scholarly journals Modulation Instability of Surface Waves in the Model with the Uniform Wind Profile

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 651
Author(s):  
Susam Boral ◽  
Trilochan Sahoo ◽  
Yury Stepanyants
Keyword(s):  
Shear Flow ◽  
Water Waves ◽  
Modulation Instability ◽  
Reference Model ◽  
Vertical Direction ◽  
Negative Energy ◽  
Tangential Discontinuity ◽  
Flow Profile ◽  
Complex Phenomena ◽  
Physical Phenomena

The modulation instability of surface capillary-gravity water waves is analysed in a shear flow model with a tangential discontinuity of velocity. It is assumed that air blows along the surface of the water with a uniform profile in the vertical direction. Such a model, despite its simplicity, plays an important role in hydrodynamics as the reference model for investigating basic physical phenomena of wave–current interactions and acquiring insights into a series of complex phenomena. In certain cases where the wavelength of interfacial perturbations is much bigger than the width of the shear flow profile, the model with the tangential discontinuity in the velocity is adequate for describing physical phenomena at least within limited spatial and temporal frameworks. A detailed analysis of the air-flow conditions under which modulation instability sets in is presented. It is also shown that the interfacial waves are subject to dissipative or radiative instability when negative-energy waves appear at the interface.

scholarly journals Modulation Instability of Surface Waves in the Model with the Uniform Wind Profile

2021 ◽  
Author(s):  
Susam Boral ◽  
Trilochan Sahoo ◽  
Yury Stepanyants
Keyword(s):  
Water Waves ◽  
Wind Profile ◽  
Modulation Instability ◽  
Reference Model ◽  
Vertical Direction ◽  
Tangential Discontinuity ◽  
Flow Conditions ◽  
Radiative Instability ◽  
Complex Phenomena ◽  
Physical Phenomena

The modulation instability of surface capillary-gravity water waves is analysed in a shear flow model with a tangential discontinuity of velocity. It is assumed that air blows along the surface of the water with a uniform profile in the vertical direction. Such a model, despite its simplicity, plays an important role in hydrodynamics as the reference model for investigating basic physical phenomena of wave-current interactions and acquiring insights into a series of complex phenomena. In certain cases where the wavelength of interfacial perturbations is much bigger than the width of the shear fow profile, the model with the tangential discontinuity in the velocity is adequate for describing physical phenomena at least within limited spatial and temporal frameworks. A detailed analysis of the air-flow conditions under which modulation instability sets in is presented. It is also shown that the interfacial waves are subject to dissipative or radiative instability when negativeenergy waves appear at the interface.

Assessment of Viscous Flows in High-Speed Micro Rotating Machinery for Energy Conversion Applications

2001 ◽  
Author(s):  
Luc G. Fréchette
Keyword(s):  
Shear Flow ◽  
Energy Conversion ◽  
Viscous Flow ◽  
High Speed ◽  
Applied Pressure ◽  
Secondary Flows ◽  
System Level ◽  
Flow Profile ◽  
System Level Design ◽  
Level Design

Abstract This paper investigates the characteristics of viscous flow in the micron-scale clearances surrounding high-speed micro-rotors currently being developed for miniature energy conversion applications. Analysis and experimental results from 4 mm diameter microfabricated rotors operated above 1 million rpm are used to describe the viscous flow characteristics, and provide guidelines for system-level design. To first order, the flow is characterized as fully developed shear flow (Couette flow) across the small gaps, induced by the rotor motion. However, secondary flows are induced perpendicular to the direction of rotor motion when externally applied pressure gradients exist along the small gaps. The developing flow in the entrance region of the small gaps in this secondary flow direction impacts the shear flow profile, hence affecting the drag on the disk. The effect of other inertial forces, such as Coriolis and centrifugal forces, are investigated analytically and numerically and found to affect the shear flow profile on the fluid in the motor gap at high rotational speeds. Since viscous losses are prevelant in microsystems, appropriate modeling is necessary for system-level design.

scholarly journals Vertically localised equilibrium solutions in large-eddy simulations of homogeneous shear flow

2017 ◽  
Vol 827 ◽  
pp. 225-249 ◽  
Author(s):  
Atsushi Sekimoto ◽  
Javier Jiménez
Keyword(s):  
Shear Flow ◽  
Vertical Direction ◽  
Large Eddy Simulations ◽  
Small Scale ◽  
Box Dimension ◽  
Equilibrium Solutions ◽  
Vortical Structures ◽  
Homogeneous Shear ◽  
Large Eddy ◽  
Homogeneous Shear Flow

Unstable equilibrium solutions in a homogeneous shear flow with sinuous (streamwise-shift-reflection and spanwise-shift-rotation) symmetry are numerically found in large-eddy simulations (LES) with no kinetic viscosity. The small-scale properties are determined by the mixing length scale $l_{S}$ used to define eddy viscosity, and the large-scale motion is induced by the mean shear at the integral scale, which is limited by the spanwise box dimension $L_{z}$. The fraction $R_{S}=L_{z}/l_{S}$, which plays the role of a Reynolds number, is used as a numerical continuation parameter. It is shown that equilibrium solutions appear by a saddle-node bifurcation as $R_{S}$ increases, and that the flow structures resemble those in plane Couette flow with the same sinuous symmetry. The vortical structures of both lower- and upper-branch solutions become spontaneously localised in the vertical direction. The lower-branch solution is an edge state at low $R_{S}$, and takes the form of a thin critical layer as $R_{S}$ increases, as in the asymptotic theory of generic shear flow at high Reynolds numbers. On the other hand, the upper-branch solutions are characterised by a tall velocity streak with multiscale multiple vortical structures. At the higher end of $R_{S}$, an incipient multiscale structure is found. The LES turbulence occasionally visits vertically localised states whose vortical structure resembles the present vertically localised LES equilibria.

