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Y Y Chen  One of the best experts on this subject based on the ideXlab platform.

transverse instability of gravity capillary solitary waves on deep water in the presence of constant Vorticity
Journal of Fluid Mechanics, 2019CoAuthors: M Abid, H C Hsu, C Kharif, Y Y ChenAbstract:The bifurcation of twodimensional gravitycapillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant Vorticity. We found that gravitycapillary solitary waves with decaying oscillatory tails exist in deep water in the presence of Vorticity. Furthermore we found that the presence of Vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the Vorticity.

a nonlinear schrodinger equation for gravity capillary water waves on arbitrary depth with constant Vorticity part 1
Journal of Fluid Mechanics, 2018CoAuthors: H C Hsu, C Kharif, M Abid, Y Y ChenAbstract:A nonlinear Schrodinger equation for the envelope of twodimensional gravity–capillary waves propagating at the free surface of a vertically sheared current of constant Vorticity is derived. In this paper we extend to gravity–capillary wave trains the results of Thomas et al. (Phys. Fluids, 2012, 127102) and complete the stability analysis and stability diagram of Djordjevic & Redekopp (J. Fluid Mech., vol. 79, 1977, pp. 703–714) in the presence of Vorticity. The Vorticity effect on the modulational instability of weakly nonlinear gravity–capillary wave packets is investigated. It is shown that the Vorticity modifies significantly the modulational instability of gravity–capillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive Vorticity and amplified in the presence of negative Vorticity; (ii) in finite depth, it is reduced when the Vorticity is positive and amplified and finally reduced when the Vorticity is negative. The combined effect of Vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the Vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative Vorticity and attenuated by positive Vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the Vorticity.

a nonlinear schr odinger equation for gravity capillary water waves on arbitrary depth with constant Vorticity part i
arXiv: Fluid Dynamics, 2018CoAuthors: H C Hsu, C Kharif, M Abid, Y Y ChenAbstract:A nonlinear Schr\"odinger equation for the envelope of twodimensional gravitycapillary waves propagating at the free surface of a vertically sheared current of constant Vorticity is derived. In this paper we extend to gravitycapillary wave trains the results of \citet{thomas2012pof} and complete the stability analysis and stability diagram of \citet{Djordjevic1977} in the presence of Vorticity. Vorticity effect on the modulational instability of weakly nonlinear gravitycapillary wave packets is investigated. It is shown that the Vorticity modifies significantly the modulational instability of gravitycapillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive Vorticity and amplified in the presence of negative Vorticity, (ii) in finite depth, it is reduced when the Vorticity is positive and amplified and finally reduced when the Vorticity is negative. The combined effect of Vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the Vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative Vorticity and attenuated by positive Vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the Vorticity.
H C Hsu  One of the best experts on this subject based on the ideXlab platform.

transverse instability of gravity capillary solitary waves on deep water in the presence of constant Vorticity
Journal of Fluid Mechanics, 2019CoAuthors: M Abid, H C Hsu, C Kharif, Y Y ChenAbstract:The bifurcation of twodimensional gravitycapillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant Vorticity. We found that gravitycapillary solitary waves with decaying oscillatory tails exist in deep water in the presence of Vorticity. Furthermore we found that the presence of Vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the Vorticity.

a nonlinear schrodinger equation for gravity capillary water waves on arbitrary depth with constant Vorticity part 1
Journal of Fluid Mechanics, 2018CoAuthors: H C Hsu, C Kharif, M Abid, Y Y ChenAbstract:A nonlinear Schrodinger equation for the envelope of twodimensional gravity–capillary waves propagating at the free surface of a vertically sheared current of constant Vorticity is derived. In this paper we extend to gravity–capillary wave trains the results of Thomas et al. (Phys. Fluids, 2012, 127102) and complete the stability analysis and stability diagram of Djordjevic & Redekopp (J. Fluid Mech., vol. 79, 1977, pp. 703–714) in the presence of Vorticity. The Vorticity effect on the modulational instability of weakly nonlinear gravity–capillary wave packets is investigated. It is shown that the Vorticity modifies significantly the modulational instability of gravity–capillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive Vorticity and amplified in the presence of negative Vorticity; (ii) in finite depth, it is reduced when the Vorticity is positive and amplified and finally reduced when the Vorticity is negative. The combined effect of Vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the Vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative Vorticity and attenuated by positive Vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the Vorticity.

