A non-hydrostatic algorithm for free-surface ocean modelling

An original implementation of a non-hydrostatic, free-surface algorithm based on a pressure correction method is proposed for ocean modelling. The free surface is implemented through an explicit scheme combined with a mode-spitting method but the depth-averaged velocity and the position of the free surface are updated at each non-hydrostatic iteration. The vertical momentum equation is also integrated up to the surface enabling a natural and accurate treatment of the surface layer. The consistent specification of the numerical schemes provides balanced transfers of potential and kinetic energy. This algorithm is well-suited for implementation as a non-hydrostatic kernel on originally hydrostatic free-surface ocean models such as Symphonie (http://poc.obs-mip.fr/pages/research_topics/modelling/symphonie/symphonie.htm) for which it has originally been developed.Energy balances associated with the propagation of short surface waves and solitary waves are presented for two dedicated well-documented configurations over closed domains. The buoyancy flux, the work rate of the pressure force together with the power of the advective terms are evaluated and discussed for the generation and the propagation of these two types of waves. The dissipation rate is in particular shown to be several orders of magnitude smaller than the work rates of the hydrostatic and non-hydrostatic pressure forces confirming the necessity for the exchanges of energy to be numerically balanced. The algorithm is subsequently applied to the complex generation of non-linear solitary internal waves by surface tides over Georges Bank, in the Gulf of Maine. The generation and the propagation of the observed non-linear and non-hydrostatic features in this region are correctly reproduced.     

A non-hydrostatic ocean model with a scalable multigrid Poisson solver

A non-hydrostatic ocean model using an effective Poisson solver is developed. The Poisson solver is a combination of the multigrid method, the Krylov-subspace method, and the sparse approximate inverse. Its numerical cost only linearly increases with total number of computational cells, and it also has high parallel computing efficiency. The numerical cost of the non-hydrostatic model described in the present paper remains only twice of that of a hydrostatic model, even with non-smooth topography and with a huge number of computational grid cells on massively parallelized computer systems. Therefore, it has a potential to expand the applicability of non-hydrostatic ocean models. We also present the preliminary result of the high-resolution non-hydrostatic experiment on Ice Shelf Water overflow in the southern Weddell Sea, which shows good agreement with observations in terms of the pathway of dense water and velocity field.     

Developments in ocean climate modelling

This paper presents some research developments in primitive equation ocean models which could impact the ocean component of realistic global coupled climate models aimed at large-scale, low frequency climate simulations and predictions. It is written primarily to an audience of modellers concerned with the ocean component of climate models, although not necessarily experts in the design and implementation of ocean model algorithms.     

A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling

We introduce a mixed discontinuous/continuous finite element pair for ocean modelling, with continuous quadratic layer thickness and discontinuous velocity. We investigate the finite element pair applied to the linear shallow-water equations on an f-plane. The element pair has the property that all geostrophically balanced states which strongly satisfy the boundary conditions have discrete divergence equal to exactly zero and hence are exactly steady states of the discretised equations. This means that the finite element pair has excellent geostrophic balance properties. We also show that the element pair applied to the non-rotating linear shallow-water equations does not have any spurious small eigenvalues. We illustrate these properties using numerical tests and provide convergence calculations which show that the numerical solutions have errors which decay quadratically with element edge length for both velocity and layer thickness.     

On the problem of numerical ocean hydrodynamics modelling

This paper describes a projection variant of the integration-interpolation technique which is used to construct monotonic difference schemes for solving the problems for an integral stream function and a level surface. The results of model numerical computations are presented which demonstrate the efficiency of the proposed techniques.Translated by Vladimir A. Puchkin.     

A three-dimensional hydrostatic model for coastal and ocean modelling using a generalised topography following co-ordinate system

A three-dimensional hydrostatic model is presented that combines a generalised vertical co-ordinate system with an efficient implicit solution technique for the free surface. The model is capable of maintaining high resolution in the surface and/or bottom boundary layers as well as dealing with steep topography. Horizontal diffusion is calculated using the Smagorinsky formulation and a k–ε turbulence model is used in the vertical. In addition the model uses higher-order advection routines. An important aspect in three-dimensional models is the choice of vertical discretisation. If one is mostly interested in problems which are governed by boundary layer flows, a terrain following or sigma co-ordinate system seems attractive. This paper focuses on the development of a generalised sigma-type grid in a three-dimensional hydrostatic model. The generalised grid offers a wide range of possibilities including grid refinement toward the bed or surface, a mixed layer transformation, and a constant layer transformation where the lowermost or uppermost grid cells can be specified to have a constant height above the bed or below the surface. A number of tests are presented which show that the model is capable of simulating both shallow nearshore, estuarine flows as well as large-scale geophysical flows. These include an extreme flooding event in the shallow North Sea and the Odden ice tongue formation in the Greenland Sea.     

