scholarly journals QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

2008 ◽  
Vol 1 (1) ◽  
pp. 187-241
Author(s):  
P. D. Williams ◽  
T. W. N. Haine ◽  
P. L. Read ◽  
S. R. Lewis ◽  
Y. H. Yamazaki
Keyword(s):  
Laboratory Experiments ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Rotating Fluids ◽  
Stochastic Forcing ◽  
Internal Interface ◽  
Time Stepping ◽  
Beta Effect ◽  
Fluid Layers ◽  
Special Case

Abstract. QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

scholarly journals QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

2009 ◽  
Vol 2 (1) ◽  
pp. 13-32 ◽  
Author(s):  
P. D. Williams ◽  
T. W. N. Haine ◽  
P. L. Read ◽  
S. R. Lewis ◽  
Y. H. Yamazaki
Keyword(s):  
Laboratory Experiments ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Rotating Fluids ◽  
Stochastic Forcing ◽  
Internal Interface ◽  
Time Stepping ◽  
Beta Effect ◽  
Fluid Layers ◽  
Special Case

Abstract. QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

Theoretical and Numerical Investigation of a Special Case of a Rotating Chain: The Helicoseir Problem

2005 ◽  
Author(s):  
Wan-Suk Yoo ◽  
Oleg Dmitrochenko ◽  
Sang-Hyuk Mun ◽  
Hyun-Woo Lee
Keyword(s):  
Bessel Functions ◽  
Absolute Nodal Coordinate Formulation ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Nonlinear Partial Differential Equations ◽  
Dimensional Model ◽  
Absolute Nodal Coordinate ◽  
Qualitative And Quantitative ◽  
Inertia Forces ◽  
Special Case

A physically simple but mathematically cumbrous problem of rotating heavy chain with one fixed top point is studied. Nonlinear partial differential equations of motion in 3D case are derived as well as ones for 2D shapes of relative equilibrium. The equations are found very complicated and solved numerically. A linear case of small displacements is analyzed in terms of Bessel functions. The qualitative and quantitative behaviour of the problem is discussed with the help of bifurcation diagram. Dynamics of the two-dimensional model near the equilibrium positions is studied with the help of simulation using the absolute nodal coordinate formulation (ANCF); the equilibriums are found unstable. The reason of instability is explained using a variational principle. Analysis of 3D motion in the rotating frame shows that Coriolis inertia forces can stabilize the motion. 3D numerical simulation using ANCF shows that the spatial motion of the helicoseir is stable and looks like self-excited oscillations near the flat instable configurations that were obtained before.

On Some Issues in Shakedown Analysis

2001 ◽  
Vol 68 (5) ◽  
pp. 799-808 ◽  
Author(s):  
G. Maier
Keyword(s):  
Heterogeneous Media ◽  
Direct Methods ◽  
Cost Effective ◽  
Upper Bounds ◽  
Saturated Porous Media ◽  
Safety Factors ◽  
Shakedown Analysis ◽  
Time Stepping ◽  
Kinematic Theorem ◽  
Special Case

Shakedown analysis, and its more classical special case of limit analysis, basically consists of “direct” (as distinct from time-stepping) methods apt to assess safety factors for variable repeated external actions and procedures which provide upper bounds on history-dependent quantities. The issues reviewed and briefly discussed herein are: some recent engineering-oriented and cost-effective methods resting on Koiter’s kinematic theorem and applied to periodic heterogeneous media; recent extensions (after the earlier ones to dynamics and creep) to another area characterized by time derivatives, namely poroplasticity of fluid-saturated porous media. Links with some classical or more consolidated direct methods are pointed out.

Model Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes

1999 ◽  
Author(s):  
E. Pesheck ◽  
C. Pierre ◽  
S. W. Shaw
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Single Equation ◽  
Rotating Beam ◽  
Model Size ◽  
Nonlinear Normal

Abstract Equations of motion are developed for a rotating beam which is constrained to deform in the transverse (flapping) and axial directions. This process results in two coupled nonlinear partial differential equations which govern the attendant dynamics. These equations may be discretized through utilization of the classical normal modes of the nonrotating system in both the transverse and extensional directions. The resultant system may then be diagonalized to linear order and truncated to N nonlinear ordinary differential equations. Several methods are used to determine the model size necessary to ensure accuracy. Once the model size (N degrees of freedom) has been determined, nonlinear normal mode (NNM) theory is applied to reduce the system to a single equation, or a small set of equations, which accurately represent the dynamics of a mode, or set of modes, of interest. Results are presented which detail the convergence of the discretized model and compare its dynamics with those of the NNM-reduced model, as well as other reduced models. The results indicate a considerable improvement over other common reduction techniques, enabling the capture of many salient response features with the simulation of very few degrees of freedom.

