Wave Hump Research Articles

Weakly two-dimensional interaction of solitons in shallow water

Nonlinear interactions of long-crested solitonic waves travelling in different directions in shallow water may serve as a possible mechanism of freak waves in certain sea areas. Several features of such interactions of equal amplitude Korteweg–de Vries (KdV) solitons in the framework of the Kadomtsev–Petviashvili equation are reviewed. In certain cases, nonlinear coupling produces a particularly high and steep wave hump. Interactions of equal amplitude solitons may lead to water surface elevations up to four times as high as the amplitude of the counterparts and the slope of the wave front may encounter eightfold increase. Exact expressions for the maximum slope in the case of interactions of unequal amplitude solitons are derived. The slope amplification for a certain class of interactions in the limiting case is twice as intense as the amplitude amplification. In the limiting case of exact resonance the interaction pattern is a new KdV soliton as in the case of the Mach stem. This feature allows to directly establish the extreme properties of the humps excited by nonlinear coupling. Evidence of such interactions and their possible consequences in realistic conditions are discussed.

Extreme elevations and slopes of interacting solitons in shallow water

The paper describes a nonlinear phenomenon of interaction of waves that may be a reason for the existence of high-amplitude wave humps on the sea surface. The properties of extreme elevation area in the vicinity of the intersection point of two long-crested shallow water waves travelling in slightly different directions are evaluated in the framework of two-soliton solution of the Kadomtsev–Petviashvili equation. The extent of the area where surface elevation exceeds a certain level is estimated analytically based on the study of corresponding surface isolines. Shown is that this area is very narrow in the direction of its propagation. The extreme slopes at the front of the interaction soliton may eight times exceed the maximum slope of the interacting solitons.

Soliton interaction as a possible model for extreme waves in shallow water

Abstract. Interaction of two long-crested shallow water waves is analysed in the framework of the two-soliton solution of the Kadomtsev-Petviashvili equation. The wave system is decomposed into the incoming waves and the interaction soliton that represents the particularly high wave hump in the crossing area of the waves. Shown is that extreme surface elevations up to four times exceeding the amplitude of the incoming waves typically cover a very small area but in the near-resonance case they may have considerable extension. An application of the proposed mechanism to fast ferries wash is discussed.

Interaction of Internal Waves with a Topographic Sill in a Two-Layered Fluid

Abstract Sills and seamounts may alter or even disrupt internal waves that approach them. The authors study by one-dimensional laboratory experiment: (i) the fission of an internal solitary wave of a two-layered fluid by a triangular obstruction, (ii) the form preservation of the transmitted wave, and (iii) the energy dissipated by the vortex induced by the obstruction. The potential energy stored in the wave signal is taken as a measure to quantify the above notions. Results are presented for upper to lower depth ratio rH = 3 and rH = ⅓. The results show in general a pronounced dependence on the degree of blocking (B ≡ depth of obstruction/lower layer depth), but experiments are less conclusive for dependence on particle speeds and slope angles of the triangle. The authors determine for a given degree of blocking how much energy of an approaching wave is fed into the reflected and transmitted wave. For B ≤ 0.6 the obstruction is virtually ineffective; for B ≥ 0.8 a compact solitary wave hump transforms i...

