Shallow Water Wave Speed Research Articles

Numerical modelling of ship-generated solitary waves

A ship sailing at the wave speed in shallow water produces a complex wave pattern including a downstream disturbance in addition to a periodically generated upstream disturbance. The upstream component consists of solitary waves which are generated at the ship bow and emitted forward as soon as the local water depth is sufficiently modified enabling them to bypass the shallow water wave speed limit. Reynolds Averaged Navier-Stokes numerical simulations are carried out to explore this phenomenon in a fully non-linear and viscous virtual towing tank in cases where a ship sails at the waterway centreline as well as off-centreline conditions. Results indicate that friction attains no more than approximately 25 % of the total resistance coefficient, justifying the use of inviscid methods by previous studies in the literature. Water depth may have a significant impact on the frequency and amplitude of ship-generated solitary waves, but the manner in which this occurs is highly sensitive to the width of the waterway.

Experimental Modeling of Tsunamis Generated by Pyroclastic Density Currents: The Effects of Particle Size Distribution on Wave Generation

AbstractVolcanic tsunamis can expand the radius of hazards posed by a volcano well beyond the reach of the eruption itself; however, their source mechanisms are poorly understood. The tsunamigenic potential of pyroclastic density currents was studied experimentally by releasing a fluidized column of glass beads from a reservoir; the beads then ran down an inclined ramp into a water‐filled flume and generated waves. The effects of the particle size distribution on the generated waves were analyzed by comparing the waves generated by flows comprising different proportions of particles of diameters 63–90 μm and 600–850 μm. The flows comprising higher proportions of large particles travel more slowly down the ramp; however, all the flows impact the water at velocities greater than the shallow water wave speed, , where h is the still‐water depth. The entrance of the fluidized flow into the water generates a solitary‐like leading wave followed by a smaller trough and trailing waves. Upon impact, the flow separates into a part advected with the wave crest and a part which turbulently mixes with water and propagates along the bottom of the flume, forming an underwater gravity current. A higher proportion of large particles makes the flows more porous, allowing the water to penetrate through the flows more easily, slightly decreasing the efficiency of the energy transfer. While this affects the celerity of the waves, the results show that, over the studied range of particle size distributions, all the flows can generate waves of similar amplitudes regardless of the particle size distribution.

Generation mechanisms of the water surface elevation induced by a moving atmospheric pressure disturbance

Forced water wave by the moving atmospheric pressure disturbance (APD) is an important factor to cause sea surface elevation during meteorological disasters, whose generation mechanism is complicated and unclear. To this end, surface elevation induced by a moving APD is theoretically studied. Based on the present analytical solution, it is confirmed that the APD-induced surface elevation consists of three components with respect to different influence factors, including the initial surface elevation, the initial vibration trend and the external force. Surface elevation induced by its initial value or initial vibration trend composes of two waves propagating in opposite directions with the shallow water wave speed. Meanwhile, the external force produces two small waves propagating backward and forward at each time instant, and the surface elevation is the superposition of these two waves. Subsequently, contributions from the above three factors to the total surface elevation are specified. Along the APD center, the initial surface elevation plays a significant role at the beginning and its function decreases as time passing by, whereas contribution of the external force shows an opposite trend. Regarding other areas, effects of these three factors cancel each other out, leading to an inconspicuous surface elevation.

Arrival of Long Ocean Waves and Hourly Sea Level Oscillations in Masan Bay, Korea on 19–22 March 2014

