Numerical error assessment and a temporal horizon for internal waves in a hydrostatic model

Hodges, Ben R.; Laval, B.; Wadzuk, Bridget

doi:10.1016/j.ocemod.2005.09.005

Cited by 50 publications

(52 citation statements)

References 18 publications

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“…If the resolution is too low unphysical solitary-like waves can be simulated due to a balance between nonlinearity and numerical dispersion (Hodges et al, 2006;Vitousek and Fringer, 2011). Vitousek and Fringer (2011) considered waves propagating in a 2000 m deep domain using a stratification based on observations in the South China Sea and found that resolutions coarser than about 250 m resulted in waves that were too wide.…”

Section: Resolutionmentioning

confidence: 99%

Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea

Lamb

Warn-Varnas

2015

Nonlin. Processes Geophys.

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Abstract. The interaction of barotropic tides with LuzonStrait topography generates some of the world's largest internal solitary waves which eventually shoal and dissipate on the western side of the northern South China Sea. Twodimensional numerical simulations of the shoaling of a single internal solitary wave at the site of the Asian Seas International Acoustic Experiment (ASIAEX) have been undertaken in order to investigate the sensitivity of the shoaling process to the stratification and the underlying bathymetry and to explore the influence of rotation. The bulk of the simulations are inviscid; however, exploratory simulations using a vertical eddy-viscosity confined to a near bottom layer, along with a no-slip boundary condition, suggest that viscous effects may become important in water shallower than about 200 m. A shoaling solitary wave fissions into several waves. At depths of 200-300 m the front of the leading waves become nearly parallel to the bottom and develop a very steep back as has been observed. The leading waves are followed by waves of elevation (pedestals) that are conjugate to the waves of depression ahead and behind them. Horizontal resolutions of at least 50 m are required to simulate these well. Wave breaking was found to occur behind the second or third of the leading solitary waves, never at the back of the leading wave. Comparisons of the shoaling of waves started at depths of 1000 and 3000 m show significant differences and the shoaling waves can be significantly non-adiabatic even at depths greater than 2000 m. When waves reach a depth of 200 m, their amplitudes can be more than 50 % larger than the largest possible solitary wave at that depth. The shoaling behaviour is sensitive to the presence of small-scale features in the bathymetry: a 200 m high bump at 700 m depth can result in the generation of many mode-two waves and of higher mode waves. Sensitivity to the stratification is considered by using three stratifications based on summer observations. They primarily differ in the depth of the thermocline. The generation of mode-two waves and the behaviour of the waves in shallow water is sensitive to this depth. Rotation affects the shoaling waves by reducing the amplitude of the leading waves via the radiation of long trailing inertiagravity waves. The nonlinear-dispersive evolution of these inertia-gravity waves results in the formation of secondary mode-one wave packets.

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Section: Resolutionmentioning

confidence: 99%

Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea

Lamb

Warn-Varnas

2015

Nonlin. Processes Geophys.

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“…The simulation began on 28 April 2010 at 23:30 LT (local time) and ended on 15 July 2010 at 23:30 LT. All of the times used in this work refer to the local time (−3 GMT, Greenwich Mean Time). The simulation was programmed to run at efficient time steps with the Courant-Friedrichs-Lewy number fixed at 1/3 (Hodges et al, 2006). Thus, the time step was set to 150 s, which was sufficient to ensure the numerical stability of the model (Cassuli and Cattani, 1994).…”

Section: Model Setup Sensitivity Analysis and Validationmentioning

confidence: 99%

Physical changes within a large tropical hydroelectric reservoir induced by wintertime cold front activity

Curtarelli

Alcântara

Rennó

et al. 2014

Hydrol. Earth Syst. Sci.

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Abstract. We investigated the influence of wintertime cold front activity on the physical processes within a large tropical reservoir located in Brazil. The period chosen for this study consisted of 49 days between 28 April 2010 and 15 July 2010. This period was defined based on information from the Brazilian Center for Weather Forecasting and Climate Studies (CPTEC), data collected in situ and the interpretation of remotely sensed images. To better understand the governing processes that drive changes in the heat balance, differential cooling and mixing dynamics, a simulation was performed that utilized a three-dimensional hydrodynamic model enforced with in situ and remote sensing data. The results showed that during a cold front passage over the reservoir, the sensible and latent heat fluxes were enhanced by approximately 77 and 16 %, respectively. The reservoir's daily averaged heat loss was up to 167 % higher on the days with cold front activity than on the days without activity. The cold front passage also intensified the differential cooling process; in some cases the difference between the water temperature of the littoral and pelagic zones reached up to 8 • C. The occurrence of cold front passages impacted the diurnal mixed layer (DML), by increasing the turbulent energy input (∼ 54 %) and the DML depth (∼ 41 %). Our results indicate that the cold front events are one of the main meteorological disturbances driving the physical processes within hydroelectric reservoirs located in tropical South America during the wintertime. Hence, cold front activity over these aquatic systems has several implications for water quality and reservoir management in Brazil.

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“…Furthermore, an ideal scheme would have low dissipation so that internal waves may be modelled without artificial damping (however, there are some limits; see [29] for a discussion of how numerical dissipation affects numerical diffusion). If | | = 1 then the numerical scheme is both stable and free from numerical dissipation (at the leading truncation error order).…”

Section: Overviewmentioning

confidence: 99%

“…Prior model results with = 1, though, have shown substantial dissipation of internal waves over the course of long simulations (e.g. [15,29,30]), which is likely due to a combination of (1) topographic effects, (2) long-term erosion of the pycnocline by numerical diffusion, and (3) barotropic/baroclinic interactions that extract energy from the baroclinic mode into the barotropic mode where it is quickly dissipated. The present theoretical stability results for the baroclinic forward-time method are verified with numerical modelling below.…”

Section: Baroclinic Forward-time Stabilitymentioning

confidence: 99%

“…As shown in [3], slightly dissipative, phase-accurate algorithms can be designed from the analysis of the numerical amplification factor. Using a slightly dissipative baroclinic method may be desirable in a nonlinear hydrostatic model to prevent artificial steepening of internal waves [29]. For the baroclinic predictor-corrector method, dissipation can be enforced by requiring a = 0 and b = 0 in Equation (55), while requiring c = 0.…”

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confidence: 99%

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Baroclinic stability for a family of two‐level, semi‐implicit numerical methods for the 3D shallow water equations

Rueda

Sanmiguel‐Rojas

Hodges

2006

Numerical Methods in Fluids

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SUMMARYThe baroclinic stability of a family of two time-level, semi-implicit schemes for the 3D hydrostatic, Boussinesq Navier-Stokes equations (i.e. the shallow water equations), which originate from the TRIM model of Casulli and Cheng (Int. J. Numer. Methods Fluids 1992; 15:629-648), is examined in a simple 2D horizontal-vertical domain. It is demonstrated that existing mass-conservative low-dissipation semiimplicit methods, which are unconditionally stable in the inviscid limit for barotropic flows, are unstable in the same limit for baroclinic flows. Such methods can be made baroclinically stable when the integrated continuity equation is discretized with a barotropically dissipative backwards Euler scheme. A general family of two-step predictor-corrector schemes is proposed that have better theoretical characteristics than existing single-step schemes.

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Numerical error assessment and a temporal horizon for internal waves in a hydrostatic model

Cited by 50 publications

References 18 publications

Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea

Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea

Physical changes within a large tropical hydroelectric reservoir induced by wintertime cold front activity

Baroclinic stability for a family of two‐level, semi‐implicit numerical methods for the 3D shallow water equations

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