scholarly journals Spherical vortices in rotating fluids

2018 ◽  
Vol 846 ◽  
Author(s):  
M. M. Scase ◽  
H. L. Terry
Keyword(s):  
Ideal Fluid ◽  
Rotation Rate ◽  
Wave Motion ◽  
Infinite Family ◽  
Vortex Rings ◽  
Rotating Fluids ◽  
Critical Rotation ◽  
Spherical Vortex ◽  
Inertial Wave ◽  
Special Case

A popular model for a generic fat-cored vortex ring or eddy is Hill’s spherical vortex (Phil. Trans. R. Soc. A, vol. 185, 1894, pp. 213–245). This well-known solution of the Euler equations may be considered a special case of the doubly infinite family of swirling spherical vortices identified by Moffatt (J. Fluid Mech., vol. 35 (1), 1969, pp. 117–129). Here we find exact solutions for such spherical vortices propagating steadily along the axis of a rotating ideal fluid. The boundary of the spherical vortex swirls in such a way as to exactly cancel out the background rotation of the system. The flow external to the spherical vortex exhibits fully nonlinear inertial wave motion. We show that above a critical rotation rate, closed streamlines may form in this outer fluid region and hence carry fluid along with the spherical vortex. As the rotation rate is further increased, further concentric ‘sibling’ vortex rings are formed.

Dynamics of the Elastica With End Mass and Follower Loading

1990 ◽  
Vol 57 (1) ◽  
pp. 203-208 ◽  
Author(s):  
J. M. Snyder ◽  
J. F. Wilson
Keyword(s):  
Internal Pressure ◽  
Large Deformations ◽  
Equations Of Motion ◽  
Dynamic Responses ◽  
Cantilever Beams ◽  
Static Responses ◽  
Tube Type ◽  
Payload Mass ◽  
Nonlinear Equations Of Motion ◽  
Special Case

Orthotropic, polymeric tubes subjected to internal pressure may undergo large deformations while maintaining linear moment-curvature behavior. Such tubes are modeled herein as inertialess, elastic cantilever beams (the elastica) with a payload mass at the tip and with internal pressure as the eccentric tip follower loading that drives the configurations through large deformations. From the nonlinear equations of motion, dynamic beam trajectories are calculated over a range of system parameters for the special case of a point mass at the tip and a terminated ramp pressure loading. The dynamic responses, which are unique because the loading history and the range of motion are fully defined, are presented in nondimensional form and are compared to static responses presented in a companion study. These results are applicable to the dynamic design of high flexure, tube-type, robotic manipulator arms.

Unilateral Impact and Contact of Elastic Structures Using Lagrangian Multipliers

2011 ◽  
Author(s):  
Sebastian Tatzko
Keyword(s):  
Equations Of Motion ◽  
Structural Equations ◽  
Contact Forces ◽  
Integration Scheme ◽  
Lagrangian Multiplier ◽  
Elastic Structures ◽  
Lagrangian Multipliers ◽  
Linear Elastic ◽  
Time Stepping ◽  
Numerical Effort

This paper deals with linear elastic structures exposed to impact and contact phenomena. Within a time stepping integration scheme contact forces are computed with a Lagrangian multiplier approach. The main focus is turned on a simplified solving method of the linear complementarity problem for the frictionless contact. Numerical effort is reduced by applying a Craig-Bampton transformation to the structural equations of motion.

The perception of light—dark transitions

1983 ◽  
Vol 303 (1116) ◽  
pp. 523-536 ◽  
Keyword(s):  
Circadian Rhythms ◽  
Circadian Clock ◽  
Laboratory Experiments ◽  
Light Quality ◽  
Accurate Method ◽  
Dark Light ◽  
Timing Mechanism ◽  
Rapid Formation ◽  
Special Case ◽  
Dark Transition

Transitions between light and darkness are particularly important where these serve as Zeitgebers to synchronize circadian rhythms. A special case is photoperiodism, which depends on the accurate detection of light—dark transitions and on the coupling of this information to a timing mechanism that appears to be based on the circadian clock. Results from laboratory experiments are considered in relation to the natural changes experienced at dawn and dusk, and evidence is presented that the light—dark transitions that couple to the timing mechanism in short-day plants are perceived through changes in irradiance rather than through changes in light quality. It has been generally accepted that the light—dark transition is sensed by a decrease of P fr levels in darkness, whereas dark—light is sensed by the rapid formation of P fr in the light. However, P fr in light-grown plants appears to be rather stable and so changes in P fr level after transfer to darkness may not be a sufficiently accurate method of detecting the light—dark transition in photoperiodism. The paper reviews some of the evidence from photoperiodic experiments and concludes that the plant may discriminate between light and darkness through the continuous or intermittent formation o f ‘new’ P fr .

Sign in / Sign up

Export Citation Format

Share Document