scholarly journals “Extraordinary” modulation instability in optics and hydrodynamics

2021 ◽  
Vol 118 (14) ◽  
pp. e2019348118
Author(s):  
Guillaume Vanderhaegen ◽  
Corentin Naveau ◽  
Pascal Szriftgiser ◽  
Alexandre Kudlinski ◽  
Matteo Conforti ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Stability Analysis ◽  
Linear Stability ◽  
Nonlinear Theory ◽  
Linear Stability Analysis ◽  
Water Waves ◽  
Modulation Instability ◽  
Nonlinear Effects ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory

The classical theory of modulation instability (MI) attributed to Bespalov–Talanov in optics and Benjamin–Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

Negative energy standing wave instability in the presence of flow

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
Michael S. Ruderman
Keyword(s):  
Standing Wave ◽  
Negative Energy ◽  
Flow Speed ◽  
Tangential Discontinuity ◽  
Positive Energy ◽  
Wave Instability ◽  
Long Wavelength ◽  
Backward Wave ◽  
Moving Plasma ◽  
The Difference

We study standing waves on the surface of a tangential discontinuity in an incompressible plasma. The plasma is moving with constant velocity at one side of the discontinuity, while it is at rest at the other side. The moving plasma is ideal and the plasma at rest is viscous. We only consider the long wavelength limit where the viscous Reynolds number is large. A standing wave is a superposition of a forward and a backward wave. When the flow speed is between the critical speed and the Kelvin–Helmholtz threshold the backward wave is a negative energy wave, while the forward wave is always a positive energy wave. We show that viscosity causes the standing wave to grow. Its increment is equal to the difference between the negative energy wave increment and the positive energy wave decrement.

Solitons and other solutions of the long-short wave equation

2015 ◽  
Vol 25 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Ghodrat Ebadi ◽  
Aida Mojaver ◽  
Sachin Kumar ◽  
Anjan Biswas
Keyword(s):  
Wave Equation ◽  
Water Waves ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Short Wave ◽  
Shallow Water Waves ◽  
Content Type ◽  
Integration Techniques ◽  
Physical Phenomena ◽  
The Waves

Purpose – The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several integration tools that are applied to obtain the soliton and other solutions to the equation. The integration techniques are traveling waves, exp-function method, G′/G-expansion method and several others. Design/methodology/approach – The design of the paper is structured with an introduction to the model. First the traveling wave hypothesis approach leads to the waves of permanent form. This eventually leads to the formulation of other approaches that conforms to the expected results. Findings – The findings are a spectrum of solutions that lead to the clearer understanding of the physical phenomena of long-short waves. There are several constraint conditions that fall out naturally from the solutions. These poses the restrictions for the existence of the soliton solutions. Originality/value – The results are new and are sharp with Lie symmetry analysis and other advanced integration techniques in place. These lead to the connection between these integration approaches.

scholarly journals Two-dimensional modulation instability of wind waves

2019 ◽  
Vol 5 (4) ◽  
pp. 413-417 ◽  
Author(s):  
Roger Grimshaw
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Water Waves ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Wind Waves ◽  
Nonlinear Schrodinger Equation ◽  
Wind Forcing ◽  
Nonlinear Schrödinger ◽  
Peregrine Breather

Abstract It is widely known that deep-water waves are modulationally unstable and that this can be modelled by a nonlinear Schrödinger equation. In this paper, we extend the previous studies of the effect of wind forcing on this instability to water waves in finite depth and in two horizontal space dimensions. The principal finding is that the instability is enhanced and becomes super-exponential and that the domain of instability in the modulation wavenumber space is enlarged. Since the outcome of modulation instability is expected to be the generation of rogue waves, represented within the framework of the nonlinear Schrödinger equation as a Peregrine breather, we also examine the effect of wind forcing on a Peregrine breather. We find that the breather amplitude will grow at twice the rate of a linear instability.

scholarly journals Arrest of the flow of wet granular matter

2013 ◽  
Vol 738 ◽  
pp. 407-422 ◽  
Author(s):  
Klaus Roeller ◽  
Johannes Blaschke ◽  
Stephan Herminghaus ◽  
Jürgen Vollmer
Keyword(s):  
External Force ◽  
Granular Matter ◽  
Three Dimensional ◽  
Vertical Direction ◽  
System Size ◽  
Critical Force ◽  
Flow Profile ◽  
Universal Method ◽  
Dynamics Simulations ◽  
Energy Dissipated

AbstractWe study the arrest of three-dimensional flow of wet granular matter subject to a sinusoidal external force and a gravitational field confining the flow in the vertical direction. The minimal strength of the external force that is required to keep the system in motion, i.e. the critical force, is determined by considering the balance of injected and dissipated power. This provides a prediction whose quality is demonstrated by a data collapse for an extensive set of event-driven molecular-dynamics simulations where we varied the system size, particle number, the energy dissipated upon rupturing capillary bridges, and the bridge length at which rupture occurs. The same approach also works for systems that are kept at a fixed density by confining walls. In both cases, this universal method provides the critical force irrespective of the flow profile, and without specifying the hydrodynamic equations.

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