Ice jams in northern rivers during winter period significantly change the flow conditions due to the extra boundary of the flow. Moreover, with the presence of bridge piers in the channel, the flow conditions can be further complicated. Ice cover often starts from the front of bridge piers, extending to the upstream. With the accumulation of ice cover, ice jam may happen during early spring, which results in the notorious ice jam flooding. In the present study, the concentration of flowing ice around bridge piers has been evaluated based on experiments carried out in laboratory. The critical condition for the initiation of ice cover around bridge piers has been investigated. An equation for the critical floe concentration was developed. The equation has been validated by experimental data from previous studies. The proposed model can be used for the prediction of formation of ice cover in front of a bridge pier under certain conditions.
Let $R$ be a commutative Noetherian ring with identity and $I$ an ideal of $R$. It is shown that, if $M$ is a non-zero minimax $R$-module such that $\dim \mathop {\rm Supp} H^i_I (M) \leq 1$ for all $i$, then the $R$-module $H^i_I(M)$ is $I$-cominimax for all $i$. In fact, $H^i_I(M)$ is $I$-cofinite for all $i\geq 1$. Also, we prove that for a weakly Laskerian $R$-module $M$, if $R$ is local and $t$ is a non-negative integer such that $\dim \mathop {\rm Supp} H^i_I (M)\leq 2$ for all $i<t$, then ${\rm Ext}^j_R (R/I, H^i_I (M))$ and ${\rm Hom}_R(R/I, H^t_I(M))$ are weakly Laskerian for all $i<t$ and all $j \geq 0$. As a consequence, the set of associated primes of $H^i_I (M)$ is finite for all $i\geq 0$, whenever $\dim R/I \leq 2$ and $M$ is weakly Laskerian.