We describe the residual circulation induced in a two‐layer system when internal waves, with a wave length equal to or longer than the slope length, propagate over a sloping bottom and either reflect or break. For the case of no wave breaking, scaling is used to derive Boussinesq‐type equations, the solution of which leads to an expression for the residual circulation adjacent to the sloping bottom. This residual circulation is maintained by a weak slope on the density interface. For breaking waves, laboratory experiments and numerical modeling were used to ascertain the details of the residual circulation arising from the formation of gravitational intrusions. Results from these three investigative tools were used to determine, as a function of bottom slope and incident wave amplitude, the internal wave reflection coefficient and the strength of the residual circulation pattern with and without wave breaking.

This study investigates the horizontal and residual circulations in Tokyo Bay using field observations, numerical simulations, and theoretical analysis. Numerical simulations show that the observed deepening of isopycnals and associated anticyclonic horizontal circulation in the bay head are mainly driven by negative wind stress curl. The effects of river discharge, surface heat fluxes, and tides are found to be small. Under strong wind events, the wind stress curl over the bay head can be large enough to make the surface Ekman layer strongly nonlinear. Theoretical and numerical analyses show that, under large negative wind stress curl, the nonlinearity tends to induce positive pumping velocity (at the base of the surface mixed layer) that counteracts the Ekman pumping; however, the typical duration of wind events in the bay head is not long enough to induce positive pumping under negative wind stress curl. These results and historical wind data suggest that the average horizontal circulation and residual circulation immediately below the surface mixed layer in Tokyo Bay are, respectively, cyclonic and convergent in summer but anticyclonic and divergent in winter.

Breaking of shoaling internal solitary waves (ISWs) is important for mixing and mass transport processes in oceans and lakes. For ISWs in a two-layer stratified fluid, previous studies identified four breaker types: surging, plunging, collapsing, and fission. The latest classification of these breaker types is based on the wave slope $S_w$ and the bottom slope $S$; however, this classification was found to be unsatisfactory in delineating collapsing and plunging breakers. The present study proposes a new classification for these two breaker types using extended data sets, consisting of published experimental data and the results of new numerical simulations. It was found that a single nondimensional index $B_{\mathrm{ISW}}=\left(S/S_w\right)\mathrm{R}{{\mathrm{e}}_{\mathrm{ISW}}}^2$ delineates collapsing and plunging breakers in the extended data, where $\mathrm{R}{\mathrm{e}}_{\mathrm{ISW}}$ is a new wave Reynolds number that accounts for nonlinear wave steepening.

This paper uses derived distribution analysis to explore the process controls of the onset of and recovery from hypoxic conditions in Tokyo Bay, Japan. A conceptual, lumped model of dissolved oxygen (DO) dynamics in Tokyo Bay is proposed and, through comparison with a three‐dimensional simulation model, is verified to have sufficient accuracy for the prediction of the onset of and recovery from hypoxia. This conceptual DO model was implemented in continuous simulation mode, with 14 years of wind data and data on streamflow entering the Tokyo Bay, and was used to identify and quantify the various process controls of the onset of and recovery from hypoxia. The underlying process controls were identified to be streamflow discharge, as well as duration and strength of both northeast “positive” winds and southwest “negative” winds. The analysis helped to isolate, in particular, the potential for rapid and strong recovery from hypoxia due to “strong negative winds”, (i.e., negative winds that exceed a wind speed threshold of 10 m s⁻¹) and the critical roles of the duration of these strong winds and the antecedent DO concentration on the strength of DO recovery. Motivated by these results, derived distribution analysis is adopted to predict the strength of DO recovery during periods of strong winds, using a simplified model of DO recovery, focused on isolated strong winds, that explicitly captures the effects of both wind duration and antecedent DO concentration.