Wave Patterns of Gravity–Capillary Waves from Moving Localized Sources
Round 1
Reviewer 1 Report
The authors presented a study of gravity-capillary wave patterns generated by a moving localized source. In the case of purely gravity waves on a deep water this problem reduces to well-known phenomenon of ship waves described in many classical books. However, in the reviewed paper the focus is made on the co-existence of two wave systems with the opposite signs of group velocities relative to the localized source. Such problem has not been studied thus far therefore, this paper in topical, interesting, and important. The author presented very detailed introduction to problem and then calculate characteristic angles of the wave patterns including the angle which separates the effects of gravity and capillary waves (“the phase Mach” cone), the angle of the minimal group velocity of gravity-capillary waves (“the group Mach” cone), the angles of cusps of isophases that appear after a threshold current speed. The amplitudes of the wave patterns are also estimated, as well as the effect of a source shape.
The paper is clearly written with a good English and well-illustrated. I did not check the details of calculations, but the derived formulae look reasonable and correct in the limiting cases. The paper can be published in the journal after minor corrections.
- On page 3 after Eq. (4) it would be good to correct the notation for \delta which is not a surface tension, but rather a “kinematic surface tension” – see my remark on the margin of p. 3.
- In the caption to Fig. 2 it would be good to show the approximate value of the velocity for the Wilton resonance.
- I am suggesting to authors to describe in detail the limiting case when the surface tension effect predominates over the gravity effect. What is a wave pattern at different speeds for purely capillary waves? Inverse limiting case when the gravity effect predominates is well-known, but the former one was not studied this far.
- I am suggesting adding a reference to the recent paper by G. Rousseaux and H. Kellay “Classical Hydrodynamics for Analogue Spacetimes: Open Channel Flows and Thin Films”. Phil Trans Royal Society, 2020. There are Fig. 7 and 10 which can be relevant to the refereed paper.
Comments for author File: 
Comments.pdf
Author Response
See the attached file
Author Response File: Author Response.pdf
Reviewer 2 Report
The manuscript ''Wave patterns of gravity-capillary waves from moving localized sources'' is devoted to the study of surface water waves propagation in the framework of linear theory. In this work, a systematic study of the processes of wave generation by moving objects is carried out. The paper discusses various modes of wave generation.
In general, the work is written in clear English understandable for a non-specialist in this field. Abstract and illustrations reflect well and fully the essence of the presented work. The manuscript also analyzes the influence of the shape of an object generating surface waves. The results of this work seem to be very important, since they were obtained for the classical problem of wave generation on the ocean surface.
I found only one small inaccuracy in the work. Formula (5) on page 3 is misspelled. The dimension of \delta^{1/2}g^{-1/2} is not a meter. The mistake is related with absence of mass density of liquid. The authors should correct this minor inaccuracy also in dispersion relation (4) and in difinition of C_m.
Author Response
See the attached file
Author Response File: Author Response.pdf
