Preamble

Interaction of flexural-gravity waves in ice cover with vertical walls

“…The potential Φ also satisfies the following boundary conditions, where N is the normal unit vector to the vertical wall Γ and ∂ Φ /∂ N is the normal derivative of the potential on the wall. The equation of thin ice plate can be written in the form, see [ 12 ], where q = ( ω 2 H / g )( H / L c ) 4 , δ = (1 − ω 2 / ω 2 0 )( H / L c ) 4 and L c = ( D i / ρg ) 1/4 is the characteristic length of the ice sheet [ 13 ], ω 0 = ( ρg / m ) 1/2 is the frequency of floating broken ice, m is the mass of the ice cover per unit area, m = ρ i h i , h i is the ice thickness, ρ i is the ice density, D i is the rigidity coefficient of the ice sheet, D i = E i h 3 i /[12(1 − ν 2 )] for an elastic plate of constant thickness, E i is the Young modulus of the ice, ν is the Poisson ratio, ρ is the water density and g is the gravitational acceleration. The condition at infinity follows from ( 2.1 ) and ( 2.2 ), where ϰ = kH is the non-dimensional wavenumber.…”

“…Condition ( 2.6 ) is imposed for x 2 + y 2 → ∞ if the vertical walls Γ do not extend to infinity. The three dimensionless parameters, δ , q and ϰ, are related by the dispersion relation [ 13 ], The conditions at the contact line, z = 0 and ( x , y )∈ Γ , between the ice cover and the surface of the cylinder can be complicated in practical problems. The present method of vertical modes is not sensitive to the types of these conditions.…”

Dynamic, in situ measurement of sea-ice characteristic length

“…So the static measurements are not necessarily relevant to the comparison between observations of responses in which dynamic flexure is the dominant process. Previous dynamic measurements have been based on the relationship between frequency and the wavelength of the travelling wave, using relatively high-frequency loading provided by a vibrating helicopter (DiMarco and others, 1993) or moving loads (Squire and others, 1996). The latter exploits the minimum phase speed that occurs at the wavelength (Doronin and Kheisin, 1977).…”

Flexural edge waves generated by steady-state propagation of a loaded rectilinear crack in an elastically supported thin plate

“…This outcome is further enhanced by the presence of cracks in the structure. An intriguing example of this is the discovery that a ground effect machine may be successfully employed as ice breaker when operated at the system's critical speed [7]. The analysis of the effect of loads moving on elastic structures has been a long-standing subject of investigation, in the light of its many practical implications.…”

“…Historically, much of this analysis has been directed by the desire to safely design bridges, rail tracks and road pavements under the ever-increasing demand of high-speed high-capacity transportation [8,9]. Recently, renewed interest has been drawn to model and design floating ice sheets as supporting structures for oil rigs, pipes, roads, runways and platforms [7]. Climate change and extensive investigation of the interaction between ice-shelf cracking and impinging sea-waves, in a process somewhat similar to that leading to edge waves excited by deep water surface waves [10], are also motivating further research in the field [11][12][13].…”