Three-Dimensional Numerical Modelling of Tidal Current in Balikpapan Bay Using Delft 3D

Balikpapan is one of the main port cities with residential areas, industry, trade, and vital objects scattered from north to south along the coast of Balikpapan Bay. This dense activity increases traffic in Balikpapan Bay. Thus, the hydrodynamic conditions in these waters are essential to be reviewed. The purpose of this research is to simulate hydrodynamics in Balikpapan Bay. The simulation results of the hydrodynamic model for sea-level elevation values are close to the conditions in the field, as indicated by the correlation coefficient 0.98, skill 0.99, and RMSE 0.15 m. The ocean current velocity verification includes the average correlation for x-direction and y-direction, up to 0.93, RMSE 0.05 m, and the percentage error of 6.7%. The significant current velocity is at low tide during spring tide with an average of 0.1 m/s and a maximum speed of 1.62 m/s. Temporally, the observation point at the mouth of Balikpapan Bay has the most significant Bed Shear Stress magnitude with an average of 0.05 N/m2. Spatially, the highest Bed Shear Stress magnitude is at the time of spring tide when it recedes towards the tide with an average Bed Shear Stress in the bay of 0.16 N/m2. The most dominant tidal components are M2 and S2, with a contribution value of 65.3%. The phase propagation from mouth to upstream of Balikpapan Bay for the M2 component in Balikpapan Bay is 10.5° (22.77 minutes) and 5.5° (11 minutes) for the S2 component.

Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling

The modelling of time-varying shallow flows, such as tides and storm surges, is complicated by the nonlinear dependency of bed shear stress on flow speed. For tidal flows, Lorentz’s linearisation circumvents nonlinearity by specifying a (steady) friction coefficient r based on a tide-averaged criterion of energy equivalence. However, this approach is not suitable for phenomena with episodic and irregular forcings such as storm surges. Here, we studied the implications of applying Lorentz’s energy criterion in an instantaneous sense, so that an unsteady friction coefficient r(t) adjusts to the temporal development of natural wind-driven flows. This new bed-stress parametrisation was implemented in an idealised model of a single channel, forced by time-varying signals of wind stress (acting over the entire domain) and surface elevation (at the channel mouth). The solution method combines analytical solutions of the cross-sectionally averaged linearised shallow-water equations, obtained in the frequency domain, with an iterative procedure to determine r(t). Model results, compared with a reference finite-difference solution retaining the quadratic bed shear stress, show that this new approach accurately captures the qualitative and quantitative aspects of the surge dynamics (height and timing of surge peaks, sloshing, friction-induced tide-surge interaction) for both synthetic and realistic wind forcings.

Mean flow structure and velocity–bed shear stress maxima phase difference in smooth wall, transitionally turbulent oscillatory boundary layers: direct numerical simulations

Direct numerical simulations of oscillatory boundary-layer flows in the transitional regime were performed to explain discrepancies in the literature regarding the phase difference ${\rm \Delta} \phi$ between the bed-shear stress and free-stream velocity maxima. Recent experimental observations in smooth bed oscillatory boundary-layer (OBL) flows, showed a significant change in the widely used ${\rm \Delta} \phi$ diagram (Mier et al., J. Fluid Mech., vol. 922, 2021, A29). However, the limitations of the point-wise measurement technique did not allow us to associate this finding with the turbulent kinetic energy budget and to detect the approach to a ‘near-equilibrium’ condition, defined in a narrow sense herein. Direct numerical simulation results suggest that a phase lag occurs as the result of a delayed and incomplete transition of OBL flows to a stage that mimics the fully turbulent regime. Data from the literature were also used to support the presence of the phase lag and propose a new ${\rm \Delta} \phi$ diagram. Simulations performed for ${\textit {Re}}_{\delta }=671$ confirmed the sensitivity in the development of self-sustained turbulence on the background disturbances ( $\textit{Re}_{\delta}=U_{o}\delta/\nu$ , where $\delta=[2\nu/\omega]^{1/2}$ is the Stokes' length, $U_{o}$ is the maximum free stream velocity of the oscillation, $\nu$ is the kinematic viscosity and $\omega=2{\rm \pi}/T$ is the angular velocity based on the period of the oscillation T). Variations of the mean velocity slope and intersect values for oscillatory flows are also explained in terms of the proximity to near-equilibrium conditions. Relaminarization and transition effects can significantly delay the development of OBL flows, resulting in an incomplete transition. The shape and defect factors are examined as diagnostic parameters for conditions that allow the formation of a logarithmic profile with the universal von Kármán constant and intersect. These findings are of relevance for environmental fluid mechanics and coastal morphodynamics/engineering applications.