Park, S.J.; Choi, B.-J.; Sim, H.S., and Byun, D.-S., 2020. Arrival of long ocean waves and hourly sea level oscillations in Masan Bay, Korea on 19-22 March 2014. In: Malvarez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1510–1514. Coconut Creek (Florida), ISSN 0749-0208.Calmness and predictability of the sea level in a harbor are essential for safe shipping and cargo-loading on vessels. Masan Bay is an inner bay located on the south coast of Korea where the mean spring tidal range is 174 cm. It has been reported that sea level often fluctuates hourly in Masan Bay in addition to the effect of tides. The cause of the hourly sea level fluctuations have not been explained. The fluctuation periods are close to the natural resonant periods which are determined by the harbor geometry and depth. To find the generating sources of the hourly sea level fluctuations and to examine their characteristics, sea level data measured minutely at Masan harbor and the neighboring 11 tidal stations were analyzed. There were 42 events of long-period sea level oscillations with a maximum height of more than 40 cm in Masan Harbor from 2013 to 2017. Power spectral analysis on the sea level data shows the presence of high energy density in the periods ranging from 48 to 125 min at Masan and neighboring tidal stations. It was found that long ocean waves frequently propagate from the southwestern region of Korea Strait (KS) and enter Masan Bay. Time-lagged correlation analysis between the time series of sea level data along the south coast of Korea in March 2014 suggests that the long waves propagated from the southwestern KS to the eastern KS and entered Masan Bay. It took 2 h 27 min for the waves to propagate from Jeju Island in the southwestern KS to Masan Harbor. The estimated traveling speeds of the long waves using time-lagged correlation analysis were similar to the shallow water wave speed in the region. Oceanic processes that generate the propagating long ocean waves might be tsunami, seismic waves, meteotsunami or internal waves in the open ocean. The long wave events were not related to local winds or air pressure variations.

A novel machine learning algorithm for tracking remotely sensed waves in the surf zone

This paper describes a novel image processing technique that detects wave breaking and tracks waves in the surf zone using machine learning procedures. Using time-space images (timestacks), the algorithm detects white pixel intensity peaks generated by breaking waves, confirms these peaks as true wave breaking events by learning from the data's true colour representation, clusters individual waves, and obtains optimal wave paths. The method was developed and tested using data from four sandy Australian beaches under different incident wave and light conditions. Results are a representation of the position of the wave front through time, i.e., space-time data, which when shown overlaid on the original timestack shows the high degree of accuracy of the method developed here. The utility of the method is demonstrated in two ways: 1) through a comparison between the instantaneous wave speed calculated from the wave paths with the theoretical shallow water wave speed, and 2) by obtaining optical intensities that could be translated into wave roller lengths. The algorithm developed here has the potential to improve understanding numerous nearshore process such as bore propagation and capture in the surf zone, surf zone energy dissipation, surf beat and infragravity waves, and as a direct speed input for depth inversion methods.

Examination of Generation Mechanisms for an English Channel Meteotsunami: Combining Observations and Modeling

AbstractOn the morning of 23 June 2016, a 0.70-m meteotsunami was observed in the English Channel between the United Kingdom and France. This wave was measured by several tide gauges and coincided with a heavily precipitating convective system producing 10 m s−1 wind speeds at the 10-m level and 1–2.5-hPa surface pressure anomalies. A combination of precipitation rate cross correlations and NCEP–NCAR Reanalysis 1 data showed that the convective system moved northeastward at 19 ± 2 m s−1. To model the meteotsunami, the finite element model Telemac was forced with an ensemble of prescribed pressure forcings, covering observational uncertainty. Ensembles simulated the observed wave period and arrival times within minutes and wave heights within tens of centimeters. A directly forced wave and a secondary coastal wave were simulated, and these amplified as they propagated. Proudman resonance was responsible for the wave amplification, and the coastal wave resulted from strong refraction of the primary wave. The main generating mechanism was the atmospheric pressure anomaly with wind stress playing a secondary role, increasing the first wave peak by 16% on average. Certain tidal conditions reduced modeled wave heights by up to 56%, by shifting the location where Proudman resonance occurred. This shift was mainly from tidal currents rather than tidal elevation directly affecting shallow-water wave speed. An improved understanding of meteotsunami return periods and generation mechanisms would be aided by tide gauge measurements sampled at less than 15-min intervals.

