By Ralf Greve, Heinz Blatter (auth.)
Dynamics of Ice Sheets and Glaciers provides an advent to the dynamics and thermodynamics of flowing ice lots on the earth. in keeping with an overview of normal continuum mechanics, the various initial-boundary-value difficulties for the movement of ice sheets, ice cabinets, ice caps and glaciers are systematically derived. designated emphasis is wear constructing hierarchies of approximations for the various platforms, and compatible numerical answer strategies are mentioned. A separate bankruptcy is dedicated to glacial isostasy. The booklet is suitable for graduate classes in glaciology, cryospheric sciences, environmental sciences, geophysics and comparable fields. typical undergraduate wisdom of arithmetic (calculus, linear algebra) and physics (classical mechanics, thermodynamics) offer a enough heritage for effectively learning the text.
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145) ∂z which vanishes at the free surface (z = H) as a consequence of the stress-free boundary condition. 146) and we obtain for the shear stress the linear proﬁle txz = η ∂vx = ρg(H − z) sin α . 148) and the integration constant C2 is evidently equal to zero due to the no-slip condition vx |z=0 = 0. Therefore, the solution for the downhill velocity is the parabolic proﬁle ρgH sin α z2 vx = z− . 149) are also shown in Fig. 11. Analogous to Eq. 150) 48 3 Elements of Continuum Mechanics and simpliﬁes for the thin ﬁlm problem to ∂p = −ρg cos α .
72), and the term tlk Lkl = tr (t·L) can again be replaced by tr (t·D) [see Eq. 85)], so that we obtain du = −div q + tr (t · D) + ρr . 64), with the corresponding densities g gs φ p s = ρu , =u =q = tr (t · D) = ρr (speciﬁc internal energy) , (heat ﬂux) , (dissipation power) , (r: speciﬁc radiation power) . 93) In contrast to the total energy, the internal energy is not a conserved quantity. 86) with a negative sign. The name “dissipation power” results from the fact that it annihilates kinetic energy and changes it into internal energy.
For an arbitrary scalar, vector or tensor ﬁeld quantity ψ(x, t), we now calculate the term (d/dt) ω ψ dv, that is, the temporal change of the ﬁeld quantity integrated over the volume ω. Fig. 5. On the Reynolds’ transport theorem: Material volume ω with boundary ∂ω in the present conﬁguration κt . To this end, we transform the integration variable to material coordinates X, which changes the integration domain ω to the volume Ω ⊂ κr in the reference conﬁguration as d dt ψ(x, t) dv = ω d dt ψ(x(X, t), t) J(X, t)dV .
Dynamics of ice sheets and glaciers by Ralf Greve, Heinz Blatter (auth.)