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The present work is devoted to the numerical study of the stability of shallow jet. The effects of important parameters on the stability behavior for large scale shallow jets are considered and investigated. Connections between the stability theory and observed features reported in the literature are emphasized. The paper aims to discuss these issues.

A linear stability analysis of shallow jet incorporating the effects of bottom topography, bed friction and viscosity has been carried out by using the shallow water stability equation derived from the depth averaged shallow water equations in conjunction with both Chézy and Manning resistance formulae. Effects of the following main factors on the stability of shallow water jets are examined: Rossby number, bottom friction number, Reynolds number, topographic parameters, base velocity profile and resistance model. Special attention has been paid to the Coriolis effects on the jet stability by limiting the rotation number in the range of Ro∈[0, 1.0].

It is found that the Rossby number may either amplify or attenuate the growth of the flow instability depending on the values of the topographic parameters. There is a regime where the near cancellation of Coriolis effects due to other relevant parameters influences is responsible for enhancement of stability. The instability can be suppressed by the bottom friction when the bottom friction number is large enough. The amplification rate may become sensitive to the relatively small Reynolds number. The stability region using the Manning formula is larger than that using the Chézy formula. The combination of these effects may stabilize or destabilize the shallow jet flow. These results of the stability analysis are compared with those from the literature.

Results of linear stability analysis on shallow jets along roughness bottom bed are presented. Different from the previous studies, this paper includes the effects of bottom topography, Rossby number, Reynolds number, resistance formula and bed friction. It is found that the influence of Reynolds number on the stability of the jet is notable for relative small value. Therefore, it is important to experimental investigators that the viscosity should be considered with comparison to the results from inviscid assumption. In contrast with the classical analysis, the use of multi-parameters of the base velocity and topographic profile gives an extension to the jet stability analysis. To characterize the large scale motion, besides the bottom friction as proposed in the related literature, the Reynolds number Re, Rossby number Ro, the topographic parameters and parameters controlling base velocity profile may also be important to the stability analysis of shallow jet flows.

The artificial compressibility method is used to analyze internal flows in rotating ducts having strong curvature. This study was concerned with the laminar flow of an incompressible Newtonian fluid having constant viscosity in circular and square ducts with a 908 bend. The emphasis of the present simulation is to determine the effect of rotation and through‐flow rate on the fluid physics and friction characteristics in the straight channel and in the curved geometric regions. The Reynolds numbers ranged from 100 to 790 and the Rossby numbers from 0 to 0.4. Coriolis forces arising from rotation produce a non‐symmetric secondary flow in the bend that increases the loss coefficient as compared with the values for non‐rotation. In addition, the wall friction losses in the straight outlet section are increased, and both effects are directly proportional to the Rossby number.

In this paper, we consider the fundamental characteristics of motion in the universe in terms of the whole and local evolutionary forms of fluids, based on the theory of blown‐ups and the experiment of spinning disc of currents. It is pointed out that the practical meaning of “the invisible Tao”, see Lao Tsu for more details, is that of currents, and the central theory of fluid dynamics is the vortex flow dynamics, and the practicability of the nonlinear evolutions of mathematical models is getting away from the assumption of continuity.

A finite element method based investigation is carried out for the determination of three‐dimensional turbulent flow structures and heat transfer rates of cooling ducts within turbine blades which rotate about an axis orthogonal to their own axis of symmetry. The effects of geometrical configurations, Coriolis forces and coolant inertias on the hydrodynamic and thermal characteristics have been systematically predicted and compared with experimental measurements.

