scholarly journals Providential Tides: the Double Low Water of Narragansett Bay

2020 ◽  
Vol 44 (1) ◽  
pp. 44-53
Author(s):  
D. G. Bowers ◽  
J. M. Brubaker
Keyword(s):  
Narragansett Bay ◽  
Diurnal Tide ◽  
Natural Period ◽  
Higher Harmonics ◽  
Selective Amplification ◽  
Quarter Wavelength ◽  
Tidal Harmonics ◽  
Higher Harmonic ◽  
The Right ◽  
Diurnal Tides

AbstractWe investigate a mechanism for producing double-lows and double-highs in the semi-diurnal tide by selective amplification of higher harmonics in a resonant gulf. A double low water is observed at Providence, RI, near the head of Narragansett Bay on days when there is a flattening of the low water tidal curve at Newport, at the mouth of the bay. The flattening is caused by an unusually large quarter-diurnal component to the tide at Newport. The quarter diurnal component has the right phase (a maximum close to the time of the minimum in the semi-diurnal tide) to produce a prolonged flattening of the tidal curve around low water. The natural period of Narragansett Bay (for quarter-wavelength resonance) is close to 4 h and the quarter diurnal tide is amplified, relative to the semi-diurnal tide, within the bay. The selective amplification of the higher harmonic further prolongs the flattening effect at Providence and, occasionally, is sufficient to create a double low water at the head of the bay from quarter and semi-diurnal tides alone. More often, though, a sixth-diurnal harmonic produced within the bay, added to the flattened low water at Providence, creates the double low water. This mechanism of selective amplification of tidal harmonics could be relevant to double tides elsewhere.

scholarly journals Unlocking higher harmonics in atomic force microscopy with gentle interactions

2014 ◽  
Vol 5 ◽  
pp. 268-277 ◽  
Author(s):  
Sergio Santos ◽  
Victor Barcons ◽  
Josep Font ◽  
Albert Verdaguer
Keyword(s):  
Atomic Force Microscopy ◽  
Thermal Fluctuations ◽  
External Excitation ◽  
Higher Harmonics ◽  
Force Microscopy ◽  
Minimal Invasiveness ◽  
Harmonic Phase ◽  
Atomic Force ◽  
Higher Harmonic ◽  
Compositional Variations

In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of the equation of motion shows that the external introduction of exact harmonic frequencies does not compromise the fundamental frequency. Thermal fluctuations are also considered within the detection bandwidth of interest and discussed in terms of higher-harmonic phase contrast in the presence and absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity.

scholarly journals Nonlinear Numerical Investigation on Higher Harmonics at Lee Side of a Submerged Bar

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
D. Ning ◽  
X. Zhuo ◽  
L. Chen ◽  
B. Teng
Keyword(s):  
Nonlinear Wave ◽  
Wave Amplitude ◽  
Harmonic Wave ◽  
Incoming Wave ◽  
Higher Harmonics ◽  
Wave Condition ◽  
Weakly Nonlinear ◽  
Higher Harmonic ◽  
Wave Nonlinearity ◽  
Method Model

The decomposition of a monochromatic wave over a submerged object is investigated numerically in a flume, based on a fully nonlinear HOBEM (higher-order boundary element method) model. Bound and free higher-harmonic waves propagating downstream the structure are discriminated by means of a two-point method. The developed numerical model is verified very well by comparison with the available data. Further numerical experiments are carried out to study the relations between free higher harmonics and wave nonlinearity. It is found that thenth-harmonic wave amplitude is growing proportional to thenth power of the incoming wave amplitude for weakly nonlinear wave condition, but higher-harmonic free wave amplitudes tend to a constant value for strong nonlinear wave condition.

Higher Harmonic Oscillations in a Noncontacting FMR Mechanical Face Seal Test Rig

1994 ◽  
Vol 116 (2) ◽  
pp. 161-167 ◽  
Author(s):  
An Sung Lee ◽  
Itzhak Green
Keyword(s):  
Fourier Series ◽  
Fourier Series Expansion ◽  
Face Seal ◽  
Test Rig ◽  
Harmonic Oscillations ◽  
Higher Harmonics ◽  
Design Modification ◽  
Contact Kinematics ◽  
Mechanical Face Seal ◽  
Higher Harmonic

In order to investigate experimentally the dynamic behavior of a noncontacting flexibly mounted rotor (FMR) mechanical face seal a test rig was designed and built. Test results showed that the FMR seal was vulnerable to higher harmonic oscillations with frequencies that are integer multiples of the shaft speed. Because system nonlinearities can cause higher harmonic oscillations, the dynamic moments acting on the rotor are derived to include the effects of imbalance and axial offset of the rotor. The analysis reveals that the nonlinear terms involved are of second order and generally can be neglected. Investigation is then directed to analyze the possibility of rubbing contact between the rotor and the stator. Rubbing contact can occur as a result of a high relative angular misalignment between the rotor and the stator. A contact kinematics model is proposed and a Fourier series analysis is performed on the resulting rotor response. The analysis shows that the proposed response contains higher harmonics. Fourier series expansion and numerical filtering of a sampled rotor response from the test rig yield resembling signals which contain higher harmonics. This suggests that rubbing contact is the source of higher harmonic oscillations. Design modification to the rotor flexible support system resulted in a virtual elimination of higher harmonic oscillations.

