The co-existence of ocean and continent makes the Earth unique in the solar system. Covering roughly 71% of the planet’s surface, oceans hold a volume of almost 1.35 billion km³, with an average depth of nearly 3700 meters [1] . Contrastingly, continents occupy around 29% of Earth’s surface and are geographically enclosed by these vast bodies of water. Mechanically, if a liquid and a solid are put together, they must interact with each other. The present study of ocean-continent interaction is focused mostly on the transition zone, where sea water erodes coast while land contributes sediment to seafloor, and the exchange of material, energy, and information takes place extensively [2] [3] . The principle of fluid mechanics stipulates that water pressure against the wall of a container that holds the water generates force. Ocean basins are naturally gigantic containers of water, in which continents form the walls of these containers. Hence, the ocean water pressure against the wall of continent may generate enormous force. Even so, the details of this force, including its magnitude and direction, are still unclear. Geochemical research on zircons indicates that the existence of liquid water on Earth is more than 4 billion years [4] - [6] . During such a long geological timescale, ocean water pressure force may exert impact on continents, since continents would deform in response to any external force. Moreover, continents are physically fixed at the top of the lithospheric plates, this attachment allows the force to be laterally transferred to the lithospheric plates. From these points, addressing the ocean water pressure force is very important for understanding the dynamics of continent (lithospheric plate) and its evolution. The objects of this study are twofold, first, to present a new force generated by ocean water; secondly, to explore the stress caused by this force in the continent and its implication.

In recent years, I have met a view stating that the difference in lateral density causes continent to extend over ocean. They think that, since the continent’s density is greater than the ocean’s density, the lateral density difference yields a force that drives continent to extend over ocean. The issue raised by this view is vital because it relates to the principle of fluid mechanics, and hence deserves a wider discussion. First of all, the view contradicts the basic knowledge of fluid mechanics. As illustrated in Figure 1(a) , we compare the hydrostatic pressure within a water body with the lithostatic pressure within a rock body. Given the two points, p1 and p2, are situated at the same depth of the water body and the rock body, respectively, the lithostatic pressure must be higher due to the rock’s greater density. Water pressure differs from rock pressure in that the former arises from the weight and movement of water molecules, whereas the latter arises solely from the weight of rocky materials. The rocky materials within continent are highly viscous and self-constrained, making it difficult for them to flow freely. Conversely, a low viscosity of water allows water particles to flow freely. This difference in physics property explains why a rock body can maintain its shape, while a water body conforms to the container holding it. Next, as illustrated in Figure 1(b) , we put the water body and the rock body together. Since the water body performs more mobile than the rock body does, some of the water body tends to flow towards the rock body and therefore exerts pressure force on the rock body. Further, as illustrated in Figure 1(c) , we put water into a container composed of rocky materials, the water exerts pressure force on the walls of the container. Second, I have asked experts regarding the question of whether or not ocean pushes continent. Several feedbacks support my argument above. There is a comment from Dr. John M. Cimbala: “Think about an empty tea cup sitting in a vacuum chamber with zero pressure. There is certainly internal pressure in the walls of the tea cup. However,