A numerical study is performed to investigate flow instability phenomena in a square channel with steady, laminar throughflow. The channel rotates around an axis perpendicular to the channel longitudinal axis. The flow field extends from the channel entrance to a distance of 120 to 600Dh. The range of Reynolds number is Re = 300−2000. The inlet flow velocity is assumed uniform. Surface vorticity intensity is introduced to indicate the variation of vortices. It is revealed that at intermediate Reynolds numbers (680 > Re > 300), the flow is characterized by three vortex patterns: at slow rotation there is one vortex pair; at intermediate rotation a secondary vortex, in addition to the original vortex, emerges near the trailing wall and then breaks down downstream; and at rapid rotation the secondary vortex does not exist with the flow being restabilized to form a single‐pair vortex pattern. At low Reynolds numbers (Re ≤ 300), the flow exhibits a single‐pair vortex pattern, while at high Reynolds numbers (Re ≥ 680), the flow experiences the emergence and breakdown of a secondary vortex, but no restabilization is found with an increase in the rotational speed. It is also disclosed that the variation of the vortices is related to the distance from the inlet.

Based on the summary and analysis of the particle dynamics, developed in the past 300 years, and of fundamental properties of unevenness of natural materials, we propose the opinion of the second stir. We analyze the gains and loses of employing the non‐dimensionalization method developed in the quantitative analysis system of the first push. Combined with some theoretical models, we also consider the epistemological failures of pure quantification, linearization, and formal logic analysis.

Blown up theory is very important in modern forecasting science, and will result in revolution not only in forecasting theories but also in applied theories and applied methods. Moreover, the blown‐up theory will involve re‐thinking and re‐formulation of some concepts in traditional theories. This article is a record of dialogue between Professor OuYang and the author on some important issues. It is believed that this record will not only benefit us greatly, but also be inductive for young generations in developing their way of thinking and research directions.

A numerical study of a quantitative analogy of fully developed turbulent flow in a straight square duct rotating about an axis perpendicular to that of the duct and a stationary curved duct of square cross‐section was carried out. In order to compare the two flows, the dimensionless parameters K_TR=Re^1/4/√Ro and the Rossby number, Ro=w_m/Ωd_h, in the rotating straight duct flow corresponded to K_TC=Re^1/4/√λ and the curvature ratio, λ=R/d_h, in the stationary curved duct flow, so that they had the same dynamical meaning as those parameters for fully developed laminar flow. For the large values of Ro or λ, the flow field satisfied the “asymptotic invariance property”; there were strong quantitative similarities between the two flows, such as in the flow patterns and friction factors for the same values of K_TR and K_TC. Based on these similarities, it is possible to predict the flow characteristics in rotating ducts by considering the flow in stationary curved ducts, and vice versa.

To investigate the effect of aspect ratio on the quantitative analogy between developing laminar flows in orthogonally rotating straight ducts and stationary curved ducts

A fractional step method is used to obtain the numerical solution of the governing equations by decoupling the solution of the momentum equations from the solution of the continuity equation. In order to clarify the similarity of the two flows, dimensionless parameters K_LR and Rossby number, Ro, in a rotating straight duct were used as a set corresponding to Dean number, K_LC, and curvature ratio, λ, in a stationary curved duct.

Under the condition that the aspect ratio was larger than one and that the magnitude of Ro or λ was large enough to satisfy the “asymptotic invariance property” the quantitative analogy between the two flows was established clearly.

As the aspect ratio decreased below one, the difference between the secondary flow intensities of these two flows increased, and therefore, the analogy between the two flows was not as evident as that for the larger aspect ratios.

Based on this methodology, the characteristics of the developing flow in orthogonally rotating ducts of higher aspect ratio can be predicted by considering the flow in stationary curved ducts, and vice versa.

The results obtained in this study will suggest an optimal criterion for the application of this approach to the flow similarity analysis in rectangular ducts with arbitrary aspect ratios.

In this paper, mathematical properties of nonlinearity of the equations in Navier‐Stokes model of currents are studied based on the reasoning logic of systems evolutions, combined with methods of analysis and synthesis. It is discovered that the derivative terms are the same as the nonlinear forcing term, in that they all evolve with time and contain discontinuous reversing changes. Consequently, a theoretical and application system is proposed. The concept of blown‐ups constitutes a key step toward the understanding of whole evolution of non‐linear models. The range of applications of this concept is not only limited to research of almost 240‐years‐old mystery of the nonlinearity of currents, but also encompasses the reconsideration of many important principled issues in various theoretical disciplines and related applications.