Magnetic Flux Density under Single Harmonic Distortion

2021 ◽  
Vol 1034 ◽  
pp. 151-157
Author(s):  
Michał Kaczmarek ◽  
Ernest Stano
Keyword(s):  
Magnetic Flux ◽  
Flux Density ◽  
Phase Angle ◽  
Harmonic Distortion ◽  
Magnetic Core ◽  
Magnetic Flux Density ◽  
Higher Harmonics ◽  
Secondary Voltage ◽  
Magnetizing Current ◽  
Higher Harmonic

In the paper the change of the magnetic flux density under single harmonic distortion is discussed. Presented results show the dependence of the value of the magnetic flux density in the toroidal magnetic core made from the Ni80Fe20 tape of the phase angle of higher harmonic in relation to the main harmonic of distorted magnetizing current. Moreover, the influence of higher harmonic depends from it frequency and it becomes undetectable above 15th higher harmonic, even if its level reaches 50% of the RMS value of the main harmonic of distorted magnetizing current. Laboratory tests were carried out for the magnetic toroidal core of iCT with a current ratio equal to 300 A / 5 A. The oscilloscope is used to measure waveforms of the excitation current and the secondary voltage through the voltage probes. Build in numerical integration is used to determine the magnetic flux density from secondary voltage. In the case of tested 5th higher harmonic the highest value of the magnetic flux density is obtained for phase angle equal to 90° between main and higher harmonics, while the lowest is obtained for 270°. This depends from the initial phase of the magnetic field strength and results from the integration of distorted secondary voltage with the particular content of higher harmonics.

scholarly journals The double high tide at Port Ellen: Doodson's criterion revisited

2017 ◽  
Author(s):  
Hannah A. M. Byrne ◽  
J. A. Mattias Green ◽  
David G. Bowers
Keyword(s):  
Phase Difference ◽  
High Tide ◽  
High Water ◽  
Diurnal Tide ◽  
Data Set ◽  
Dominant Component ◽  
A Value ◽  
Tidal Harmonic ◽  
Higher Harmonic ◽  
Limiting Value

Abstract. Doodson proposed a criterion to predict the occurrence of double high (or double low) waters when a higher frequency tidal harmonic is added to the semi-diurnal tide. If the phasing of the harmonic is optimal, the condition for a double high water can be written bn2/a > 1 where b is the amplitude of the higher harmonic, a is the amplitude of the semi-diurnal tide and n is the ratio of their frequencies. Here we expand this criterion to allow for (i) a phase difference φ between the semi-diurnal tide and the harmonic and (ii) the fact that the double high water will disappear in the event that b/a becomes large enough for the higher harmonic to be the dominant component of the tide. This can happen, for example, at places or times where the semi-diurnal tide is very small. The revised parameter is br2/a, where r is a number generally less than n, although equal to n when φ = 0. The theory predicts that a double high tide will form when this parameter exceeds 1 and then disappear when it exceeds a value of order n2 and the higher harmonic becomes dominant. We test these predictions against observations at Port Ellen in the Inner Hebrides of Scotland. For most of the data set, the largest harmonic of the semi-diurnal tide is the 6th diurnal component, for which n = 3.The principal lunar and solar semi-diurnal tides are about equal at Port Ellen and so the semi-diurnal tide becomes very small twice a month at neap tides. A double high water forms when br2/a first exceeds a minimum value of about 1.5 as neap tides are approached and then disappears as br2/a then exceeds a second limiting value of about 10 at neap tides in agreement with the revised criterion.

scholarly journals The double high tide at Port Ellen: Doodson's criterion revisited

Ocean Science ◽  
2017 ◽  
Vol 13 (4) ◽  
pp. 599-607 ◽  
Author(s):  
Hannah A. M. Byrne ◽  
J. A. Mattias Green ◽  
David G. Bowers
Keyword(s):  
High Tide ◽  
High Water ◽  
Diurnal Tide ◽  
Tidal Range ◽  
Data Set ◽  
Dominant Component ◽  
A Value ◽  
Tidal Harmonic ◽  
Higher Harmonic ◽  
Limiting Value

Abstract. Doodson proposed a minimum criterion to predict the occurrence of double high (or double low) waters when a higher-frequency tidal harmonic is added to the semi-diurnal tide. If the phasing of the harmonic is optimal, the condition for a double high water can be written bn2∕a > 1 where b is the amplitude of the higher harmonic, a is the amplitude of the semi-diurnal tide, and n is the ratio of their frequencies. Here we expand this criterion to allow for (i) a phase difference ϕ between the semi-diurnal tide and the harmonic and (ii) the fact that the double high water will disappear in the event that b∕a becomes large enough for the higher harmonic to be the dominant component of the tide. This can happen, for example, at places or times where the semi-diurnal tide is very small. The revised parameter is br2∕a, where r is a number generally less than n, although equal to n when ϕ = 0. The theory predicts that a double high tide will form when this parameter exceeds 1 and then disappear when it exceeds a value of order n2 and the higher harmonic becomes dominant. We test these predictions against observations at Port Ellen in the Inner Hebrides of Scotland. For most of the data set, the largest harmonic of the semi-diurnal tide is the sixth diurnal component, for which n = 3. The principal lunar and solar semi-diurnal tides are about equal at Port Ellen and so the semi-diurnal tide becomes very small twice a month at neap tides (here defined as the smallest fortnightly tidal range). A double high water forms when br2∕a first exceeds a minimum value of about 1.5 as neap tides are approached and then disappears as br2∕a then exceeds a second limiting value of about 10 at neap tides in agreement with the revised criterion.

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