a nonlinear schr odinger equation for gravity capillary water waves on arbitrary depth with constant Vorticity part i
arXiv: Fluid Dynamics, 2018CoAuthors: H C Hsu, C Kharif, M Abid, Y Y ChenAbstract:A nonlinear Schr\"odinger equation for the envelope of twodimensional gravitycapillary waves propagating at the free surface of a vertically sheared current of constant Vorticity is derived. In this paper we extend to gravitycapillary wave trains the results of \citet{thomas2012pof} and complete the stability analysis and stability diagram of \citet{Djordjevic1977} in the presence of Vorticity. Vorticity effect on the modulational instability of weakly nonlinear gravitycapillary wave packets is investigated. It is shown that the Vorticity modifies significantly the modulational instability of gravitycapillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive Vorticity and amplified in the presence of negative Vorticity, (ii) in finite depth, it is reduced when the Vorticity is positive and amplified and finally reduced when the Vorticity is negative. The combined effect of Vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the Vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative Vorticity and attenuated by positive Vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the Vorticity.
M Abid  One of the best experts on this subject based on the ideXlab platform.

transverse instability of gravity capillary solitary waves on deep water in the presence of constant Vorticity
Journal of Fluid Mechanics, 2019CoAuthors: M Abid, H C Hsu, C Kharif, Y Y ChenAbstract:The bifurcation of twodimensional gravitycapillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant Vorticity. We found that gravitycapillary solitary waves with decaying oscillatory tails exist in deep water in the presence of Vorticity. Furthermore we found that the presence of Vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the Vorticity.

a nonlinear schrodinger equation for gravity capillary water waves on arbitrary depth with constant Vorticity part 1
Journal of Fluid Mechanics, 2018CoAuthors: H C Hsu, C Kharif, M Abid, Y Y ChenAbstract:A nonlinear Schrodinger equation for the envelope of twodimensional gravity–capillary waves propagating at the free surface of a vertically sheared current of constant Vorticity is derived. In this paper we extend to gravity–capillary wave trains the results of Thomas et al. (Phys. Fluids, 2012, 127102) and complete the stability analysis and stability diagram of Djordjevic & Redekopp (J. Fluid Mech., vol. 79, 1977, pp. 703–714) in the presence of Vorticity. The Vorticity effect on the modulational instability of weakly nonlinear gravity–capillary wave packets is investigated. It is shown that the Vorticity modifies significantly the modulational instability of gravity–capillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive Vorticity and amplified in the presence of negative Vorticity; (ii) in finite depth, it is reduced when the Vorticity is positive and amplified and finally reduced when the Vorticity is negative. The combined effect of Vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the Vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative Vorticity and attenuated by positive Vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the Vorticity.

a nonlinear schr odinger equation for gravity capillary water waves on arbitrary depth with constant Vorticity part i
arXiv: Fluid Dynamics, 2018CoAuthors: H C Hsu, C Kharif, M Abid, Y Y ChenAbstract:A nonlinear Schr\"odinger equation for the envelope of twodimensional gravitycapillary waves propagating at the free surface of a vertically sheared current of constant Vorticity is derived. In this paper we extend to gravitycapillary wave trains the results of \citet{thomas2012pof} and complete the stability analysis and stability diagram of \citet{Djordjevic1977} in the presence of Vorticity. Vorticity effect on the modulational instability of weakly nonlinear gravitycapillary wave packets is investigated. It is shown that the Vorticity modifies significantly the modulational instability of gravitycapillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive Vorticity and amplified in the presence of negative Vorticity, (ii) in finite depth, it is reduced when the Vorticity is positive and amplified and finally reduced when the Vorticity is negative. The combined effect of Vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the Vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative Vorticity and attenuated by positive Vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the Vorticity.
A C Birch  One of the best experts on this subject based on the ideXlab platform.

time distance helioseismology a new averaging scheme for measuring flow Vorticity
Astronomy and Astrophysics, 2014CoAuthors: Jan Langfellner, L Gizon, A C BirchAbstract:Context. Timedistance helioseismology provides information about vector flows in the nearsurface layers of the Sun by measuring wave travel times between points on the solar surface. Specific spatial averages of travel times have been proposed for distinguishing between flows in the eastwest and northsouth directions and measuring the horizontal divergence of the flows. No specific measurement technique has, however, been developed to measure flow Vorticity. Aims. Here we propose a new measurement technique tailored to measuring the vertical component of Vorticity. Fluid Vorticity is a fundamental property of solar convection zone dynamics and of rotating turbulent convection in particular. Methods. The method consists of measuring the travel time of waves along a closed contour on the solar surface in order to approximate the circulation of the flow along this contour. Vertical Vorticity is related to the di erence between clockwise and anticlockwise travel times. Results. We applied the method to characterize the vortical motions of solar convection using helioseismic data from the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) and from the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO/MDI). Away from the equator, a clear correlation between vertical Vorticity and horizontal divergence is detected. Horizontal outflows are associated with negative Vorticity in the northern hemisphere and positive Vorticity in the southern hemisphere. The signal is much stronger for HMI than for MDI observations. We characterize the spatial power spectrum of the signal by comparison with a noise model. Vertical Vorticity at horizontal wavenumbers below 250=R can be probed with this helioseismic technique.