Climate Change Impacts on Coastal Wave Dynamics at Vougot Beach, France

Wave dynamics contribute significantly to coastal hazards and were thus investigated at Vougot Beach by simulating both historical and projected future waves considering climate change impacts. The historical period included a major storm event. This period was projected to the future using three globally averaged sea level rise (SLR) scenarios for 2100, and combined SLR and wave climate scenarios for A1B, A2, and B1 emissions paths of the IPCC. The B1 wave climate predicts an increase in the occurrence of storm events. The simulated waves in all scenarios showed larger relative changes at the beach than in the nearshore area. The maximum increase of wave energy for the combined SLR and wave scenarios was 95%, while only 50% for the SLR-only scenarios. The effective bed shear stress from waves and currents showed different spatial variability than that of the wave height, emphasizing the importance of interactions between nearshore waves and currents. Increases in the effective bed shear stress (combined scenarios: up to 190%, and SLR-only scenarios: 35%) indicate that the changes in waves and currents will likely have significant impacts on the nearshore sediment transport. This work emphasizes that combined SLR and future wave climate scenarios need to be used to evaluate future changes in local hydrodynamics and their impacts. These results provide preliminary insights into potential future wave dynamics at Vougot Beach under different climate change scenarios. Further studies are necessary to generalize the results by investigating the wave dynamics during storm events with different hydrodynamical conditions and to evaluate potential changes in sediment transport and morphological evolution due to climate change.

A Numerical Study of Sheet Flow Driven by Skewed-Asymmetric Shoaling Waves Using SedWaveFoam

SedWaveFoam, an OpenFOAM-based two-phase model that concurrently resolves the free surface wave field, and the bottom boundary layer is used to investigate sediment transport throughout the entire water column. The numerical model was validated with large-scale wave flume data for sheet flow driven by shoaling skewed-asymmetric waves with two different grain sizes. Newly obtained model results were combined with previous nonbreaking and near-breaking wave cases to develop parameterization methods for time-dependent bed shear stress and sediment transport rate under various sediment sizes and wave conditions. Gonzalez-Rodriguez and Madsen (GRM07) and quasi-steady approaches were compared for intra-wave bed shear stress. The results show that in strongly asymmetric flows, considering the separated boundary layer development processes at each half wave-cycle (i.e., GRM07) is essential to accurately estimating bed shear stress and highlights the impact of phase-lag effects on sediment transport rates. The quasi-steady approach underpredicts (∼60%) sediment transport rates, especially for fine grains under large velocity asymmetry. A modified phase-lag parameter, incorporating velocity asymmetry, sediment stirring, and settling processes is proposed to extend the Meyer-Peter and Mueller type power law formula. The extended formula accurately estimated the enhanced net onshore sediment transport rate observed under skewed-asymmetric wave conditions.

Numerical investigation of flow field around T-shaped spur dyke in a reverse-meandering channel

In this paper the flow characteristics near around T-shape spur dyke situated in reverse meandering channel having rigid bed is simulated using Renormalization Group (RNG) turbulence model with an ANSYS 2018 Fluent software. To solve the model in 3D ways we used Navier-Stroke's equation based on principle of conservation of mass and momentum within a moving fluid. For studying the flow characteristics, Computational Fluid Dynamics ware applied with all geometric parameter and the turbulence was simulated using (RNG) equations of model. In this simulation the structured meshes are used with different diameter and diameter of meshes is high at exit channel for obtaining accuracy in result. In this study we mainly focus on effect of Froude number on flow pattern and several other characteristics like velocity distribution, flow separation, bed shear stress distribution. The final result of this research work is compare with the condition when no structure is present in the channel.

Three-Dimensional Numerical Investigations of the Flow Pattern and Evolution of the Horseshoe Vortex at a Circular Pier during the Development of a Scour Hole

In the current study, a three-dimensional CFD model is utilized to investigate the variation of the flow structure and bed shear stress at a single cylindrical pier during scour development. The scour development is presented by seven solidified geometries of the scour hole, collected during previous experimental work at different scour stages. Different turbulence models are evaluated and the (k-ω) model is chosen due to its relative accuracy in capturing the flow oscillation and vortex shedding at the pier downstream side with personal computer computational and storage resources. The numerical results are verified against dimensionless parameters from different previous experimental works. This research describes in detail the flow structure and bed shear stress variations through seven stages of the scour hole development. The dimensionless area-averaged circulation coefficient (Ψi) is developed to evaluate the changes in the vortex strength through the scouring process by eliminating the calculation area effect. It was concluded that the circulation in the (Y) direction is the main driving factor in the development of the scour hole more than the circulation in the (X) direction. The ratio between the horseshoe vortex (HV) mean size and the scouring depth (DV/dS) in addition to the location of the maximum bed shear stress are investigated during different stages of the scour development.