Shelf edge reflection of atmospherically generated long ocean waves along the central U.S. East Coast

This paper describes an investigation of unusual large-amplitude high­frequency sea level events (∼40–60cm) observed during the period 2006–2012 along the central U.S. East Coast. These events occurred 2–3h after offshore propagating atmospheric pressure disturbances crossed the coastline. The large amplitudes of the oscillations may be explained by Proudman resonance, as the average speed of the atmospheric pressure disturbances, estimated to be between 16 and 25m/s, was similar to the shallow-water wave speed over the shelf, ∼15–20m/s. The observed lag of 2–3h of the events can be explained by shoreward-propagating free waves generated as the atmospheric-forced waves crossed the shelf edge. The estimated pathways of the forced and reflected free ocean waves seem to have been coherent and in good agreement with the lag observed at tide gauge stations.

Resonance and trapping of topographic transient ocean waves generated by a moving atmospheric disturbance

Proudman resonance amplifies the oceanic forced wave beneath moving atmospheric pressure disturbances. The amplification varies with water depth; consequently, the forced wave beneath a disturbance crossing topography radiates transient free waves. Transients are shown to magnify the effects of Proudman resonance for disturbances crossing the coast or shelf at particular angles. A Snell like reflection law gives rise to a type of resonance for relatively slow moving disturbances crossing a coast in an otherwise flat-bottomed ocean. This occurs for translation speeds less than the shallow water wave speed for disturbances approaching the coast at a critical angle given by the inverse sine of the Froude number of the disturbance. A disturbance crossing the shelf at particular angles can also excite seiche modes of the shelf via generation of a transient at the continental slope. Beyond a typically small angle of incidence, transients generated by a disturbance crossing the continental slope and coast will be trapped on the shelf by internal reflection. The refraction law for a fast-moving forced wave crossing an ocean ridge at greater than a small angle of incidence also results in trapped free-wave transients with tsunami-like periods propagating along the ridge. The subcritical resonance, excitation of shelf modes and trapping of the transients may have implications for storm surges and the generation of destructive meteotsunami.

Propagation of tsunami‐driven gravity waves into the thermosphere and ionosphere

Recent observations have revealed large F‐region electron density perturbations (∼100%) and total electron content (TEC) perturbations (∼30%) that appear to be correlated with tsunamis. The characteristic speed and horizontal wavelength of the disturbances are ∼200 m/s and ∼400 km. We describe numerical simulations using our spectral full‐wave model (SFWM) of the upward propagation of a spectrum of gravity waves forced by a tsunami, and the interaction of these waves with the F‐region ionosphere. The SFWM describes the propagation of linear, steady‐state acoustic‐gravity waves in a nonisothermal atmosphere with the inclusion of eddy and molecular diffusion of heat and momentum, ion drag, Coriolis force, and height‐dependent mean winds. The tsunami is modeled as a deformation of our model lower boundary traveling at the shallow water wave speed of 200 m/s with a maximum vertical displacement of 50 cm and described by a modified Airy function in the horizontal direction. The derived vertical velocity spectrum at the surface describes the forcing at the lower boundary of the SFWM. A steady‐state 1‐D ionospheric perturbation model is used to calculate the electron density and TEC perturbations. The molecular diffusion strongly damps the waves in the topside (>300‐km altitude) ionosphere. In spite of this, the F‐region response is large, with vertical displacements of ∼2 to 5 km and electron density perturbations of ∼100%. Mean winds have a profound effect on the ability of the waves to propagate into the F‐region ionosphere.

An experimental investigation of roll waves in high pressure two-phase inclined pipe flows

This paper examines the effects of small upward inclinations on the formation of roll waves and the properties of fully developed roll waves at high pressure conditions. A total of 984 experiments were conducted at six positive pipe inclinations θ = 0.00°, 0.10°, 0.25°, 1.00°, 2.50° and 5.00° using a 25 m long 10 cm i.d. pipe. Sulfur hexafluoride (SF 6) was used at 8 bara giving a gas density of 50 kg/m 3. Two independent mechanisms for the formation of roll waves were identified; (1) interaction between 2D shallow water waves and (2) a visible long wavelength instability of the stratified layer. Viscous long wavelength linear stability analysis predicted the critical liquid flow rate and liquid height for the initiation of roll waves when roll waves were formed due to the second mechanism. A simple equation from shallow water wave theory agreed with measurements for critical liquid flow rate when roll waves were formed due to the first mechanism. Shallow water wave speed agreed with critical wave speeds at transition and nonlinear wave speeds for fully developed roll waves in certain cases. The increase in interfacial friction due to the presence of large waves was compared with models from the literature.

