On the baroclinic dynamics, hamiltonian formulation and general stability characteristics of density-driven surface currents and fronts over a sloping continental shelf

1993 ◽  
Vol 345 (1675) ◽  
pp. 295-325 ◽  
Keyword(s):  
Continental Shelf ◽  
Nonlinear Stability ◽  
Shallow Water Equation ◽  
Hamiltonian Formulation ◽  
Sufficient Conditions ◽  
Regularity Conditions ◽  
Mean Flow ◽  
Governing Equations ◽  
Flow Vorticity ◽  
Formal Stability

A new theory is presented to describe the baroclinic dynamics of density-driven currents and fronts over a sloping continental shelf. The frontal dynamics is geostrophic to leading-order but not quasi-geostrophic since the dynamic frontal height is not small in comparison with the scale frontal thickness. The evolution of the underlying slope water is modelled quasigeostrophically and includes the influence of a background vorticity gradient due to the sloping bottom . The two layers are coupled together via baroclinic vortex-tube stretching associated with the perturbeddensity-driven current. The current dynamics includes the advection of mean flow vorticity . The model equations are obtained in a formal asymptotic expansion of there levant two-layer shallow-water equation sand boundary conditions. It is shown that the governing equations for the model can be put in to non-canonical hamiltonian form. A comprehensive analysis of the general linear and nonlinear stability characteristics of the governing equations is given. The normal mode problem associated with steady along-shore currents is studied and sufficient stability and necessary instability conditions are presented. It is shown that a zero in the frontal vorticity gradient is not needed for instability. Jump conditions for the perturbation frontal thickness are systematically derived associated with the continuity of pressure and normal mass flux for steady frontal configurations that possess discontinuities in the velocity or vorticity, and rigorous regularity conditions are obtained for the perturbation thickness on outcroppings. The formal stability of arbitrary steady currents is studied. It is shown how to obtain general steady current solutions as a variational solution to a suitably constrained hamiltonian. General criteria are obtained for establishing the linear stability of these steady density-driven currents in the sense of Liapunov. In the limit of steady parallel along-shore flow, the formal stability results reduce to the sufficient conditions found for the normal modes. Finally, the nonlinear stability of steady density-driven currents and fronts is studied. Based on the formal stability analysis, appropriate convexity hypothesis are found that rigorously establish nonlinear stability of steady currents in the sense of Liapunov, and establish nonlinear saturation bounds on the perturbation flow with respect to a potential enstrophy/energy norm .

Mixed State Hamiltonian Element for Plane Transversely Isotropic Magnetoelectroelastic Solids

2013 ◽  
Vol 275-277 ◽  
pp. 1978-1983
Author(s):  
Xiao Chuan Li ◽  
Jin Shuang Zhang
Keyword(s):  
Mixed State ◽  
Hamiltonian Formulation ◽  
Transversely Isotropic ◽  
Laminated Plates ◽  
Governing Equations ◽  
Time Coordinate ◽  
First Order ◽  
Linear Elements ◽  
Propagation Matrix ◽  
Magnetoelectroelastic Solids

Hamiltonian dual equation of plane transversely isotropic magnetoelectroelastic solids is derived from variational principle and mixed state Hamiltonian elementary equations are established. Similar to the Hamiltonian formulation in classic dynamics, the z coordinate is treated analogous to the time coordinate. Then the x-direction is discreted with the linear elements to obtain the state-vector governing equations, which are a set of first order differential equations in z and are solved by the analytical approach. Because present approach is analytic in z direction, there is no restriction on the thickness of plate through the use of the present element. Using the propagation matrix method, the approach can be extended to analyze the problems of magnetoelectroelastic laminated plates. Present semi-analytical method of mixed Hamiltonian element has wide application area.

Mesoscale, tidal and seasonal/interannual drivers of the Weddell Sea overturning circulation

2021 ◽  
Keyword(s):  
Continental Shelf ◽  
Shelf Break ◽  
Weddell Sea ◽  
Global Ocean ◽  
Mean Flow ◽  
Ice Shelf ◽  
Overturning Circulation ◽  
Global Circulation ◽  
Interannual Fluctuations ◽  
Continental Shelf Break

Abstract The Weddell Sea supplies 40–50% of the Antarctic BottomWaters that fill the global ocean abyss, and therefore exerts significant influence over global circulation and climate. Previous studies have identified a range of different processes that may contribute to dense shelf water (DSW) formation and export on the southern Weddell Sea continental shelf. However, the relative importance of these processes has not been quantified, which hampers prioritization of observational deployments and development of model parameterizations in this region. In this study a high-resolution (1/12°) regional model of the southern Weddell Sea is used to quantify the overturning circulation and decompose it into contributions due to multi-annual mean flows, seasonal/interannual variability, tides, and other sub-monthly variability. It is shown that tides primarily influence the overturning by changing the melt rate of the Filchner-Ronne Ice Shelf (FRIS). The resulting ~0.2 Sv decrease in DSW transport is comparable to the magnitude of the overturning in the FRIS cavity, but small compared to DSW export across the continental shelf break. Seasonal/interannual fluctuations exert a modest influence on the overturning circulation due to the relatively short (8-year) analysis period. Analysis of the transient energy budget indicates that the non-tidal, sub-monthly variability is primarily baroclinically-generated eddies associated with dense overflows. These eddies play a comparable role to the mean flow in exporting dense shelf waters across the continental shelf break, and account for 100% of the transfer of heat onto the continental shelf. The eddy component of the overturning is sensitive to model resolution, decreasing by a factor of ~2 as the horizontal grid spacing is refined from 1/3° to 1/12°.

