A non-hydrostatic numerical model for calculating free-surface stratified flows

Kanarska, Y.; Maderich, Vladіmir

doi:10.1007/s10236-003-0039-6

Cited by 62 publications

(51 citation statements)

References 37 publications

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“…In the projection method, the momentum equations are first integrated using a hydrostatic pressure gradient to obtain the intermediate velocities. This intermediate field is then corrected using the nonhydrostatic pressure gradient to produce a solenoidal velocity field [Mahadevan et al, 1996b;Marshall et al, 1997b;Casulli and Stelling, 1998;Kanarska and Maderich, 2003;Heggelund et al, 2004]. Similar to the projection method, the pressure correction method also solves the momentum equations using a fractional step approach.…”

Section: Introductionmentioning

confidence: 99%

A nonhydrostatic version of FVCOM: 1. Validation experiments

et al. 2010

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[1] The unstructured grid finite volume coastal ocean model (FVCOM) system has been expanded to include nonhydrostatic dynamics. This addition uses the factional step method with both split mode explicit and semi-implicit schemes. The unstructured grid finite volume method, combined with a correction of the final free surface from its intermediate value with inclusion of nonhydrostatic effects, efficiently reduces numerical damping and thus ensures second-order accuracy of the solutions with local/global volume conservation. Numerical experiments have been made to fully validate the nonhydrostatic FVCOM, including surface standing and solitary waves in idealized flat-and slopingbottomed channels in homogeneous conditions, the density adjustment problem for lock exchange flow in a flat-bottomed channel, and two-layer internal solitary wave breaking on a sloping shelf. The model results agree well with the relevant analytical solutions and laboratory data. These validation experiments demonstrate that the nonhydrostatic FVCOM is capable of resolving complex nonhydrostatic dynamics in coastal and estuarine regions.

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Section: Introductionmentioning

confidence: 99%

A nonhydrostatic version of FVCOM: 1. Validation experiments

et al. 2010

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“…The applicability of the Kortewegde Vries and Gardner equations to model interface solitary waves is discussed in this section. Then we use a numerical model based on the Princeton Ocean Model (POM) (see Kanarska and Maderich, 2003;Brovchenko et al, 2007), which is briefly described in Sect. 3.…”

Section: Observations Show That There Is a Wide Variety Of Processesmentioning

confidence: 99%

The transformation of an interfacial solitary wave of elevation at a bottom step

Maderich

Talipova

Grimshaw

et al. 2009

Nonlin. Processes Geophys.

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Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up onehalf, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

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“…A free-surface non-hydrostatic numerical model for variabledensity flows using the Navier-Stokes equations under the Boussinesq approximation (Kanarska and Maderich, 2003;Maderich et al, 2012) was applied in the simulations of a numerical flume emulating a laboratory basin filled with salinity-stratified water. The numerical flume and experimental configurations are shown in Fig.…”

Section: The Numerical Model Set-upmentioning

confidence: 99%

“…For large ε, these allow for the simulation of the interaction of mode-1 ISWs with a trapped core, propagating in stratified layers near the surface and the ISWs interaction near the bottom, as considered here, and the interaction of mode-2 ISWs, assuming symmetry in the Boussinesq approximation around the horizontal midplane (Maderich et al, 2015). The numerics of the model is described in detail in (Kanarska and Maderich, 2003;Maderich et al, 2012). A total of 40 runs were performed in Series A-D.…”

Section: The Numerical Model Set-upmentioning

confidence: 99%

Head-on collision of internal waves with trapped cores

Maderich

Jung

Terletska

et al. 2017

Nonlin. Processes Geophys.

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Abstract. The dynamics and energetics of a head-on collision of internal solitary waves (ISWs) with trapped cores propagating in a thin pycnocline were studied numerically within the framework of the Navier-Stokes equations for a stratified fluid. The peculiarity of this collision is that it involves trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly non-linear waves without trapped cores, (ii) stable strongly non-linear waves with trapped cores, and (iii) shear unstable strongly nonlinear waves. The wave phase shift of the colliding waves with equal amplitude grows as the amplitudes increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum run-up amplitude, normalized by the amplitude of the waves, over the sum of the amplitudes of the equal colliding waves increases almost linearly with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The colliding waves of class (ii) lose fluid trapped by the wave cores when amplitudes normalized by the thickness of the pycnocline are in the range of approximately between 1 and 1.75. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions with little mass loss. The collision of locally shear unstable waves of class (iii) is accompanied by the development of instability. The dependence of loss of energy on the wave amplitude is not monotonic. Initially, the energy loss due to the interaction increases as the wave amplitude increases. Then, the energy losses reach a maximum due to the loss of potential energy of the cores upon collision and then start to decrease. With further amplitude growth, collision is accompanied by the development of instability and an increase in the loss of energy. The collision process is modified for waves of different amplitudes because of the exchange of trapped fluid between colliding waves due to the conservation of momentum.

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A non-hydrostatic numerical model for calculating free-surface stratified flows

Cited by 62 publications

References 37 publications

A nonhydrostatic version of FVCOM: 1. Validation experiments

A nonhydrostatic version of FVCOM: 1. Validation experiments

The transformation of an interfacial solitary wave of elevation at a bottom step

Head-on collision of internal waves with trapped cores

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