cell proliferation. The assessment of the effect of serum and hypoxia on cell culture was carried out visually using microscopy, assessment of changes in cell morphology during cultivation, and the results of testing the action of sera by the intensity of respiration of free and immobilized cells under the action of inhibitors. CONCLUSION : As a result of the experiments, the influence of the type of serum on the initiation of cell expansion from primary explants and further cell proliferation in vitro was established. Hypoxia during exposure of primary explants en-hances the expansion of cells from tissue fragments of Wharton’s jelly tissue.
The results of experiments on turbulent flows excited by the Ampere force in a thin layer of a conducting fluid over a solid surface upon the passage of a current and the action of a spatially periodic magnetic field are considered. Third-order longitudinal structure functions of the velocity field are shown to be approximately linear in the spatial shift and negative even at horizontal scales that exceed the layer thickness by an order of magnitude. This is how the three-dimensional dynamics is manifested as a result of the dominant contribution of energy dissipation when the no-slip boundary condition is satisfied on the lower surface. Dissipation and the main summands of energy production have been estimated for the energy-balance equation.
The results of experiments for turbulent flows in a thin layer of conducting fluid above a solid surface generated by the Ampere force when passing a current and under the action of a spatially periodic magnetic field are considered. The statistical characteristics of the flows are shown to exhibit three-dimensional (3D) dynamics even on horizontal scales exceeding the layer thickness by an order of magnitude. In this case, the third-order longitudinal structure functions of the velocity field are approximately linear in spatial displacement and negative, as in 3D turbulence, due to the dominant contribution of energy dissipation when the boundary condition for adhesion on the lower surface is met. The dissipation and basic energy production terms are estimated for the energy balance equation.
This paper analyzes the properties of solutions to the equations describing the motion of a stratified fluid in the class of velocity and temperature fields linear in coordinates. For an ideal fluid, these equations, on the one hand, are exact for the corresponding hydrodynamic problem and, on the other hand, are identical to the equations of motion for a heavy top. In a conservative case, the equations of motion of a top share common solutions with the equations of geophysical fluid dynamics and reproduce motions similar to those existing in the theory of the large-scale atmospheric circulation. This study considers the effects of viscosity and heat conduction in the fluid, which are, in a sense, similar to the effect of friction in the case of a top. The influence of deflections of the vectors of gravity and external rotation from their standard directions for a plane-parallel atmosphere is also considered. The regimes of motions that are described by the starting equations and approximations commonly used to model the atmospheric general circulation (the quasi-geostrophic approximation) are analyzed. It is shown that these equations correctly describe the Hadley and Rossby circulation regimes and transitions between them that are observed in numerical and laboratory experiments. Particular attention is given to the consistency between different regimes of the exact equations and their quasi-geostrophic approximations, which is manifested for small Rossby numbers and is generally absent for large Rossby numbers. The asymptotic behaviors of the curves of transition between the Hadley and Rossby regimes under the conditions of breaking the external symmetry of flows are obtained. These asymptotics explain the corresponding transition boundaries for the regimes observed in the known experiments in annuluses.
Finite-dimensional Galerkin approximations taking into account the vertical distribution of the velocity field in thin layers are used to determine bottom-friction effects in a plane-parallel incompressible flow. The resulting simplified equations governing the quasi-two-dimensional dynamics of the velocity field involve, in addition to the Rayleigh friction, relaxation-type terms with a characteristic dependence on the preceding history. For long-wavelength disturbances, these dependences are equivalent to the renormalization of non-linear terms and linear-friction values. When the corresponding approximations are used for two-dimensional hydrodynamic equations (in particular, for shallow-water equations), a scheme with a relatively small number of variables is obtained from calculations with a low-resolution finite-element method. This scheme includes higher (than linear) functions of horizontal coordinates in the representations of the velocity field and the height of the free surface. It is shown that including such fields results in the smoothing of oscillations on scales on the order of the sizes of finite elements. Such oscillations arise from an insufficient resolution of small-scale motions in the numerical scheme. As a consequence, the amplitudes of large-scale motions change.
This paper proposes a sequence of dynamic systems that are intermediate between the ceostrophic approximation [1], which determines slow motions, and exact equations of a stratified fluid in a ellipsoidal hollow. Allowance for fast oscillations leads to both a significant change in the frequencies of slow motions with increasing stratification parameter and a change in the amplitudes of the motions compared to that of the geostrophic motion, for which fast modes are filtered out. One of the reductions represents a linearized form of the equations of a heavy top and makes it possible to analytically estimate the deviation of phase trajectories from the geostrophic one. Based on an estimate made for the ageostrophic component, two systems extending the oeostrophic approximation are obtained. These systems more accurately describe the slow dynamics of a top even near the critical parameter of vertical stratification. An averaging procedure for the equations of a top that are reduced to a normal form is also discussed. It is found that, near the critical stratification, such averaging C, yields a greater deviation of trajectories from the exact ones in comparison with one of the systems obtained in extending the geostrophic approximation.
An ocean eddy is modeled by a rotating cylindrical eddy in the incident flow. If flow parameters (flow velocity, the eddy radius or angular velocity of rotation) are nonstationary, passive pollutant particles can exchange between external-flow and vortex areas. In this work, estimates of the width of this exchange boundary layer are obtained depending on the parameters of nonstationary perturbations. Comparison with the results of numerical experiments is performed for a model dynamical system.