time distance helioseismology a new averaging scheme for measuring flow Vorticity
arXiv: Solar and Stellar Astrophysics, 2014CoAuthors: Jan Langfellner, L Gizon, A C BirchAbstract:Timedistance helioseismology provides information about vector flows in the nearsurface layers of the Sun by measuring wave travel times between points on the solar surface. Specific spatial averages of travel times have been proposed for distinguishing between flows in the eastwest and northsouth directions and measuring the horizontal divergence of the flows. No specific measurement technique has, however, been developed to measure flow Vorticity. Here we propose a new measurement technique tailored to measuring the vertical component of Vorticity. Fluid Vorticity is a fundamental property of solar convection zone dynamics and of rotating turbulent convection in particular. The method consists of measuring the travel time of waves along a closed contour on the solar surface in order to approximate the circulation of the flow along this contour. Vertical Vorticity is related to the difference between clockwise and counterclockwise travel times. We applied the method to characterize the vortical motions of solar convection using helioseismic data from the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) and from the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO/MDI). Away from the equator, a clear correlation between vertical Vorticity and horizontal divergence is detected. Horizontal outflows are associated with negative Vorticity in the northern hemisphere and positive Vorticity in the southern hemisphere. The signal is much stronger for HMI than for MDI observations. We characterize the spatial power spectrum of the signal by comparison with a noise model. Vertical Vorticity at horizontal wavenumbers below 250/R_Sun can be probed with this helioseismic technique.
C Kharif  One of the best experts on this subject based on the ideXlab platform.

transverse instability of gravity capillary solitary waves on deep water in the presence of constant Vorticity
Journal of Fluid Mechanics, 2019CoAuthors: M Abid, H C Hsu, C Kharif, Y Y ChenAbstract:The bifurcation of twodimensional gravitycapillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant Vorticity. We found that gravitycapillary solitary waves with decaying oscillatory tails exist in deep water in the presence of Vorticity. Furthermore we found that the presence of Vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the Vorticity.

a nonlinear schrodinger equation for gravity capillary water waves on arbitrary depth with constant Vorticity part 1
Journal of Fluid Mechanics, 2018CoAuthors: H C Hsu, C Kharif, M Abid, Y Y ChenAbstract:A nonlinear Schrodinger equation for the envelope of twodimensional gravity–capillary waves propagating at the free surface of a vertically sheared current of constant Vorticity is derived. In this paper we extend to gravity–capillary wave trains the results of Thomas et al. (Phys. Fluids, 2012, 127102) and complete the stability analysis and stability diagram of Djordjevic & Redekopp (J. Fluid Mech., vol. 79, 1977, pp. 703–714) in the presence of Vorticity. The Vorticity effect on the modulational instability of weakly nonlinear gravity–capillary wave packets is investigated. It is shown that the Vorticity modifies significantly the modulational instability of gravity–capillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive Vorticity and amplified in the presence of negative Vorticity; (ii) in finite depth, it is reduced when the Vorticity is positive and amplified and finally reduced when the Vorticity is negative. The combined effect of Vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the Vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative Vorticity and attenuated by positive Vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the Vorticity.

a nonlinear schr odinger equation for gravity capillary water waves on arbitrary depth with constant Vorticity part i
arXiv: Fluid Dynamics, 2018CoAuthors: H C Hsu, C Kharif, M Abid, Y Y ChenAbstract:A nonlinear Schr\"odinger equation for the envelope of twodimensional gravitycapillary waves propagating at the free surface of a vertically sheared current of constant Vorticity is derived. In this paper we extend to gravitycapillary wave trains the results of \citet{thomas2012pof} and complete the stability analysis and stability diagram of \citet{Djordjevic1977} in the presence of Vorticity. Vorticity effect on the modulational instability of weakly nonlinear gravitycapillary wave packets is investigated. It is shown that the Vorticity modifies significantly the modulational instability of gravitycapillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive Vorticity and amplified in the presence of negative Vorticity, (ii) in finite depth, it is reduced when the Vorticity is positive and amplified and finally reduced when the Vorticity is negative. The combined effect of Vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the Vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative Vorticity and attenuated by positive Vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the Vorticity.