4.3 Generation of high-frequency internal waves

High-frequency internal waves propagating offshore in small river plumes are regularly observed in satellite imagery in many world regions. In particular, Landsat 8 and Sentinel-2 ocean-color composites regularly reveal surface expressions of high-frequency internal waves propagating in small river plumes of RCBS [72]. Sources of these internal waves are small areas (100–200 m long and 25–100 m wide) adjacent to river mouths and elongated in directions of river inflows (Figure 5a). These waves propagate offshore from their source areas, and their surface expressions are distinctly observed at optical satellite imagery only within river plumes. These waves dissipate within river plumes at a distance of order of several kilometers from the river mouths or at lateral boundaries of river plumes, if size of a river plume is less than the decay distance of the internal waves. Ranges of wavelengths, phase speeds, and periods of internal waves reconstructed at multiple river plumes of the study region using satellite imagery are equal to 30–60 m, 0.45– 0.65 m/s, and 65–90 s, respectively.

We presume the following mechanism of generation of internal waves described above by discharges of small and rapid rivers (Figure 5b). Velocity of a river runoff is of one order of magnitude higher than velocity of coastal circulation. It causes abrupt deceleration of a freshened flow, increase of its depth, and formation of a hydraulic jump. The resulting switch of flow conditions from supercritical to

#### Figure 5.

WorldView-3 ocean color composite of the Mzymta plume from April 4, 2017 illustrating the formation and propagation of internal waves with high spatial resolution (a). Schematic of formation of a hydraulic jump and generation of internal waves by river discharge (b).

subcritical state causes generation of high-frequency internal waves. These waves propagate offshore in a stratified layer between the river plume and the subjacent saline sea. If the internal waves reach lateral boundary of a river plume, they abruptly dissipate due to relatively low stratification in the ambient sea. Thus, energy of internal waves is transformed to turbulence and increase mixing between the river plume and the subjacent sea.

A hydraulic jump described above is formed by river runoff under certain conditions that depend on properties of a river flow, ambient sea water, and a local topography. First, a supercritical freshened flow in vicinity of a river mouth is formed only if a river current is fast enough. At the same time, a freshened flow is abruptly decelerated by friction with ambient sea only if its kinetic energy, i.e., river discharge rate, is relatively low. Second, transformation of kinetic energy of a river flow to potential energy of a hydraulic jump depends on local salinity anomaly. Therefore, ambient sea salinity has to be high enough, which occurs in absence of intense freshwater accumulation in vicinity of a river mouth. Third, depth of a plume has to be smaller than sea depth near a river mouth. In this case, a river plume does not exhibit friction with sea bottom, which can hinder formation of a hydraulic jump.

Many small and rapid mountainous rivers that inflow to deep coastal sea areas correspond to the conditions listed above. These rivers have small but steep drainage basins that result in high flow velocities and small discharge rates. Steep coastal bathymetry typical for mountainous coasts provides quick renewal of sea water in vicinity of river mouths by coastal circulation. Discharges of such rivers form hydraulic jumps and generate internal waves in many world coastal regions (New Guinea, New Zealand, Mexico, Peru, Chile, Taiwan, etc.), which is regularly observed by satellite imagery. Moreover, many of these regions have regular flash flooding events on small rivers during rainfall [25, 30, 73]. The resulting simultaneous generation of high-frequency internal waves from multiple and closely spaced river mouths was registered in several of the mountainous regions listed above.

The processes of generation, propagation, and dissipation of internal waves described above induce transformation of river flow kinetic energy to turbulence in frontal zones of a river plume. As a result, these processes increase mixing in bottom and lateral boundaries of a plume and reduce freshwater volume accumulated in a river plume. This pattern of energy transform observed for small rivers of RCBS is significantly different from those that are typical for larger rivers and/or rivers with less rapid currents, which discharges form recirculating bulges in vicinity of river mouths instead of hydraulic jumps [9, 15, 56]. As a result, a kinetic energy of a river flow transforms to pressure gradient potential energy and kinetic energy of a bulge anticyclonic flow. In this case, increase in a kinetic energy of a

river flow increases freshwater accumulation rate within a bulge and decreases mixing between a river plume and ambient sea [9, 15]. Therefore, generation of internal waves is an important feature of river plumes formed by small and rapid rivers, which strongly affects their structure and dynamics.
