Interactions between mean flow and finite-amplitude mesoscale eddies in a barotropic ocean

Abstract

For the purpose of deriving an analytical parametrization, oceanic mesoscale eddies are represented as a horizontally propagating wave field in a non-uniform environment. The mathematical analysis rests upon the assumption of scale disparity between a short eddy scale and a long mean-flow scale. The novelty resides in the treatment of finite-amplitude eddies, which, moreover, form either a band-like or a cell-like pattern. A barotropic ocean is chosen as a first step to illustrate the mathematical analysis, but dissipation is included. The main result is an analytical derivation of a mesoscale-eddy parametrization: the mean-flow equation contains Reynolds-stress terms which are computed from parameters of the eddy field, which, in turn, are predicted by separate evolution equations. Due to restrictive assumptions (barotropy, orthogonal waves,…), the parametrization established here should be viewed only as a first step toward the design of a more practical parameterization for large-scale modelling.     

Spectral multigrid and collocation methods for barotropic nondivergent flow over irregular coastal topography

Abstract

We describe the high-resolution spectral modelling of nondivergent barotropic linearized flow over steep irregular topography. We use collocation to evaluate spatial derivatives in the barotropic vorticity equation, and a spectral multigrid technique to accelerate the iterative solution of the vorticity—stream function relation. The computational domain is a rectangular channel, which can be conformally mapped into more interesting shapes, as we also discuss. A Fourier-series representation is used in the (periodic) direction parallel to the walls of the channel, and a sine series in the cross-channel direction. For much of the paper we concentrate on the numerical techniques, though results are provided, including an application to the Bass Strait region of southeast Australia.     

Critical-level crossing of rossby-gravity wave-packets in a linear-shear,stratified flow

Abstract

The propagation of Rossby-gravity waves, which are of astronomical interest near the critical level (or corotation point), is considered in a linear-shear, exponentially stratified flow by means of a ray tracing method. It is shown, using the analytic solutions for the stream function, that for a Richardson number J > 1/4 a wave-packet can cross the critical level in a finite time. In the unstable stratified case (J < 0), it cannot cross the critical level for large |J| (J < 0), but may do so for some intermediate |J| values.

Based on the above results, the possible existence of the regular normal mode with a discrete point eigenvalue in the continuous spectrum is discussed for bounded systems.     

Variational principles for topological barotropic fluid dynamics

Barotropic fluid flows with the same circulation structure as steady flows generically have comoving physical surfaces on which the vortex lines lie. These become Bernoullian surfaces when the flow is steady. When these surfaces are nested (vortex line foliation) with the topology of cylinders, toroids or a combination of both, we show how a Clebsch representation of the flow velocity can be introduced. This is then used to reduce the number of functions to be varied in the variational principles for such flows. We introduce a three function variational formalism for steady and non-steady barotropic flows.     

Form-drag instability in a barotropic and a baroclinic atmosphere

We discuss the form-drag instability for a quasi-geostrophic channel flow. We first study the characteristics of this instability in a barotropic flow, considering in detail the influence of the meridional scale and discussing which structure of the perturbation zonal flow must be chosen in order to describe properly this instability.We then consider a continuous quasi-geostrophic channel model in which the topography enters only through the bottom boundary condition, and we discuss how in this case the effects of the form-drag are felt by the mean zonal flow through the ageostrophic mean meridional circulation. Because the meridional structure of the perturbation zonal flow cannot simply be extended from the barotropic to the continuous case, we show how to modify it properly.We then study the baroclinic model in the particular case of constant (in the vertical) basic-state zonal flow and show how this case closely resembles the barotropic, demonstrating the barotropic nature of the form-drag instability.Symbols _t is the partial derivative with respect tot. - _x is the partial derivative with respect tox. - _y is the partial derivative with respect toy. - represents the geostrophic stream function. - u is the eastward component of the geostrophic wind. - v is the northward component of the geostrophic wind. - u _a is the eastward component of the ageostrophic wind. - v _a is the northward component of the ageostrophic wind. - w is the vertical component of the wind. - f is the Coriolis parameter=2 sin f _o+y. - f _o is the Coriolis parameter evaluated at mid-latitude. - N is the Brunt-Vaisala frequency. - [A] is the zonal (x) average ofA at constantp andy. - <A> is the horizontal (x andy) average ofA at constantp     

Improved bounds on linear instability of barotropic zonal flow within the shallow water equations

Here we develop mathematical results to describe the location of linear instability of a parallel mean flow within the framework of the shallow water equations; growth estimates of near neutral modes (for disturbances subcritical with respect to gravity wave speed) in the cases of non-rotating and rotating shallow water. The bottom topography is taken to be one-dimensional and the isobaths are parallel to the mean flow. In the case of a rotating fluid, the isobaths and the mean flow are assumed to be zonal. The flow is front-like: there is a monotonic increase of mean flow velocity. Our results show that for barotropic flows the location of instabilities will be a semi-ellipse region in the complex wave velocity plane, that is based on the wave-number, Froude number, and depth of the fluid layer. We also explore the instability region for the case of spatially unbounded mean velocity profiles for non-rotating shallow water.     

