The modulational instability in deep water under the action of wind and dissipation
Summary (4 min read)
1. Introduction
- Coronavirus disease 2019 (COVID-19) is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).
- As of 1st August 2021, more than 196.9 million cases have been reported across 213 countries and territories with more than 4.2 million deaths and more than 1135.19 million people have been fully vaccinated.
- Visiting the hospital has become a part of life, but after the attack of the COVID-19 pandemic, it has been observed a serious reduction in people visiting the hospitals, or even the health care workers avoiding patients visiting the hospitals.
- (2) Nevertheless, the relative decline in visits remains largest among surgical and procedural specialties and paediatrics.
- Therefore, their study aims to ask and find out the answers to all these major concerns and to address them properly.
2.1 Study Design and Sampling Technique
- This is a cross-sectional survey among common people in two states of India (Maharashtra and Karnataka).
- Conventional non-probability sampling technique was used to analyse the questions given to the respondents.
- (4) The inclusion criteria were common people (undergraduate, postgraduate, and the people from medical field) at the time of data collection and having access to an internet connection to fill out the online questionnaire.
- Individuals who did not fill the form completely were excluded from the study.
2.1 Study Instrument and Administration
- A short online questionnaire was developed after a review of a similar study.
- (4) Outcome variables include the respondent’s attitude towards visiting the hospitals and the reasons for not visiting the hospitals during the COVID-19 pandemic.
- The following ten questions were formulated for the online survey through google forms as shown in Table 1.
- The link to respondents was distributed across social media platforms and the data collection took place in June 2021.
- The typical Google form is shown in Fig 2.
2.2 Data Analysis
- There were around 636 respondents representing females and males from two states of India who responded to the survey through google forms.
- Google forms data were downloaded and data were analysed using different statistical tools.
- The tools are being used to verify the normal distribution of variables and comparisons between groups for categorical variables.
- Binary logistic regression analysis was carried out to identify parameters more strongly associated with respondent’s Attitudes and behavior of people towards visiting the hospitals during the pandemic.
3. Results
- Distribution and sociodemographic characteristics of respondents: A total of 1590 respondents representing females (48.4%) and males (50.3%) from two states of India completed the online survey.
- The mean age of participants was 39.9 years.
- There were 37.4% respondents were postgraduate & above and 35.8% respondents were undergraduate and remaining respondents were high school graduates and college graduates.
- Table 2 shows the distribution of sociodemographic characteristics used in the study.
- The analysis of each questionnaire are as follows:.
3.1 Were you going to the hospital for common illness before the pandemic started?
- More than half of respondents i.e. about 62.6% were visiting the hospital for common illnesses like the common cold, cough headache, body ache, first degree burns, acidity, indigestion, eye, ear, joint, or skin related problems, etc. before the pandemic started.
- On the other hand, 37.1% of respondents were not visiting the hospitals for such common illnesses even before the pandemic started.
- Fig. 3 shows the percentage of people visiting to the hospital before the pandemic started.
3.4 Are you under treatment of any long term diseases (like Diabetes or BP)?
- About 86.5% of respondents were not under any long- term treatment because of the average age group of respondent being 39.9 years, on the other hand, 13.5% of respondents were under the treatment of long term disease.
- This question was asked to know how people are maintaining the long term diseases like diabetes or blood pressure during the COVID-19 pandemic when they are afraid to go out for regular follow-ups and laboratory tests.
- Fig. 6 shows the percentage of people having long term diseases.
3.5 How often were you going to the hospital before the pandemic started?
- About 73% of respondents are visiting the hospital less than two times a year, 19.8% of respondents are visiting three-four times a year and 7.2% of respondents are visiting more than four times a year for any disease before pandemic started.
- Fig. 7 shows the percentage of visits to the hospital before the pandemic started.
3.6 Has the frequency of you visiting the hospital reduced after the pandemic started?
- About 74.8% of respondents stated that the frequency of visiting the hospital has reduced after the pandemic started and 25.2% of respondents stated that the frequency of visiting the hospital has not reduced even after the pandemic started.
- Fig. 8 shows the percentage of people who have reduced the number of visits to the hospital after the pandemic started.
3.7 How often do you go to the hospital after the pandemic started?
- About 49.7% of respondents are visiting the hospital once or twice a year for any disease, 5.3% of respondents are visiting three-four times a year to the hospitals, 40.6% of the respondents have not visited the hospital since the pandemic has started and other 3.8% of the respondents visit more than four times a year to the hospital.
- Fig. 9 shows the percentage of visits a person makes to the hospital after the pandemic started.
3.9 If you are reducing the number of visits how are you managing your health
- Problem About 58.4% of respondents are managing their health problems by online consultation of doctors, 20.1% of respondents by taking medications on their own, 19.4% of respondents by calling the doctor home for consultation or lab technician to collect samples if needed.
- Whereas other respondents are managing by home remedies like homeopathy, yoga, Ayurveda medicines, and immunity boosters.
- But Some of the patients who have long term diseases go to the hospital for regular follow-ups to avoid unavoidable risks.
- About 53.7% of respondants have not increased the frequency of visiting the hospitals even after taking both the doses of vaccination, on the other hand 27.3% of respondents have gained the confidence to visit the hospital for the treatment after vaccination.
4. Discussion
- Total of 636 respondent’s forms data was analysed.
- This analysis reveals that more percentage of respondents have reduced the visit to the hospitals due to getting infected within the hospitals.