Strength modelling in stiffened FRP structures with viscoelastic inserts for ocean structures

The purpose of this paper is to investigate the static structural response of a new type of composite stiffener containing a viscoelastic insert. The introduction of this material has proven benefits in terms of noise and vibration attenuation across the joint. House, 1997 describes the use of this material in sonar dome/hull connections — equipment sensitive to noise and vibration. Structural stiffeners incorporating this material would have positive implications for not only marine and ocean structures but for structural applications in general. The effects of introducing this new material on the structural response of the joint are numerically examined by using a progressive damage model. Application of this method allows the initiation and progression of failure and ultimate failure load to be predicted. Experimental results show good qualitative and quantitative agreement with the predictive damage model.     

Joint modelling of extreme ocean environments incorporating covariate effects

Characterising the joint distribution of extremes of ocean environmental variables such as significant wave height (H_S) and spectral peak period (T_P) is important for understanding extreme ocean environments and in the design and assessment of marine and coastal structures. Many applications of multivariate extreme value analysis adopt models that assume a particular form of extremal dependence between variables without justification. Models are also typically restricted to joint regions in which all variables are extreme, but regions where only a subset of variables is extreme can be equally important for design. The conditional extremes model of Heffernan and Tawn (2004) provides one approach to overcoming these difficulties.Here, we extend the conditional extremes model to incorporate covariate effects in all of threshold selection, marginal and dependence modelling. Quantile regression is used to select appropriate covariate-dependent extreme value thresholds. Marginal and dependence modelling of extremes is performed within a penalised likelihood framework, using a Fourier parameterisation of marginal and dependence model parameters, with cross-validation to estimate suitable model parameter roughness, and bootstrapping to estimate parameter uncertainty with respect to covariate.We illustrate the approach in application to joint modelling of storm peak H_S and T_P at a Northern North Sea location with storm direction as covariate. We evaluate the impact of incorporating directional effects on estimates for return values, including those of a structure variable, similar to the structural response of a floating structure. We believe the approach offers the ocean engineer a straightforward procedure, based on sound statistics, to incorporate covariate effects in estimation of joint extreme environmental conditions.     

Toward a general theory of the age in ocean modelling

Seawater is a mixture of several constituents. The age of a parcel of a constituent is defined to be the time elapsed since the parcel under consideration left the region where its age is prescribed to be zero. Estimating the age is an invaluable tool for understanding complex flows and the functioning of the numerical models used for representing them. A general theory of the age is developed, according to which the age of a constituent of seawater is a time-dependent, pointwise quantity that may be obtained from the solution of two partial differential equations governing the evolution of the concentration of the constituent under study and an auxiliary variable called the ``age concentration''. It is seen that previous applications of the notion of age are in agreement with the present theory, or may be viewed as approximations deriving from this theory. A few particular problems are touched upon, including the estimation of the age of the water and the determination of the age with the help of radioactive tracers.     

Urban and ocean ensembles for improved meteorological and dispersion modelling of the coastal zone

A high-resolution (1.67 km) ensemble transform (ET)-based meso-scale modelling system utilizing urbanization and sea surface temperature (SST) perturbations is used to examine characteristics of sea breeze/heat island interactions and atmospheric transport and dispersion for Tokyo. The ensemble displays a positive spread–skill relationship, with the addition of urban perturbations enabling the ensemble variance to distinguish a larger range of forecast error variances. Two synoptic regimes are simulated. For a pre-frontal period (stronger synoptic flow), there is less variability among ensemble members in the strength of the urban heat island and its interaction with the sea breeze front. During the post-frontal time period, the sea breeze frontal position is very sensitive to the details of the urban representation, with horizontal frontal variation covering the width of the urban centre (∼30 km) and displaying significant impacts on the development and strength of the heat island. Moreover, the dosage values of a tracer released at offshore and urban sites have considerable variability among ensemble members in response to small-scale features such as coastally upwelled water, enhanced anthropogenic heating and variations in building heights. Realistic variations in SST (i.e. warm Tokyo Bay or local upwelling) produce subtle sea breeze variations that dramatically impact tracer distributions.     