1027-42 Usefulness of T wave ″Humps″in the Diagnosis of Long QT Syndrome

Family members of long QT syndrome (LQTS) prebands, who present with QTc ≥0.47 sec 1/2 , are diagnosed as LQTS affected. It remains unclear, however, how to evaluate family members with borderline QTc value (0.42–0.46 see 1/2 ). Recent ECG and genetic linkage correlation studies suggest that T wave ″humps″ (defined as bulges or protuberances just beyond the apex on the downslope of the T wave) in left precordial or limb leads may represent an ECG marker of the LQTS genotype. Therefore, the aim of this study was to investigate the clinical significance of T wave humps (in at least 1 limb or 2 left precordial leads) in 427 family members with borderline QTc in their rust ECG. The occurrence of cardiac events (syncope, cardiac arrest) or QTc≥0.47 sec 1/2 during a mean 46 ± 28 mo. follow-up was used as a basis to diagnose family member as LQTS-affected. The presence of T wave humps, recorded in 45 (11%) family members, was significantly associated with younger age (for ≤15 vs > 15 years old, odds ratio [OR] = 6.0; p < 0.001), longer QTc (0.45–0.46 vs 0.42–0.44, OR = 3.8; p < 0.001) and higher heart rate (>80 vs ≤80 bpm, OR = 2.8; p < 0.02). The diagnosis of LOTS was attained in 36% of family members with and in 14% without T wave humps (p < 0.001). Multivariate logistic regression revealed an independent contribution of T wave humps to the LQTS diagnosis: ECG Variable OR 95%CI pValue T wave humps (yes vs no) 3.1 (1.5;6.6) 0.003 QTc(>0.44–0.46 vs≤0.44) 5.6 (3.2;9.9) <0.001 Bradycardia (age-adjusted) 3.6 (1.8;7.3)≤ <0.001 In LQTS family members with borderline QTc: (1) T wave humps are more likely to occur in individuals at young age, with longer QTc and at higher heart rates. (2) The diagnosis of LQTS is enhanced by identification of T wave humps for the entry ECG.

T wave “humps” as a potential electrocardiographic marker of the long QT syndrome

Objectives. This study attempted to determine the prevalence and electrocardiographic (ECG) lead distribution of T wave “humps” (T2, after an initial T wave peak, T1) among families with long QT syndrome and control subjects.Background. T wave abnormalities have been suggested as another facet of familial long QT syndrome, in addition to prolongation of the rate-corrected QT interval (QTc), that might aid in the diagnosis of affected subjects.Methods. The ECGs from 254 members of 13 families with long QT syndrome (each with two to four generations of affected members) and from 2,948 healthy control subjects (age ≥ 16 years, QTc interval 0.39 to 0.46 s) were collected and analyzed. Tracings from familes with long QT syndrome were read without knowledge of QTc interval or family member status (210 blood relatives and 44 spouses).Results. We found that T2 was present in 53%, 27% and 5% of blood relatives with a “prolonged” (≥ 0.47 s), “borderline” (0.42 to 0.46 s) and “normal” (≤0.41 s) QTc interval, respectively (p < 0.0001), but in only 5% and 0% of spouses with a borderline and normal QTc interval, respectively (p = 0.06 vs. blood relatives). Among blood relatives with T2, the mean [±SD] maximal T1T2 interval was 0.10 ± 0.03 s and correlated with the QTc interval (p < 0.01); a completely distinct U wave was seen in 23%. T2 was confined to leads V2and V3in 10%, whereas V4, V5, V6or a limb lead was involved in 90% of blood relatives with T2. Among blood rotatives with a borderline QTc interval, 50% of those with versus 20% of those without major symptoms manifested T2 in at least one left precordial or limb lead (p = 0.05). A T2 amplitude > 1 mm (grade III) was observed, respectively, in 19%, 6% and 0% of blood relatives with a prolonged, borderline and normal QTc interval with T2 in at least one left precordial or limb lead. Among the 2,948 control subjects, 0.6% exhibited T2 confined to leads V2and V3, and 0.9% had T2 involving one or more left precordial lead (but none of the limb leads). Among 37 asymptomatic adult blood relatives with QTc intervals 0.42 to 0.46 s, T2 was found in left precordial or limb leads in 9 (24%; 5 with limb lead involvement) versus only 1.9% of control subjects with a borderline QTc interval (p < 0.0001).Conclusions. These findings are consistent with the hypothesis that in families with long QT syndrome, T wave humps involving left precordial or (especially) limb leads, even among asymptomatic blood relatives with a borderline QTc interval, suggest the presence of the long QT syndrome trait.