On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

Submarine landslides and the importance of the initial sediment composition for run-out length and final deposit

-Much remains to understand the dynamic processes during the flow of submarine landslides. A first relevant problem is to explain the extraordinary mobility of submarine landslides, which has no comparison in subaerial mass movement. Another challenging question is the apparent disparity between submarine landslides that remain compact for hundreds of kilometres and those that disintegrate during the flow, finally evolving into turbidity currents. This problem is linked to a central ongoing debate on the relative importance of turbidity currents versus submarine landslides in reshaping the continental margin. Based on three epitomic case studies and on laboratory experiments with artificial debris flows of various composition, we suggest a possible explanation for the disparity between compact and disintegrating landslides, identifying the clay-to-sand ratio as the key control parameter

Emerging insights into the dynamics of submarine debris flows

Recent experimental and theoretical work on the dynamics of submarine debris flows is summarized. Hydroplaning was first discovered in laboratory flows and later shown to likely occur in natural debris flows as well. It is a prime mechanism for explaining the extremely long runout distances observed in some natural debris flows even of over-consolidated clay materials. Moreover, the accelerations and high velocities reached by the flow head in a short time appear to fit well with the required initial conditions of observed tsunamis as obtained from back-calculations. Investigations of high-speed video recordings of laboratory debris flows were combined with measurements of total and pore pressure. The results are pointing towards yet another important role of ambient water: Water that intrudes from the water cushion underneath the hydroplaning head and through cracks in the upper surface of the debris flow may drastically soften initially stiff clayey material in the "neck" of the flow, where significant stretching occurs due to the reduced friction at the bottom of the hydroplaning head. This self-reinforcing process may lead to the head separating from the main body and becoming an "outrunner" block as clearly observed in several natural debris flows. Comparison of laboratory flows with different material composition indicates a gradual transition from hydroplaning plug flows of stiff clay-rich material, with a very low suspension rate, to the strongly agitated flow of sandy materials that develop a pronounced turbidity current. Statistical analysis of the great number of distinguishable lobes in the Storegga slide complex reveals power-law scaling behavior of the runout distance with the release mass over many orders of magnitude. Mathematical flow models based on viscoplastic material behavior (e.g. BING) successfully reproduce the observed scaling behavior only for relatively small clay-rich debris flows while granular (frictional) models fail at all scales. For very large release masses, hydroplaning or significant softening of the shear layer due to water incorporation must be invoked to recover the observed scaling behavior; a combination of both effects likely will give the most realistic description of the phenomenon. Detailed studies of the neck behavior and the compositional dependence of the material properties are needed to arrive at a quantitative model. Other related and important open questions concern the rheological model appropriate for sandy debris flows and the suspension rate from the dense body into the associated turbidity current

SAR Sea Surface Wind Field Estimation: The APPLICAVEMARS Project

X International Conference AIT, PlanetCare from Space, 13-15 September 2021, Cagliar

Modeling Potential Tsunami Generation by the BIG’95 Landslide

6th International Symposium on Submarine Mass Movements and Their Consequences (ISSMMTC), 23-25 September 2013, Kiel, GermanyThe BIG’95 landslide was emplaced 11,500 years ago and is one of the largest known submarine landslides in the Mediterranean Sea. The simulated landslide dynamics matches the observed run-out and deposited thickness. Water elevation simulated by using a dispersive tsunami model exceed 10 m close to the landslide area and at the nearest shorelines. Modeling further indicates that the tsunami probably had widespread consequences in the Mediterranean. Compared to previous studies, this new simulation provides larger waves. There is, however, still a need to better constrain the landslide dynamics in order to illuminate the uncertainties related to the tsunamigenic power of this, and other, submarine landslidesPeer reviewe

Modeling Potential Tsunami Generation by the BIG'95 Landslide

6th International Symposium on Submarine Mass Movements and Their Consequences (ISSMMTC), 23-25 September 2013, Kiel, Germany.-- 9 pagesThe BIG’95 landslide was emplaced 11,500 years ago and is one of the largest known submarine landslides in the Mediterranean Sea. The simulated landslide dynamics matches the observed run-out and deposited thickness. Water elevation simulated by using a dispersive tsunami model exceed 10 m close to the landslide area and at the nearest shorelines. Modeling further indicates that the tsunami probably had widespread consequences in the Mediterranean. Compared to previous studies, this new simulation provides larger waves. There is, however, still a need to better constrain the landslide dynamics in order to illuminate the uncertainties related to the tsunamigenic power of this, and other, submarine landslidesPeer Reviewe