those walls do not exert any kind of pressure or force on the surroundings (which is a vacuum). And the cup stays the same shape and holds its shape regardless of its surroundings. Now take the cup out of the vacuum chamber and into the air. Now air exerts a pressure on the cup walls. The cup walls exert and equal and opposite pressure on the air due to Newton’s third law. Now fill the cup with water. The pressure inside the cup increases, and the cup expands ever so slightly, but it still maintains its shape. The cup exerts pressure on the water and vice-versa. But it is the water that causes this pressure, not the cup. Water is a liquid and cannot maintain its shape unless it is in some kind of container. That is where the pressure comes from.” As illustrated in Figure 1(d) , the continents are staying in the uppermost part of the Earth’s crust. The formation of the Earth’s crust was earlier than the appearance of liquid water, because the crust provides place for liquid water to be hold. The loading of liquid water onto the Earth’s crust is just like that water is filled into the tea cup. Therefore, when ocean basins are treated as containers, the ocean water must exert pressure force on the walls of the continents. There is another comment from Dr. Chris Hughes: “The ocean does indeed push on the continents, and they push back with an equal pressure. The force that makes things move is the gradient of the stress tensor, which in the ocean is effectively the pressure gradient, but in the continents is a combination of pressure and response to internal strains. Without those extra forces, the continents would simply be another, denser fluid, and would flow beneath the ocean.” There is third comment from Dr. Gerald Shubert: “If you imagine the edge of a continent to be a vertical plane then the water pressure will push against the continent. But the situation is more complex than that. There are continental shelves that extend under the oceans.” As illustrated in Figure 1(e) , the edge of a continent includes the continental shelf and slope, and they all are situated under the water. If we project them horizontally, a vertical plane can be reached. The ocean water pressure forces exerted on the continental shelf and slope can be geometrically decomposed into horizontal and vertical forces. As a result, all horizontal forces are laterally exerted on that vertical plane. Last, discussing the topic of force has to involve two objects: the object exerting force and the object receiving the force. For one object using force to push another object, the first object has to move (i.e., change its position) to exert force on the second object. As ocean water moves more easily relative to continent, there can be push force from ocean to continent.

As shown in Figure 2(top) , according to the principle of fluid mechanics [7] , the water pressure force generated on the wall of a cubic container can be expressed as F = PS = ρgy²x/2, where P and S are the pressure and wall area, g and ρ are the gravitational acceleration and water density, respectively, and x and y are the water width and depth, respectively, in the container. Ocean basins are naturally gigantic containers, and their depths reach more than a few kilometers and vary from one place to another. Consequently, the application of ocean water pressure against the continent’s walls, which are also the sides of ocean basins, can yield enormous forces on continents. Geometrically, as shown in Figure 2(middle) , ocean water pressure is exerted vertically to the continental slope, by which a normal force is formed. This normal force is called the ocean-generated force, denoted as F_R on the right and F_L on the left. The horizontal force decomposed from this normal force is denoted as ${F^{\prime }}_{\text{R}}\left({F^{\prime }}_{\text{L}}\right)$on the right (left), while the vertical force decomposed from this normal force is denoted as ${F^{″}}_{\text{R}}\left({F^{″}}_{\text{L}}\right)$ on the right (left). In general, the horizontal force on the wall of continent can be approximately written as

$F=0.5\rho gL{h}^2$ (1)

where ρ, g, L, and h are the water density, gravitational acceleration, ocean width that fits the continent wall’s width, and ocean depth, respectively. And Lh denotes the area of the continent wall.

Practically, continent appears more like a broad cylinder standing in the ocean, and its wall is not flat. We imaginarily project a continent into a polygonal column along the horizontal direction, then dissect the whole wall of this column into smaller rectangular walls connecting one to another, and finally calculate the horizontal force generated on each of these rectangular walls ( Figure 2(middle) ). We now design many geographical sites (e.g. 1, 2, 3, 4, etc.) along the edges of continents. The latitudes and longitudes of these sites are extracted from the ETOPO1 Global Relief Model ( Figure 2(bottom) ). A geographical distance between two adjacent sites is calculated using their respective latitudes and longitudes through a spherical geometry, and treated as the width of a smaller rectangular wall. The geographical distance of two sites is expressed as

$L=R\ast \text{arcos}\left(\sin \left(q_j\right)\ast \sin \left(q_j{}_{+1}\right)+\cos \left(q_j\right)\ast \cos \left(q_j{}_{+1}\right)\ast \cos \left(d_j{}_{+1}-d_j\right)\right)$ (2)

where R is the Earth’s radius and R = 6371 km, q_j and d_j are the latitude and longitude of a site, while q_j+1 and d_j+1 are the latitude and longitude of another site. Using the NOAA bathymetric data viewer, we estimate the corresponding ocean depth of each rectangular wall. ρ = 1000 kg/m³, and g = 9.8 m/s. We then use the expression above and these parameters to work out the horizontal forces around continents. It is assumed that the horizontal force exerts on a hypothetical geometric center of the wall, with the direction of the force being orthogonal to the direction of the wall. We use the direction of a side that connects two sites to represent the direction of the wall. Using this direction, the inclination of the force to latitude is determined. The latitude and longitude of the geometric center are established as the average of the latitudes and longitudes of two adjacent sites. The horizontal forces and the parameters for calculating them have been listed in Table 1 .