Numerical modelling of liquefaction in loose sand deposits subjected to ocean waves

The failure of marine structures is often attributed to liquefaction in loose sand deposits that are subjected to ocean waves. In this study, a two-dimensional integrated numerical model is developed to characterize the liquefaction behaviours of loosely deposited seabed foundations under various types of ocean waves. In the present model, Reynolds-Averaged Navier–Stokes (RANS) equations are used to simulate the surface wave motion, and Biot's consolidation equations are used to link the solid-pore fluid interactions in a porous medium. A poro-elasto-plastic solution is used to reproduce foundation behaviour under cyclic shearing. Unlike previous investigations, both oscillatory and residual soil responses were considered; they are coupled in an instantaneous approach. Verification of the model results to the previous centrifugal wave tests is carried out, obtaining fairly good agreement. Numerical examples show that foundation behaviour under various types of wave loading, particularly standing waves or a solitary wave, embodies a completely two-dimensional process in terms of residual pore pressure development. The parametric studies demonstrate that liquefaction caused by the build-up of pore pressures is more likely to occur in loosely deposited sand foundations with poor drainage and under large waves.     

Statistical estimation of extreme ocean environments: The requirement for modelling directionality and other covariate effects

With increasing availability of good directional data, provision of directional estimates of extreme significant wave heights, in addition to the omni-directional estimates, is more common. However, interpretation of directional together with omni-directional design criteria is subject to inconsistency, even in design guidelines. In particular, omni-directional criteria are usually estimated ignoring directional effects. In this article, for data which exhibit directional effects, we show that a directional extreme value model generally explains the observed variation significantly better than a model which ignores directionality, and that omni-directional criteria developed from a directional model are different from those generated when directionality is not accounted for. We also show that omni-directional criteria derived from a directional model are more accurate and should be preferred in general over those based on models which ignore directional effects. We recommend use of directional extreme value models for estimation of both directional and omni-directional design criteria in future, when good directional data are available. If effects of other covariates (e.g. time or space) are suspected, we similarly recommend use of extreme value models which adequately capture sources of covariate variability for all design analysis.     

Parametrical modelling of the spectra of small-scale electrical conductivity pulsations in the ocean

Parametrical models of the spectra of small-scale electrical conductivity and current velocity pulsations in the ocean are considered.Translated by V. Puchkin     

On some uncertainties related to the short term stochastic modelling of ocean waves

A short-term model for the representation of ocean waves is considered. The model is described and the associated uncertainties are briefly reviewed. Emphasis is placed on a discussion of the validity of the basic assumptions regarding stationarity and Gaussianity, together with an elaboration on uncertainties related to the shape of the spectral density function. The basis for the present investigation is 4586 time series for the sea surface elevation, representing a rather wide range of different sea states. Conclusions presented subsequently rest to some extent on the assumption that the actual time series reproduce the true time fluctuations of the surface with a sufficient accuracy. A verification of this assumption requires a very extensive investigation, and could not be included within the scope of this work.     

A random number generator for ocean noise statistics

Ocean noise is characterized by both temporal and spectral properties. Time-domain statistics are often non-Gaussian, and spectra are typically non-white. Both attributes can be simulated at the same time by applying a spectral shaping filter to random numbers having a specified kurtosis. A method for generating random numbers with arbitrary kurtosis is presented     

一种移动式海洋地震仪的硬件电路研究

针对移动式海洋地震仪对控制系统电路设计的可靠性和低功耗的需求,提出了一种基于Cor-tex-M4内核芯片的硬件电路设计方案.首先选用超低功耗的STM32L4芯片作为微控制单元,在保证高运行能力的同时降低自身功耗;其次针对MCU(Microprogrammed Control Unit)、传感器等超低功耗模块提出针对性的...     

Accurate representation of geostrophic and hydrostatic balance in unstructured mesh finite element ocean modelling

Accurate representation of geostrophic and hydrostatic balance is an essential requirement for numerical modelling of geophysical flows. Potentially, unstructured mesh numerical methods offer significant benefits over conventional structured meshes, including the ability to conform to arbitrary bounding topography in a natural manner and the ability to apply dynamic mesh adaptivity. However, there is a need to develop robust schemes with accurate representation of physical balance on arbitrary unstructured meshes. We discuss the origin of physical balance errors in a finite element discretisation of the Navier–Stokes equations using the fractional timestep pressure projection method. By considering the Helmholtz decomposition of forcing terms in the momentum equation, it is shown that the components of the buoyancy and Coriolis accelerations that project onto the non-divergent velocity tendency are the small residuals between two terms of comparable magnitude. Hence there is a potential for significant injection of imbalance by a numerical method that does not compute these residuals accurately. This observation is used to motivate a balanced pressure decomposition method whereby an additional “balanced pressure” field, associated with buoyancy and Coriolis accelerations, is solved for at increased accuracy and used to precondition the solution for the dynamical pressure. The utility of this approach is quantified in a fully non-linear system in exact geostrophic balance. The approach is further tested via quantitative comparison of unstructured mesh simulations of the thermally driven rotating annulus against laboratory data. Using a piecewise linear discretisation for velocity and pressure (a stabilised P₁P₁ discretisation), it is demonstrated that the balanced pressure decomposition method is required for a physically realistic representation of the system.