Long Barotropic Waves Generated by a Storm Crossing Topography

Abstract Storms crossing topography are shown to radiate long surface gravity waves. The waves are transients generated by changes in the depth-dependent amplitude of the atmospherically forced pressure wave beneath a storm. This generation mechanism for long waves, known as “meteorological tsunamis” or rissaga, does not appear to have been previously discussed. The transients have periods equal to the passage time of the storm, of order 30 min for small fast-moving storms. A 1D model is used to give the amplitudes of the transient waves generated by a small fast-moving storm crossing a topographic step on to a continental shelf and across a ridge. Large transients are generated by storms whose translation speed is subcritical in deep water and supercritical in shallow water, that is, faster than the shallow-water wave speed. Surprisingly, when the depth difference between the deep water and the continental shelf is large, a gentle transition from deep to shallow water over 10 storm widths only slightly reduces the amplitudes of the transients. The influence of a finite-width shelf on the enhancement of coastal storm surge is also discussed. A 2D numerical model illustrates the topographic transients generated by sub- and supercritical storms moving across a ridge. Topographic transients are suggested as a source of energy for seiches on shelves and within embayments. The energy may come from a storm crossing the adjacent continental slope and possibly from distant open-ocean storms crossing multiple ridges and seamounts.

Physical response of the coastal ocean to Hurricane Isabel near landfall

Abstract. Hurricane Isabel made landfall near Drum Inlet, North Carolina on 18 September 2003. In nearby Onslow Bay an array of 5 moorings captured the response of the coastal ocean to the passage of the storm by measuring currents, surface waves, bottom pressure, temperature and salinity. Temperatures across the continental shelf decreased by 1–3°C, consistent with a surface heat flux estimate of 750 W/m2. Salinity decreased at most mooring locations. A calculation at one of the moorings estimates rainfall of 11 cm and a net addition of fresh water at the surface of 8 cm. The low-pass current field shows a shelf-wide movement of water, first to the southwest, with an abrupt reversal to the northeast along the shelf after landfall. Close analysis of this reversal shows it to be a disturbance propagating offshore at a speed somewhat less than the local shallow water wave speed. The high-pass current field at one of the moorings shows a significant increase in kinetic energy at periods between 10 min and 2 h during the approach of the storm. This high-pass flow is isotropic and has a short (<5 m) vertical decorrelation scale. It appears to be closely associated with the winds, Finally we examined the surface wave field at one of the moorings. It shows the swell energy peaking well before the wind waves. At the height of the storm, as the winds rotated rapidly in the cyclonic sense, the wind wave direction rotated as well, with a lag of 45–90°.

Nonlinear Dispersion of Surface Gravity Waves in Shallow Water*

The nonlinear dispersion of random, directionally spread surface gravity waves in shallow water is examined with Boussinesq theory and field observations. A theoretical dispersion relationship giving a directionally averaged wavenumber magnitude as a function of frequency, the local water depth, and the local wave spectrum and bispectrum is derived for waves propagating over a gently sloping beach with straight and parallel depth contours. The linear, nondispersive shallow water relation is recovered as the first-order solution, with weak frequency and amplitude dispersion appearing as second-order corrections. Wavenumbers were estimated using four arrays of pressure sensors deployed in 2‐6-m depth on a gently sloping sandy beach. When wave energy is low, the observed wavenumbers agree with the linear, finitedepth dispersion relation over a wide frequency range. In high energy conditions, the observed wavenumbers deviate from the linear dispersion relation by as much as 20%‐30% in the frequency range from two to three times the frequency of the primary spectral peak, but agree well with the nonlinear Boussinesq dispersion relation, confirming that the deviations from linear theory are finite amplitude effects. In high energy conditions, the predicted frequency and amplitude dispersion tend to cancel, yielding a nearly nondispersive wave field in which waves of all frequencies travel with approximately the linear shallow water wave speed, consistent with the observations. The nonlinear Boussinesq theory wavenumber predictions (based on the assumption of irrotational wave motion) are accurate even within the surf zone, suggesting that wave breaking on gently sloping beaches has little effect on the dispersion relation.