As exhibited in Figure 2 , the ocean-generated forces uniformly exert inwards the continents. The continents are situated on the top of continental plates, and therefore, the forces exerted on the plates have inevitably related to the stress in the continents. Our understanding of the stress yielded by ocean-generated force begins with a dynamic distribution around a straight continental plate ( Figure 3(a) ). We assume that Plate A moves towards the left, Plate B exerts a collisional force (F_c) on its left side, the oceanic ridge exerts a push force (F_RF) on its right side, and the asthenosphere exerts a friction force (F_b) on its base, and ocean water exerts pressure forces (F_LW and F_RW) at the two sides of its top. Ridge push force is widely considered either as a boundary force or a body force. As a boundary force, it is derived from a “gravity wedging” effect of a warm, buoyant mantle upwelling and acts at the edge of the lithospheric plate. Turcotte and Schubert [9] outlined the ridge push force through Figure 3(a) and expressed it as F_RP = F₁-F₂-F₃, where F₁ = F₅, F₂ = F₄. Since F₃, F₄, and F₅ relate to the pressure that linearly increases with depth, it may be expected that the minimal ridge push force appears at the uppermost part of the oceanic ridge, whereas the maximal ridge push force appears at the lowermost part. Ocean tides represent the daily regular alternations of high and low water in the oceans. The tides cause the water depth to vary, and thereby, the ocean water pressure varies timely. In consideration of this present status, we demonstrate the resultant stress by means of three combinations of different forces. In reality, the Earth’s surface is curved, and the vertical dimension of a continental plate is far less than its horizontal dimension, making it challenging

Notes: all geographic sites refer to Figure 2 .

Notes: all geographic sites refer to Figure 2 .

Notes: all geographic sites refer to Figure 2 .

Notes: all geographic sites refer to Figure 2 .

to represent stress with this geometry. To overcome this shortage, we develop a simplified model (see Figure 3(b) ) consisting of rocks that are straight. The model assumes homogeneity and isotropy and has a length and thickness of 290 km and 100 km, respectively.

The coupling of water and earthquake occurrence is a highly active area of research, with reservoir-induced earthquakes being the most notable artificial seismicity events. It has been extensively reported that there have been hundreds of instances, including at least five sites, where earthquakes exceeding M 6 have occurred [20] , indicating that earthquakes near reservoirs are widespread [21] [22] . The primary process for reservoir-induced earthquakes is a stress change within rocks due to the water loading [21] [23] , and the frequencies of these earthquakes closely correlate with the loading and unloading rate of water [24] [25] . These authors [26] - [28] have theorized/modelled the link between seismicity and stress caused by reservoir water impoundment. In addition to these reservoir-induced earthquakes, ocean water-related earthquakes were also recently reported. Guillas et al. [29] identified a connection between the El Niño-Southern Oscillation (ENSO) and earthquakes on the East Pacific Rise (EPR), proposing that seismicity may increase due to a reduction in ocean-bottom pressure over the EPR. Martínez-Garzón et al. [30] discovered that changes in sea level affect seismicity rates in a hydrothermal system near Istanbul. Tanaka et al. [31] concluded that the most likely component to control the earthquake occurrence is the stress. As exhibited in Figure 7 , the stress variation caused by the tide may have penetrated a 50 km depth crust. The result of our modelling, combined with these existing understanding of reservoir-induced and ocean water-related earthquakes, leads us to speculate that the ocean-generated force may potentially contribute to earthquake occurrence, although integrate data (i.e., seismic events and oceanic pressure measurements) to support this coupling are still waited.

We express sincere thanks to John M. Cimbala, Chris Hughes, and Gerald Shubert for their comments on the force between ocean and continent. The author declares no conflicts of interest. This research received no funding.

The latitude and longitude of the controlling sites on the continental plates in Figure 2 are determined through the ETOPO1 Global Relief Model [8] , and the ocean depths are artificially resolved through the NOAA Bathymetric Data Viewer ( https://ngdc.noaa.gov/mgg/global/global.html ).