Tao Gao

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Verified

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• PhD
• Lecturer at University of Essex

Hydroelastic waves propagating at a constant velocity at the surface of a fluid are considered. The flow is assumed to be two-dimensional and potential. Gravity is included in the dynamic boundary condition. The fluid is bounded above by an elastic sheet which is described by the Plotnikov-Toland model. Fully nonlinear solutions are computed by a s...

A numerical study of fully nonlinear waves propagating through a two-dimensional deep fluid covered by a floating flexible plate is presented. The nonlinear model proposed by Toland (Arch. Rat. Mech. Anal., vol. 289, 2008, pp. 325–362) is used to formulate the pressure exerted by the thin elastic sheet. The symmetric solitary waves previously found...

This work concerns the structural vibration of a bladeless wind turbine, modelled by a two-deck Euler–Bernoulli beam, due to a surrounding potential flow. The deflection is governed by the Euler–Bernoulli equation which is studied first by a linear theory and then computed numerically by a finite difference method in space with a collocation method...

The stochastic analysis of the deflection behaviour of an idealised slender structure subject to stochastic disturbance is studied. In a previous work by the authors, the response of an Euler-Bernoulli beam subject to stochastic disturbance was studied. The current work extends the same techniques to a modified Euler-Bernoulli beam with both flexur...

As summarized by Papageorgiou (Annu. Rev. Fluid Mech., vol. 51, 2019, pp. 155-187), a strong normal electric field can cause instability of the interface in a hydrodynamic system. In the present work, singularities arising in electrocapillary-gravity waves on a dielectric fluid of finite depth due to an electric field imposed in the direction perpe...

This work concerns the stochastic analysis of the bending of a slender cantilever beam subject to an external force with the inclusion of a stochastic effect characterised by white noise. The beam deflection is governed by the classic dynamic Euler-Bernoulli equation. Its response to the stochastic external load is investigated by learning pattern...

As summarized by Papageorgiou (Annu. Rev. Fluid Mech., vol. 51, 2019, pp. 155-187), a strong normal electric field can cause instability of the interface in a hydrodynamic system. In the present work, singularities arising in electrocapillary-gravity waves on a dielectric fluid of finite depth due to an electric field imposed in the direction perpe...

The motion of an interface separating two fluids under the effect of electric fields is a subject that has picked the attention of researchers from different areas. While there is an abundance of studies investigating the free surface wave properties, very few works have examined the associated velocity field within the bulk of the fluid. Therefore...

The motion of an interface separating two fluids under the effect of electric fields is a subject that has picked the attention of researchers from different areas. While there is an abundance of studies investigating the free surface wave properties, very few works have examined the associated velocity field within the bulk of the fluid. Therefore...

In this paper, we are concerned with capillary-gravity waves propagating on a two-dimensional conducting fluid under the effect of an electric field imposed in the direction perpendicular to the undisturbed free surface. The full problem is two-layered and mathematically difficult to solve since the interface dynamics are governed by the Euler equa...

Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. Coupling of electric fields and vorticity is of significant research interest. In this paper, we study the flow structure of steady pe...

Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. The coupling of electric fields and vorticity is of significant research interest. In this paper, we study the flow structure of stead...

This work concerns the bending of a slender cantilever beam subject to an external force with the inclusion of a stochastic effect characterised by white noise. The beam deflection is governed by the classic dynamic Euler-Bernoulli equation. Its response to the stochastic external load is investigated by learning pattern from the simulation data wh...

This article is concerned with capillary-gravity waves travelling on the interface of a dielectric gas and a conducting fluid under the effect of a vertical electric field. A boundary integral equation method is employed to compute fully nonlinear steady travelling wave solutions. The global bifurcation diagram of periodic waves, solitary waves, ge...

In this paper, we are concerned with capillary-gravity waves propagating on a two-dimensional conducting fluid under the effect of an electric field imposed in the direction perpendicular to the undisturbed free surface. The full problem is two-layered and mathematically difficult to solve since the interface dynamics are governed by the Euler equa...

The problem of two-dimensional capillary-gravity waves on an inviscid fluid of finite depth interacting with a linear shear current is considered. The shear current breaks the symmetry of the irrotational problem and supports simultaneously counter-propagating waves of different types: KdV-type long solitary waves and wave-packet solitary waves who...

In this article, we consider capillary-gravity waves propagating on the interface of two dielectric fluids under the influence of normal electric fields. The density of the upper fluid is assumed to be much smaller than the lower one. Linear and weakly nonlinear theories are studied. The connection to the results in other limit configurations is di...

This work is concerned with waves propagating on water of finite depth with a constant-vorticity current under a deformable flexible sheet. The pressure exerted by the sheet is modelled by using the Cosserat thin shell theory. By means of multi-scale analysis, small amplitude nonlinear modulation equations in several regimes are considered, includi...

In this work we consider two-dimensional capillary-gravity waves propagating under the influence of a vertical electric field on a dielectric of finite depth bounded above by a perfectly conducting and hydrodynamically passive fluid. Both linear and weakly nonlinear theories are developed, and long-wave model equations are derived based on the anal...

In this work, two-dimensional hydroelastic solitary waves in the presence of constant vorticity are studied. Time-dependent conformal mapping techniques first developed for irrotational waves are applied subject to appropriate modification. An illustrative high-order Nonlinear Schrödinger Equation is presented to investigate whether a given envelop...

Capital efficiency and asset/liability management are part of the Enterprise Risk Management Process of any insurance/reinsurance conglomerate and serve as quantitative methods to fulfill the strategic planning within an insurance organization. A considerable amount of work has been done in this ample research field, but invariably one of the last...

This work is concerned with flexural-gravity solitary waves on water of finite depth. The deformation of the elastic sheet is modelled based on the Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypotheses. Both steady and unsteady waves are computed numerically for the full Euler equations by using a conformal mapping technique. Com...

Two-dimensional capillary-gravity waves travelling under the effect of a vertical electric field are considered. The fluid is assumed to be a dielec-tric of infinite depth. It is bounded above by another fluid which is hy-drodynamically passive and perfectly conducting. The problem is solved numerically by time-dependent conformal mapping methods....

In this paper, fully nonlinear non-symmetric periodic gravity–capillary waves propagating at the surface of an inviscid and incompressible fluid are investigated. This problem was pioneered analytically by Zufiria (J. Fluid Mech., vol. 184, 1987c, pp. 183–206) and numerically by Shimizu & Shōji (Japan J. Ind. Appl. Maths, vol. 29 (2), 2012, pp. 331...

Generalised solitary waves propagating at the surface of a fluid of finite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. Both the effects of gravity and surface tension are included. It is shown that in addition to the classical symmetric waves, there are new asymmetric solutions. Thes...

The thesis is mainly concerned with linear and nonlinear water waves travelling beneath an elastic sheet. Such waves are known as exural-gravity waves. The basic mathematical formulation is introduced in Chapter 2 . Several numerical methods are presented in Chapter 3 . Related problems involving gravity-capillary waves are also considered. Nonline...

We focus on two-dimensional separated flows past sharp corners. A vortex sheet is needed to render the velocity field finite at the corner , and the roll-up of the sheet is modelled by a vortex with tune-dependant circulation. Then the equation of motion for the starting vortex is given by from the Brown-Michael equation and solved either analytica...

In this paper, we investigate the extreme eigenvalue distribution function of a n-dimensional random matrix from Laguerre Matrices Ensemble in the unitary case(call it simply LUE later). namely P(λmax ≤ t). We start by writing down the joint probability density whose weight function is Laguerre weight defined as ω(x) = x α e −x. where α > −1, x > 0...