DSpace Collection:
https://dspace.lboro.ac.uk/2134/2484
2016-05-03T12:35:56ZExpansion shock waves in regularised shallow water theory
https://dspace.lboro.ac.uk/2134/21113
Title: Expansion shock waves in regularised shallow water theory
Authors: El, G.A.; Hoefer, M.A.; Shearer, Michael
Abstract: We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularised shallow water equations that include the Benjamin-Bona-Mahoney (BBM) and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock’s existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.
Description: THIS ITEM WILL REMAIN CLOSED ACCESS UNTIL 12 MONTHS AFTER THE DATE OF ITS COMMERCIAL PUBLICATION.2016-01-01T00:00:00ZMixing rates and limit theorems for random intermittent maps
https://dspace.lboro.ac.uk/2134/21030
Title: Mixing rates and limit theorems for random intermittent maps
Authors: Bahsoun, Wael; Bose, Christopher
Abstract: We study random transformations built from intermittent maps on the unit
interval that share a common neutral fixed point. We focus mainly on random
selections of Pomeu-Manneville-type maps T using the full parameter range
0< < , in general. We derive a number of results around a common theme
that illustrates in detail how the constituent map that is fastest mixing (i.e.
smallest α) combined with details of the randomizing process, determines
the asymptotic properties of the random transformation. Our key result
(theorem 1.1) establishes sharp estimates on the position of return time intervals
for the quenched dynamics. The main applications of this estimate are to limit
laws (in particular, CLT and stable laws, depending on the parameters chosen
in the range 0< <1) for the associated skew product; these are detailed
in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1 <
we study a second class of random transformations derived from piecewise
affine Gaspard–Wang maps, prove existence of an infinite (σ-finite) invariant
measure and study the corresponding correlation asymptotics. To the best of
our knowledge, this latter kind of result is completely new in the setting of
random transformations.
Description: This paper is embargoed until March 2017.2016-01-01T00:00:00ZThe added mass for two-dimensional floating structures
https://dspace.lboro.ac.uk/2134/21025
Title: The added mass for two-dimensional floating structures
Authors: McIver, M.; McIver, P.
Abstract: The diagonal terms in the added mass matrix for a two-dimensional surface-piercing structure, which satisfies a geometric condition known as the John condition, are proven to be non-negative. It is also shown that the heave coefficient, associated with a symmetric system of two such structures, is non-negative when the length of the free surface connecting the structures lies between an odd, and the next higher even, number of half-wavelengths. The sway and roll coefficients, associated with antisymmetric motion of the system, are non-negative in the complementary intervals. For a specific geometry these intervals are equivalent to frequency ranges. Negative added mass is associated with rapid variations with frequency, due to complex resonances that correspond to simple poles of the associated radiation potential in the complex frequency domain. Approximate techniques are used to show that, for systems of two structures, complex resonances are located at frequencies consistent with the intervals in which negative added mass is able to occur.
Description: THIS ITEM WILL REMAIN CLOSED ACCESS UNTIL 08/03/2017.2016-01-01T00:00:00ZLong ring waves in a stratified fluid over a shear flow
https://dspace.lboro.ac.uk/2134/21018
Title: Long ring waves in a stratified fluid over a shear flow
Authors: Khusnutdinova, Karima R.; Zhang, Xizheng
Abstract: Oceanic waves registered by satellite observations often have curvilinear fronts and propagate over various currents. In this paper we study long linear and weakly nonlinear ring waves in a stratified fluid in the presence of a depth-dependent horizontal shear flow. It is shown that, despite the clashing geometries of the waves and the shear flow, there exists a linear modal decomposition (different from the known decomposition in Cartesian geometry), which can be used to describe distortion of the wavefronts of surface and internal waves, and systematically derive a $2+1$2+1-dimensional cylindrical Korteweg–de Vries-type equation for the amplitudes of the waves. The general theory is applied to the case of the waves in a two-layer fluid with a piecewise-constant current, with an emphasis on the effect of the shear flow on the geometry of the wavefronts. The distortion of the wavefronts is described by the singular solution (envelope of the general solution) of the nonlinear first-order differential equation, constituting generalisation of the dispersion relation in this curvilinear geometry. There exists a striking difference in the shapes of the wavefronts of surface and interfacial waves propagating over the same shear flow.
Description: This paper is embargoed until September 2016.2016-01-01T00:00:00Z