A String Function for Describing the Propagation of Baroclinic Anomalies in the Ocean

The authors derive a string function that describes the propagation of large-scale, potentially large amplitude, baroclinic energy anomalies in a two-layer ocean with variable topography and rotation parameter. The generality of the two-layer results allows results for the 1-layer, 1.5-layer, inverted 1.5-layer, lens, and dome models to be produced as limiting-cases. The string function is a scalar field that acts as a streamfunction for the propagation velocity. In the linear case the string function is simply c2o/f, where co is the background baroclinic shallow water wave speed, and typically describes propagation poleward on the eastern boundaries, westward (with some topographic steering) over the middle ocean, and equatorward on the western boundaries. In the more general nonlinear case, the string function is locally distorted by the anomaly. In the fully nonlinear examples of a lens or dome, there is no rest or background string function; the string function is generated entirely by the disturbance and propagation is due to asymmetric distribution of the anomalous mass over the string function contours. It is shown that conventional beta/topographic propagation results (e.g., beta drift of eddies, the Nof speed of cold domes) can be obtained as limiting cases of the string function. The string function provides, however, more general propagation velocities that are also usually simpler to derive. The first baroclinic mode string function for the global oceans is calculated from hydrographic data. The westward propagation speeds in the ocean basins as derived from the meridional gradient of the string function are typically two to five times faster than those expected from standard theory and agree well with the propagation speeds observed for long baroclinic Rossby waves in the TOPEX/Poseidon data.

Time-dependent response of a floating flexible plate to an impulsively started steadily moving load

The time-dependent response of a floating flexible plate to an impulsively started steadily moving load defines the time taken to approach a steady-state deflection due to the load, or indeed whether such a steady state is achieved at all. The asymptotic analysis for large time reported here, for both a concentrated point load and a uniformly distributed circular load, confirms that a steady-state deflection is achieved at both subcritical and supercritical load speeds. This analysis also predicts a logarithmically growing response near the critical speed corresponding to the minimum phase speed of the hybrid waves generated, but an eventual steady-state response when the load speed moves at the shallow water wave speed. These results are supported by numerical computation.

The Daytona Beach Wave of 3–4 July 1992: A Shallow-Water Gravity Wave Forced by a Propagating Squall Line

An unexpected run-up of the ocean along Daytona Beach, Florida, on 3–4 July 1992 was associated with at least one large ocean wave. The wave, which reached a height of about 3 m above normal tide, injured 75 people and damaged property along Daytona Beach. Analyses of meteorological and oceanographic observations are consistent with the hypothesis that a squall line generated a long water wave. The critical evidence is that the propagation speed of the squall line matched the shallow-water wave speed that prevailed along the direction of motion of the squall line. The squall line exerted force on the ocean for at least 3 h. The issues of recurrence and public safety are discussed.

Modulation of coherent microwave backscatter by shoaling waves

The orbital speed of long shoaling waves and the modulation of centimetric wind‐generated waves by the shoaling waves were obtained from the frequency and amplitude modulations, respectively, of the backscattered signal of a coherent CW 9.375‐GHz radar operated from the end of a pier on the Outer Banks of North Carolina. Modulations anomalously large in comparison with those predicted by the relaxation time model (Keller and Wright, 1975) were observed in the range of wind speeds 4.5–6.5 m s−1, which was perhaps coincidentally near the shallow water wave speed. Outside this range of wind speeds the model qualitatively accounted for the magnitude and wind speed dependence of the measured modulations. The phase of the modulation leads to the inference that the maximum amplitude of the short waves occurs near, and generally leeward of, the crests of long waves for wind speeds of up to 8 m s−1, the highest wind speed encountered in the experiment.