Truncated model of a barotropic atmosphere with a periodic forcing

The effect of variations in time of the zonal flow is investigated by the study of a simplified truncated model of a barotropic atmosphere in the presence of an oscillating zonal forcing. Long-time numerical simulations of a triadic model in spherical geometry are carried out for various values of both the frequency and the amplitude of the oscillating part of the zonal forcing. It is found that the reaction of the system to simple sinusoidal forcing is characterized, as happens for strongly nonlinear systems, by complicated trajectories in the phase-space and that the spectrum of the zonal component is much more complicated than that of the forcing function, with interesting relative maxima in the range of very low climatological frequencies. Moreover it is shown that, for proper values of both the frequency and the amplitude of the sinusoidally oscillating part of the forcing function, our simplified model of the large-scale planetary circulation oscillates between an essentially zonal regime (a flow pattern dominated by the zonal flow component) and a wave regime (a flow pattern characterized by significant values of the meridional component of the velocity field associated with the wave components). The transitions between the two regimes are strongly asymmetric: in fact, the time needed for a wave-like flow to evolve into an essentially zonal one is, in the limit of our model, typically 4 to 5 times greater than that needed for the inverse transition. The results are intuitively interpreted in the limit of very long periods of the oscillations of the forcing function. Other interesting features of the results are considered.     

Dynamic equations for steady spatially varied open channel flow: a critical review

A review of the dynamic equations governing steady spatially varied flow in open channels is presented. These equations are derived by employing either the momentum or the energy principle: the choice of the method employed is based on convenience. Nevertheless, the two approaches yield different results when applied to a particular flow situation. Recent researches have established that this anamoly is due to the omission of the influence of the lateral flow. The inconsistencies existing among the different forms of these equations and the rather incomplete nature of their derivation are discussed. It is believed that with the present state of knowledge, it is possible to obtain identical spatially varied flow profiles when the influencing parameters are properly evaluated whether one uses the momentum or the energy approach. The need for further study to provide a better understanding of this practically important phenomenen is established and potential research directions are defined. Recent contributions to the analysis of the hydraulic characteristics of the spatially varied flow phenomenon and the delineation of the spatially varied flow profiles into eight possible patterns are also presented.     

Chaotic behaviour in a low-order unforced,inviscid barotropic model

A low-order model of the unforced, inviscid barotropic model is examined as a dynamical system. Analytic solutions, consisting of linear and nonlinear oscillations (Rossby waves), are obtained in appropriate limiting initial conditions. These solutions are periodic. With less restrictive initial conditions the system shows quasi-periodic behaviour at low energies and chaotic behviour at high energies. This transition is accompanied by frequency-locking and period-doubling. Quasi-periodic and chaotic behaviour may coëxist in phase space for the same values of the model invariants. The results are interpreted in terms of perturbed integrable Hamiltonian systems. Considerations of the low-frequency variability of the atmosphere are also made.     

Efficiency verification of a horizontal flow barrier via flowmeter tests and multilevel sampling

The remediation strategy for an industrial site located in a coastal area involves a pump and treat system and a horizontal flow barrier (HFB) penetrating the main aquifer. To validate the groundwater flow conceptual model and to verify the efficiency of the remediation systems, we carried out piezometric measurements, slug tests, pumping tests, flowmeter tests and multilevel sampling. Flowmeter tests are used to infer vertical groundwater flow directions, and base exchange index is used to infer horizontal flow directions at a metric scale. The selected wells are located both upstream and downstream of the HFB. The installation of the HFB produced constraints to the groundwater flow. A stagnant zone of contaminated freshwater floating over the salt wedge in the upper portion of the aquifer is detected downstream of the HFB. This study confirms that the adopted remediation system is efficiently working in the area upstream of the HFB and even downstream in the bottom part of the aquifer. At the same time, it has also confirmed that hot spots are still present in stagnant zones located downstream of the HFB in the upper part of the aquifer, requiring a different approach to accomplish remediation targets. The integrated approach for flow quantification used in this study allows to discriminate the direction and the magnitude of groundwater fluxes near an HFB in a coastal aquifer. Copyright © 2012 John Wiley & Sons, Ltd.     

Stable and unstable barotropic shelf waves in a coastal current

Abstract

We consider the linearized stability of a barotropic coastal current flowing parallel to a straight coastline over a continental shelf and slope whose depth varies monotonically with distance from the coast. Some necessary conditions for stability and various semi-circle theorems are reviewed for general current profiles and bottom topography. A criterion for topography to be a destabilizing influence is derived. Some general results for stable waves are also described. Analytic solutions are obtained for a piece-wise linear current profile and the exponential depth profile (Buchwald and Adams, 1968). Dispersion diagrams are obtained for a monotonic current profile, where it is shown that the effect of topography is destabilizing, and for a triangular current profile. The dispersion diagrams generally contain a finite number (usually one or two) of unstable waves, and a set of stable waves, which may be infinite in number. The results are applied to some specific coastal regimes.     