Subsonic Turbulent Flow Past a Planar Fence

1979 ◽  
Vol 101 (3) ◽  
pp. 373-375
Author(s):  
M. L. Agarwal ◽  
P. K. Pande ◽  
Rajendra Prakash
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flow Field ◽  
Boundary Conditions ◽  
Mean Flow ◽  
Governing Equations ◽  
Flow Past ◽  
Entire Flow ◽  
The Mean ◽  
Shape And Size

The mean flow past a fence submerged in a turbulent boundary layer is numerically simulated. The governing equations have been simplified by neglecting the convective effects of turbulence and solved numerically using experimental boundary conditions. The information obtained includes the shape and size of the upstream and downstream separation bubbles and the streamline pattern in the entire flow field. General agreement between the simulated and the experimental flow field was found.

A Practical Combined Computation Method of Mean Through-Flow for 3D Inverse Design of Hydraulic Turbomachinery Blades

2005 ◽  
Vol 127 (6) ◽  
pp. 1183-1190 ◽  
Author(s):  
Guoyi Peng
Keyword(s):  
Inverse Design ◽  
Computation Method ◽  
Rotational Flow ◽  
Computational Results ◽  
Mean Flow ◽  
Governing Equations ◽  
Kaplan Turbine ◽  
Through Flow ◽  
Turbomachinery Blades ◽  
The Mean

A practical combined computation method of the circumferentially averaged mean through-flow is presented for 3D inverse computations of hydraulic turbomachinery blades to consider the influence of interrelated hydraulic components. A comprehensive computation domain including the runner blades and related components is adopted and the mean flow is calculated altogether by solving a set of rotational flow governing equations simultaneously. The method has been applied to the case of Kaplan turbine. Computational results were compared to experimental data and their agreement was confirmed. Numerical investigation indicates that the mean flow is dependent on the configuration of guide vanes and the effect of runner blades reaches to the far upstream. The importance of properly taking account of the effect of blade geometry and the influence of interrelated hydraulic components is demonstrated.

On the Propagation of Sound in a High-Speed Non-Isothermal Shear Flow

2009 ◽  
Vol 8 (3) ◽  
pp. 199-230 ◽  
Author(s):  
L.M.B.C. Campos ◽  
M.H. Kobayashi
Keyword(s):  
Wave Equation ◽  
Shear Flow ◽  
Acoustic Wave ◽  
Sound Speed ◽  
High Speed ◽  
Shear Flows ◽  
Critical Layer ◽  
Acoustic Wave Equation ◽  
Mean Flow ◽  
Flow Vorticity

The propagation of sound in shear flows is relevant to the acoustics of wall and duct boundary layers, and to jet shear layers. The acoustic wave equation in a shear flow has been solved exactly only for a plane unidirectional homentropic mean shear flow, in the case of three velocity profiles: linear, exponential and hyperbolic tangent. The assumption of homentropic mean flow restricts application to isothermal shear flows. In the present paper the wave equation in an plane unidirectional shear flow with a linear velocity profile is solved in an isentropic non-homentropic case, which allows for the presence of transverse temperature gradients associated with the ***non-uniform sound speed. The sound speed profile is specified by the condition of constant enthalpy, i.e. homenergetic shear flow. In this case the acoustic wave equation has three singularities at finite distance (besides the point at infinity), viz. the critical layer where the Doppler shifted frequency vanishes, and the critical flow points where the sound speed vanishes. By matching pairs of solutions around the singular and regular points, the amplitude and phase of the acoustic pressure in calculated and plotted for several combinations of wavelength and wave frequency, mean flow vorticity and sound speed, demonstrating, among others, some cases of sound suppression at the critical layer.

Orientation and rotation of inertial disk particles in wall turbulence

2015 ◽  
Vol 766 ◽  
Author(s):  
Niranjan Reddy Challabotla ◽  
Lihao Zhao ◽  
Helge I. Andersson
Keyword(s):  
Translational Motion ◽  
Turbulent Channel Flow ◽  
Stokes Number ◽  
Wall Turbulence ◽  
Rotational Inertia ◽  
Inertial Particles ◽  
Mean Flow ◽  
Flow Vorticity ◽  
Oblate Spheroids ◽  
The Mean

AbstractThe translational and rotational dynamics of oblate spheroidal particles suspended in a directly simulated turbulent channel flow have been examined. Inertial disk-like particles exhibited a significant preferential orientation in the plane of the mean shear. The rotational inertia about the symmetry axis of the disk-like particles hampered the spin-up of the flattest particles to match the mean flow vorticity. The influence of the particle shape on the orientation and rotation diminished as the translational inertia increased from Stokes number 1 to 30. An isotropization of both orientation and rotation could be observed in the core region of the channel. The translational motion of the oblate spheroids had a weak dependence on the aspect ratio. We therefore concluded that inertial particles sample nearly the same flow field irrespective of shape. Nevertheless, the orientation and rotation of disk-like particles turned out to be qualitatively different from the dynamics of fibre-like particles.