- The data shows that 58.4% of respondents manage their health themselves by online consultation of doctors, 20.1% by taking medications on their own, 19.4% by calling the doctor or lab technician home for sample collection and others by home remedies.
- The increased online consultations have increased demand for the relevant clinical services and reduced hospital visits, thus decreasing COVID-19 spread.
- (11) Instead of increasing stress of some patients at home with the fear of isolation and family member’s misconception towards the disease, it’s better to visit the hospital and get treated, this will reduce the serious mental health problems of patients.
5. Conclusion
- This study reveals that there is drastic reduction in hospital visits due to a reduction in attitude and behaviour of common people towards visiting the hospital during the COVID-19 pandemic due to the fear of getting an infection by the virus.
- Informed consent was obtained from all subjects involved in the study, also known as Informed Consent Statement.
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Citations
120 citations
74 citations
Cites background or methods from "The modulational instability in dee..."
...0004 (the same value has been used in [15])....
[...]
...Note that we use a different definition of the surface elevation from the one in [15] where the 1/2 factor is not included (the consequence is that the coefficient in the nonlinear term in equation (2) differs by a factor of 4 from the one in equation (3....
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...In [15] the equation is written in a nondimensional form and the coefficient K = Γ/ω0 is introduced)....
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...We considered the NLS equation discussed in [15]...
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...More recently, the role of dissipation and wind in the modulational instability has been considered together within the NLS equation, [15] (then confirmed by fully nonlinear simulations, [16])....
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70 citations
63 citations
Cites background from "The modulational instability in dee..."
...The case ΓM/ f = O( 2) gives rise to the following damped/forced nonlinear Schrödinger equation [11, 8, 12]...
[...]
...For a logarithmic velocity profile in the boundary layer, the Miles growth rate ΓM results in [4, 7, 8]...
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...The pressure P induced at the water surface then depends on the surface elevation η as follows [4, 8] 1 ρw P(x, t) = ΓM f c(2)p 2π ηx(x, t) (2)...
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41 citations
Cites background from "The modulational instability in dee..."
... (2014). New terms which appear in that modification of the NLS equation may be eliminated after appropriate change of variables, and then the equation turns to the form considered in (Leblanc, 2007; Kharif et al, 2010; Onorato & Proment, 2012). Numerical simulations of individual wave groups affected by wind were performed within different frameworks in (Yan and Ma, 2010; Adcock and Taylor, 2011). Laboratory a...
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References
56 citations
"The modulational instability in dee..." refers methods in this paper
...Conte & Miles (1959) developed a numerical method to treat this singularity and solve the Rayleigh equation....
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...Conte & Miles (1959) computed the values of β as a function of κc0/u∗ for a logarithmic wind profile of the form U (z) = u∗ κ ln(z/z0), (3.7) where z0 is the roughness length given by z0 = αchu 2 ∗/g (αch is the Charnock constant ≈0.011–0.018)....
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42 citations
"The modulational instability in dee..." refers methods in this paper
...Following Miles (1996), the coefficient β is given by the following expression: β = −π k (d2U/dz2)(zc) |(dU/dz)(zc)| w2(zc) U 21 (∂η/∂x) 2 , (2.10) where z = η(x) is the equation of the surface wave profile....
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41 citations
"The modulational instability in dee..." refers background or methods or result in this paper
...In the regime we are considering, we have shown that the effect of the wind is contrary, as expected (Leblanc 2007)....
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...Our aim is to extend the works of Segur et al. (2005a) and Leblanc (2007) who investigated this problem by considering damping and wind effects separately....
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...To study the modulational stability of this solution we follow Segur et al. (2005a) and Leblanc (2007), and we superimpose to the solution (4.1) a small perturbation Ψ = Ψs(1 + δζ (ξ, τ )), (4.4) where δ 1....
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Frequently Asked Questions (10)
Q2. What is the recurrence of the Fermi–Pasta–Ul?
The evolution of a two-dimensional nonlinear wave train on deep water, in the absence of dissipative effects, exhibits the Fermi–Pasta–Ulam recurrence phenomenon.
Q3. Why did they assume that damping might affect the early development of rogue waves?
Since damping affects the modulational instability of waves in deep water, they assumed that it might affect the early development of rogue waves.
Q4. What is the phase shift between the wind and the water waves?
For an energy flux to occur from the wind to the water waves, there must be a phase shift between the fluctuating pressure and the interface.
Q5. What is the purpose of this paper?
The present paper is aimed at reporting on the behaviour of Benjamin–Feir instability when dissipation and wind input are both taken into account.
Q6. What is the effect of wind and dissipation on the modulation of a?
In the presence of wind and dissipation, the unstable domain shrinks for low-frequency regime: this means that young waves are more sensitive to modulational instability than old waves.
Q7. What is the email address for correspondence?
Email address for correspondence: kharif@irphe.univ-mrs.frnearly uniform wave trains become modulated and then demodulated until they are again nearly uniform.
Q8. How can damping stop the growth of the sidebands?
when the perturbations are small initially, they cannot grow large enough for nonlinear resonant interaction between the carrier and the sidebands to become important.
Q9. What is the name of the potential water wave problem?
Since Stokes (1847), it is well known that the potential water wave problem admits as solutions uniform wave trains of two-dimensional progressive waves.
Q10. What is the criterion for linear stability?
This situation was discussed by Segur et al. (2005a, see their comment (iii) p. 238), and it was claimed that even with substantial growth of the perturbation, the Stokes solution of (3.4) is still linearly stable: it is always possible to find a gap (denoted ∆) between unperturbed and perturbed solution that satisfies the linear stability criterion.