An externally forced barotropic circulation model for the New York Bight

The sea level and the barotropic, frictional circulation response for the New York Bight are used to demonstrate the effects of external sea-level forcing, bathymetry, and variable friction. The governing equation is the steady, integrated vorticity equation and is computed by finite differencing over a curvilinear grid conforming to the 10- and 100-m isobaths and extending for 250 km alongshore. The boundary conditions are based on the hypothesis that the dynamics of the shelf are driven by the external sea-level gradient and the coastal no-flux condition; and consequently the conditions at the lateral boundaries are dependent thereon. Therefore, the external sea-level slope must be independently specified, and the lateral boundary conditions must be dependently generated. The diabathic component of the external sea slope forces the calm wind circulation by its effect on the transport through the upstream boundary; and the parabathic component has also an important modifying effect by forcing a shelf convergent transport. The parabathic sea slope at the coast is independent of its offshore value, being instead a direct product of the coastal boundary condition.The bottom friction is expressed as related to the sea level through a bottom length parameter and a veer angle, both of which are taken to increase shoreward. An additional bottom stress component, related to the surface stress, is determined for bottom depths less than the Ekman depth. Such bottom stress variability produces significant alterations in the nearshore flow field, over the constant bottom stress formulation, by reducing it and causing it to veer downgradient and downwind in the nearshore.The model is forced by different wind directions and the results are discussed. The circulations generally conform to the observed mean flow patterns, but with several smaller-scale features. The strong bathymetric feature of the Hudson Shelf Valley causes a polarized up- and downvalley flow for winds with an eastward or westward component, respectively. Under mean westerly winds, there is a divergence in the shelf valley flow at about the 60-m isobath. The Apex gyre existing off the western tip of Long Island becomes more extensive for winds changing from northeast to southwest. Mean flow reversals (to the northeast) occur off both Long Island and New Jersey for wind directions changing counterclockwise from northwest to southeast and from west to east, respectively. Southeastward transport over the outer New Jersey shelf tends to be enhanced by wind and external sea-level conditions; and the transport over the New Jersey midshelf, particularly in the lee of the shelf valley, tends to be weak and variable also under these mean conditions.     

Application of implicit normal mode initialization to a limited-area mesoscale prediction model

Summary An implicit nonlinear normal mode initialization scheme proposed by Temperton is modified and applied to a limited-area mesoscale baroclinic model. Stress is put on the numerical aspects of the method.     

On the stability properties of the nongeostrophic disturbances in a barotropic zonal current

Summary The stability properties of the nongeostrophic disturbances are studied in a barotropic zonal current. The growth rate of the nongeostrophic disturbances is increased and the instability is generally shifted towards shorter wavelengths. Even in the structure of the nongeostrophic disturbances large differences are found as compared to geostrophic disturbances.On leave from Physical Research Laboratory, Ahmedabad, India.     

地震区跨活动断层桥梁桩基动力时程响应分析

为了研究强震区桥梁跨活动断层时,桩基在地震中的动力响应,以海文大桥为工程背景,利用Midas GTS有限元软件建立其强震区桩-海床岩土体-断层耦合作用的数值模型,研究不同强度(0.20g～0.60g)的50年超越概率为10%的地震波(后文简称5010地震波)作用下,桥梁桩基加速度、位移、弯矩及剪力的动力时程响应特性。结果表明：上部大厚度松散土体对桩身加速度有放大及滤波作用,而基岩对桩身加速度几乎不产生作用;断层上、下盘桩基础的桩顶水平位移随输入地震动强度的增大而增大,但达到振幅的时刻一致;上、下盘桩基础桩顶竖向位移时程响应都在50 s以后产生永久沉降;桩身最大弯矩截面处时程响应均在40 s以后产生永久弯矩;应重点考虑上部覆盖层软硬土体界面和基岩界面的抗弯承载力设计,及桩顶和基岩面附近的抗剪承载力设计;上盘桩基础按桩身加速度、弯矩、桩顶水平位移等动参数控制设计,下盘桩基础按动剪应力控制设计。     

Back‐barrier flooding by storm surges and overland flow

Low‐elevation areas within a sandy barrier island are subject to flooding via saturation overland flow following moderate storm surges and rainfall events. Using a high resolution topographic survey and simple hydrology models, we estimate the discharge and velocities from storm surge return flow and saturation overland flow. Results show that return flow velocities are of the same magnitude as the critical velocity necessary to mobilize sand when a hydraulic connection between the watershed and back‐barrier bay is present. Storms of moderate strength and rainfall intensity may be sufficient to keep the return channels open within the back‐barrier, thus providing natural conduits for water exchange from overwash events during extreme storm surges triggered by hurricanes. Copyright © 2011 John Wiley & Sons, Ltd.