A STUDY OF MICROPOLAR FLUID IN AN ANNULAR TUBE WITH APPLICATION TO BLOOD FLOW

2008 ◽  
Vol 08 (04) ◽  
pp. 561-576 ◽  
Author(s):  
P. MUTHU ◽  
B. V. RATHISH KUMAR ◽  
PEEYUSH CHANDRA
Keyword(s):  
Cross Section ◽  
Micropolar Fluid ◽  
Oscillatory Flow ◽  
Flow Characteristics ◽  
Annular Region ◽  
Mean Flow ◽  
Governing Equations ◽  
Tube Radius ◽  
Annular Tube ◽  
Fluid Parameters

The oscillatory flow of micropolar fluid in an annular region with constriction, provided by variation of the outer tube radius, is investigated. It is assumed that the local constriction varies slowly over the cross-section of the annular region. The nonlinear governing equations of the flow are solved using a perturbation method to determine the flow characteristics. The effect of micropolar fluid parameters on mean flow and pressure variables is presented.

scholarly journals Two Different Classes of Wronskian Conditions to a (3 + 1)-Dimensional Generalized Shallow Water Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Yaning Tang ◽  
Pengpeng Su
Keyword(s):  
Shallow Water ◽  
Shallow Water Equation ◽  
Sufficient Conditions ◽  
Wronskian Technique ◽  
Rational Solutions ◽  
Bilinear Method ◽  
Wronskian Determinant ◽  
Linear Partial Differential Equations ◽  
Hirota Bilinear Equation ◽  
Hirota Bilinear

Based on the Hirota bilinear method and Wronskian technique, two different classes of sufficient conditions consisting of linear partial differential equations system are presented, which guarantee that the Wronskian determinant is a solution to the corresponding Hirota bilinear equation of a (3+1)-dimensional generalized shallow water equation. Our results show that the nonlinear equation possesses rich and diverse exact solutions such as rational solutions, solitons, negatons, and positons.

Nonlinear Shallow-Water Flow on Deck

1996 ◽  
Vol 40 (04) ◽  
pp. 303-315
Author(s):  
Zhenjia Huang ◽  
Chi-Chao Hsiung
Keyword(s):  
Shallow Water ◽  
Water Flow ◽  
Shallow Water Equation ◽  
Splitting Method ◽  
Numerical Results ◽  
Governing Equations ◽  
Shallow Water Flow ◽  
Step Method ◽  
Fractional Step Method ◽  
Flux Difference

Euler's equations have been used for nonlinear shallow-water flow on deck. The equations are simplified under the shallow-water assumption to obtain the governing equations. The Flux-Difference Splitting method is devised to solve this shallow-water flow problem. The flux-difference in the governing equations is split based on characteristic directions. The Superbee flux limiter is employed in the algorithm to make the finite-difference scheme of second order with high resolution. For two-dimensional decks, numerical results are presented to reveal the characteristics of shallowwater flow on deck. For three-dimensional decks, the Flux-Difference Splitting method together with the Fractional Step method are used, so that solutions of the shallow-water equation can be obtained by solving two sets of one-dimensional differential equations. Numerical results are presented to show the wave patterns for different modes of motion excitation. Velocity vectors in the flow field are also given to help understand the flow properties.

Some Remarks Concerning (f, dn) and [F, dn] Summability Methods

1969 ◽  
Vol 21 ◽  
pp. 1361-1365 ◽  
Author(s):  
C. F. Koch
Keyword(s):  
Entire Function ◽  
Sufficient Conditions ◽  
Regularity Conditions ◽  
Complex Numbers ◽  
Lebesgue Constants ◽  
Regularity Theorem ◽  
Summability Methods

In this paper we note a simple connection between the (ƒ, dn) method of summability (defined by Smith (8)) and a composition of [F, dn] (defined by Jakimovski (4)) and Sonnenschein methods (9; 10). This connection is then used to supply some sufficient conditions for the regularity of (ƒ, dn) methods by using known regularity conditions for various [F, dn] and Sonnenschein methods. Finally, the connection is further exploited to obtain information about the Lebesgue constants for a certain class of [F, dn] methods by investigating related (ƒ, dn) methods.2. Definitions and the regularity theorem. The (ƒ, dn) method of summability is defined by Smith (8) essentially as follows. Letƒ(z) be a nonconstant entire function satisfying ƒ (l) = 1 and let {dn} be a sequence of complex numbers satisfying dt ≠ – 1, di ≠ – ƒ(0) (i ≧ 1).

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